StanとRでベイズ統計モデリング09
UPDATE: 2023-12-26 23:06:56.666156
はじめに
このノートは「StanとRでベイズ統計モデリング」の内容を写経することで、ベイズ統計への理解を深めていくために作成している。
基本的には気になった部分を写経しながら、ところどころ自分用の補足をメモすることで、「StanとRでベイズ統計モデリング」を読み進めるための自分用の補足資料になることを目指す。私の解釈がおかしく、メモが誤っている場合があるので注意。
今回は第8章「階層モデル」のチャプターを写経していく。非線形モデルのところから。
8.3 非線形モデルの階層モデル
7.3節のモデルを16人に拡張して階層モデルを適用する。
options(max.print = 999999)
library(dplyr)
library(ggplot2)
library(rstan)
d <- read.csv('https://raw.githubusercontent.com/MatsuuraKentaro/RStanBook/master/chap08/input/data-conc-2.txt')
N <- nrow(d)
Time <- c(1, 2, 4, 8, 12, 24)
T_new <- 60
Time_new <- seq(from = 0, to = 24, length = T_new)
data <- list(N = N, T = length(Time), Time = Time, Y = d[,-1],
T_new = T_new, Time_new = Time_new)
head(d, 10)## PersonID Time1 Time2 Time4 Time8 Time12 Time24
## 1 1 2.4 5.0 7.5 11.9 12.5 12.7
## 2 2 1.4 3.9 4.4 7.7 6.4 8.3
## 3 3 5.2 9.4 19.4 20.2 22.7 24.9
## 4 4 6.7 12.6 19.1 23.4 25.8 26.1
## 5 5 0.3 4.7 7.0 10.2 12.9 14.8
## 6 6 6.3 3.8 11.8 9.2 13.9 18.2
## 7 7 3.0 4.2 8.8 15.4 10.7 16.2
## 8 8 6.2 6.8 9.4 11.3 12.4 14.7
## 9 9 14.4 17.0 22.7 29.8 33.0 32.2
## 10 10 7.7 10.0 14.8 15.3 18.0 18.78.3.1 解析の目的とデータの分布の確認
各個人において、頭打ちになる\(Y\)の値と、頭打ちになるまでの時間を知りたい。また個人差のばらつきも分析したいとする。各個人のデータを可視化すると、頭打ちになるものの、個人ごとに上限が異なることがわかる。
d %>%
tidyr::pivot_longer(cols = -PersonID, values_to = 'Y') %>%
mutate(Time = readr::parse_number(name)) %>%
select(-name) %>%
ggplot(data = ., aes(x = Time, y = Y)) +
theme_bw(base_size = 15) +
facet_wrap(~PersonID) +
geom_line(linewidth = 1) +
geom_point(size = 3) +
labs(x = 'Time (hour)', y = 'Y') +
scale_x_continuous(breaks = c(0,6,12,24), limit = c(0,24)) +
scale_y_continuous(breaks = seq(0,40,10), limit = c(-3,37))
最終時点ごとの\(Y\)の値も個人によって異なる。
d_last <- d[ncol(d)]
bw <- 3.0
ggplot(data = d_last, aes(x = Time24)) +
theme_bw(base_size = 15) +
geom_histogram(binwidth = bw, color = 'black', fill = 'white') +
geom_density(aes(y = after_stat(count)*bw), alpha = 0.2, color = 'black', fill = 'gray20') +
geom_rug(sides = 'b') +
labs(x = 'Time24', y = 'count') +
xlim(range(density(d_last$Time24)$x))
8.3.2 メカニズムの想像
ここではa[n],b[n]が特定の分布に従うと仮定して、階層モデルを適用する。a[n],b[n]は正の値をとることを考慮し、対数をとったlog(a)[n],log(b)[n]が正規分布に従うと仮定する。考えるだけで、logはとってないので注意。
8.3.3 モデル式の記述
ここで想定しているモデルは下記の通り。
\[ \begin{eqnarray} Y[n,t] &\sim& Normal(a[n]\{1 -\exp(-b[n] Time[t]) \}, \sigma_{Y}) \\ log(a[n]) &\sim& Normal(a_{全体平均}, \sigma_{a}) \\ log(b[n]) &\sim& Normal(b_{全体平均}, \sigma_{b}) \end{eqnarray} \]
データから\(\sigma_{Y}, a[n], a_{全体平均}, \sigma_{a}, b[n], b_{全体平均}, \sigma_{b}\)を推定する。
8.3.4 Stanで実装
Stanファイルは下記の通り。
data {
int N;
int T;
real Time[T];
real Y[N,T];
int T_new;
real Time_new[T_new];
}
parameters {
real a0;
real b0;
real log_a[N];
real log_b[N];
real<lower=0> s_a;
real<lower=0> s_b;
real<lower=0> s_Y;
}
transformed parameters {
real a[N];
real b[N];
for (n in 1:N) {
// expは、logはとってないが想定する値がマイナスにならないようにする.
// `a[n],b[n]`は正の値をとることを考慮
a[n] = exp(log_a[n]);
b[n] = exp(log_b[n]);
}
}
model {
for (n in 1:N) {
// logはとってない、対数をとったものが正規分布に従うと考える
log_a[n] ~ normal(a0, s_a);
log_b[n] ~ normal(b0, s_b);
}
for (n in 1:N)
for (t in 1:T)
Y[n,t] ~ normal(a[n]*(1 - exp(-b[n]*Time[t])), s_Y);
}
generated quantities {
real y_new[N,T_new];
for (n in 1:N)
for (t in 1:T_new)
y_new[n,t] = normal_rng(a[n]*(1 - exp(-b[n]*Time_new[t])), s_Y);
}
ここでは、stan_model()関数で最初にコンパイルしておいてから、
sampling()関数でサンプリングする。
パラメタの推定結果はこちら。\(\sigma_{Y}\)以外は対数スケールとなっている。少し混乱するが、a[1],b[1]は通常スケールでexpで変換する前のa0,b0が対数スケールということ(対数変換したものが正規分布に従うと考えている)。
## Inference for Stan model: anon_model.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 50% 97.5% n_eff Rhat
## a0 2.9 0.0 0.1 2.6 2.9 3.1 4986 1
## b0 -1.2 0.0 0.1 -1.4 -1.2 -0.9 3387 1
## log_a[1] 2.6 0.0 0.1 2.4 2.6 2.8 4154 1
## log_a[2] 2.1 0.0 0.1 1.8 2.1 2.4 4509 1
## log_a[3] 3.2 0.0 0.1 3.1 3.2 3.3 5360 1
## log_a[4] 3.3 0.0 0.0 3.2 3.3 3.3 4168 1
## log_a[5] 2.6 0.0 0.1 2.4 2.6 2.9 3789 1
## log_a[6] 2.7 0.0 0.1 2.6 2.7 2.9 3439 1
## log_a[7] 2.7 0.0 0.1 2.5 2.7 2.9 5375 1
## log_a[8] 2.6 0.0 0.1 2.4 2.6 2.8 4394 1
## log_a[9] 3.5 0.0 0.0 3.4 3.5 3.5 5042 1
## log_a[10] 2.9 0.0 0.1 2.8 2.9 3.0 5028 1
## log_a[11] 3.0 0.0 0.1 2.9 3.0 3.1 5627 1
## log_a[12] 2.8 0.0 0.1 2.7 2.8 2.9 4754 1
## log_a[13] 2.4 0.0 0.1 2.2 2.4 2.7 4070 1
## log_a[14] 3.2 0.0 0.1 3.1 3.2 3.3 4718 1
## log_a[15] 2.8 0.0 0.1 2.7 2.8 2.9 5345 1
## log_a[16] 3.5 0.0 0.0 3.4 3.5 3.5 5109 1
## log_b[1] -1.4 0.0 0.2 -1.9 -1.4 -0.9 3756 1
## log_b[2] -1.4 0.0 0.3 -2.1 -1.3 -0.7 3831 1
## log_b[3] -1.2 0.0 0.2 -1.5 -1.2 -0.9 5122 1
## log_b[4] -1.1 0.0 0.1 -1.4 -1.1 -0.9 4526 1
## log_b[5] -1.6 0.0 0.3 -2.2 -1.6 -1.1 2992 1
## log_b[6] -1.4 0.0 0.3 -2.0 -1.4 -0.9 3293 1
## log_b[7] -1.4 0.0 0.2 -1.9 -1.4 -1.0 3942 1
## log_b[8] -1.1 0.0 0.3 -1.6 -1.1 -0.5 5038 1
## log_b[9] -0.9 0.0 0.1 -1.2 -0.9 -0.7 4715 1
## log_b[10] -0.9 0.0 0.2 -1.3 -0.9 -0.5 4343 1
## log_b[11] -1.0 0.0 0.2 -1.4 -1.0 -0.6 4759 1
## log_b[12] -0.7 0.0 0.2 -1.1 -0.7 -0.2 4411 1
## log_b[13] -1.5 0.0 0.3 -2.1 -1.5 -0.9 3733 1
## log_b[14] -1.4 0.0 0.2 -1.7 -1.4 -1.1 4292 1
## log_b[15] -1.2 0.0 0.2 -1.5 -1.2 -0.8 5784 1
## log_b[16] -0.7 0.0 0.1 -0.9 -0.7 -0.4 4909 1
## s_a 0.4 0.0 0.1 0.3 0.4 0.6 4460 1
## s_b 0.4 0.0 0.1 0.2 0.4 0.7 1724 1
## s_Y 1.7 0.0 0.2 1.4 1.7 2.0 3538 1
## a[1] 13.0 0.0 1.2 10.8 12.9 15.6 4046 1
## a[2] 8.3 0.0 1.2 6.2 8.2 10.9 4315 1
## a[3] 23.9 0.0 1.2 21.6 23.8 26.3 5311 1
## a[4] 25.9 0.0 1.2 23.6 25.9 28.4 4195 1
## a[5] 14.1 0.0 1.6 11.3 14.0 17.5 3762 1
## a[6] 15.7 0.0 1.5 13.0 15.6 18.9 3244 1
## a[7] 14.8 0.0 1.3 12.4 14.8 17.6 5296 1
## a[8] 13.4 0.0 1.1 11.4 13.4 15.8 4347 1
## a[9] 31.9 0.0 1.1 29.7 31.9 34.2 5048 1
## a[10] 17.9 0.0 1.1 15.8 17.9 20.1 4997 1
## a[11] 19.7 0.0 1.1 17.5 19.7 22.0 5563 1
## a[12] 16.3 0.0 1.0 14.4 16.3 18.4 4753 1
## a[13] 11.6 0.0 1.3 9.2 11.5 14.6 3950 1
## a[14] 24.8 0.0 1.3 22.3 24.8 27.5 4730 1
## a[15] 16.7 0.0 1.2 14.5 16.7 19.1 5526 1
## a[16] 31.9 0.0 1.0 29.9 31.9 34.0 5104 1
## b[1] 0.3 0.0 0.1 0.2 0.3 0.4 3982 1
## b[2] 0.3 0.0 0.1 0.1 0.3 0.5 3880 1
## b[3] 0.3 0.0 0.0 0.2 0.3 0.4 5262 1
## b[4] 0.3 0.0 0.0 0.2 0.3 0.4 4383 1
## b[5] 0.2 0.0 0.1 0.1 0.2 0.3 2931 1
## b[6] 0.2 0.0 0.1 0.1 0.2 0.4 3541 1
## b[7] 0.2 0.0 0.1 0.2 0.2 0.4 3944 1
## b[8] 0.4 0.0 0.1 0.2 0.3 0.6 4978 1
## b[9] 0.4 0.0 0.0 0.3 0.4 0.5 4806 1
## b[10] 0.4 0.0 0.1 0.3 0.4 0.6 4236 1
## b[11] 0.4 0.0 0.1 0.3 0.4 0.6 4693 1
## b[12] 0.5 0.0 0.1 0.3 0.5 0.8 4262 1
## b[13] 0.2 0.0 0.1 0.1 0.2 0.4 3849 1
## b[14] 0.3 0.0 0.0 0.2 0.3 0.3 4221 1
## b[15] 0.3 0.0 0.1 0.2 0.3 0.5 5262 1
## b[16] 0.5 0.0 0.1 0.4 0.5 0.6 4866 1
## y_new[1,1] 0.0 0.0 1.7 -3.4 0.0 3.2 4062 1
## y_new[1,2] 1.3 0.0 1.7 -2.2 1.3 4.6 4080 1
## y_new[1,3] 2.4 0.0 1.8 -1.0 2.5 5.9 3938 1
## y_new[1,4] 3.5 0.0 1.8 -0.1 3.5 7.2 4026 1
## y_new[1,5] 4.5 0.0 1.8 1.0 4.5 8.2 3994 1
## y_new[1,6] 5.2 0.0 1.8 1.7 5.2 8.8 3439 1
## y_new[1,7] 6.0 0.0 1.9 2.2 6.0 9.9 3615 1
## y_new[1,8] 6.7 0.0 1.9 2.9 6.7 10.5 4168 1
## y_new[1,9] 7.3 0.0 1.9 3.5 7.3 11.1 3932 1
## y_new[1,10] 7.9 0.0 2.0 4.0 7.8 11.8 4026 1
## y_new[1,11] 8.3 0.0 1.9 4.5 8.3 12.1 4092 1
## y_new[1,12] 8.8 0.0 2.0 5.0 8.8 12.7 4138 1
## y_new[1,13] 9.2 0.0 1.9 5.5 9.2 13.1 4072 1
## y_new[1,14] 9.5 0.0 1.9 5.7 9.5 13.3 4039 1
## y_new[1,15] 9.9 0.0 1.9 6.3 9.8 13.7 4264 1
## y_new[1,16] 10.1 0.0 1.9 6.5 10.1 13.9 4185 1
## y_new[1,17] 10.4 0.0 1.9 6.8 10.4 14.0 4379 1
## y_new[1,18] 10.6 0.0 1.9 6.9 10.6 14.3 4124 1
## y_new[1,19] 10.8 0.0 1.9 7.1 10.9 14.5 4041 1
## y_new[1,20] 11.0 0.0 1.9 7.3 11.0 14.8 3999 1
## y_new[1,21] 11.2 0.0 1.9 7.4 11.2 15.1 4031 1
## y_new[1,22] 11.3 0.0 1.9 7.6 11.4 15.0 4035 1
## y_new[1,23] 11.5 0.0 1.9 7.7 11.5 15.3 4253 1
## y_new[1,24] 11.7 0.0 1.9 7.9 11.7 15.3 3702 1
## y_new[1,25] 11.8 0.0 1.9 8.0 11.8 15.4 3971 1
## y_new[1,26] 11.8 0.0 1.9 8.1 11.8 15.7 4291 1
## y_new[1,27] 12.0 0.0 2.0 8.2 12.0 15.8 4547 1
## y_new[1,28] 12.1 0.0 1.9 8.3 12.1 16.0 3963 1
## y_new[1,29] 12.2 0.0 1.9 8.3 12.2 16.1 4205 1
## y_new[1,30] 12.2 0.0 1.9 8.4 12.2 16.0 4100 1
## y_new[1,31] 12.3 0.0 1.9 8.6 12.3 16.2 4119 1
## y_new[1,32] 12.4 0.0 2.0 8.4 12.4 16.2 4266 1
## y_new[1,33] 12.4 0.0 2.0 8.6 12.4 16.3 4334 1
## y_new[1,34] 12.5 0.0 2.0 8.5 12.5 16.3 4156 1
## y_new[1,35] 12.5 0.0 2.0 8.7 12.6 16.3 4256 1
## y_new[1,36] 12.5 0.0 2.0 8.7 12.5 16.4 3497 1
## y_new[1,37] 12.6 0.0 2.0 8.7 12.6 16.5 4066 1
## y_new[1,38] 12.6 0.0 2.0 8.5 12.6 16.5 4143 1
## y_new[1,39] 12.7 0.0 2.0 8.6 12.6 16.6 4073 1
## y_new[1,40] 12.7 0.0 2.0 8.7 12.7 16.6 4087 1
## y_new[1,41] 12.7 0.0 2.1 8.7 12.7 16.8 4175 1
## y_new[1,42] 12.7 0.0 2.0 8.7 12.7 16.6 4391 1
## y_new[1,43] 12.8 0.0 2.0 8.9 12.8 16.7 3919 1
## y_new[1,44] 12.8 0.0 2.0 8.9 12.7 16.7 4324 1
## y_new[1,45] 12.8 0.0 2.1 8.7 12.8 16.9 4047 1
## y_new[1,46] 12.8 0.0 2.1 8.7 12.8 16.8 4269 1
## y_new[1,47] 12.9 0.0 2.0 8.9 12.9 17.0 4126 1
## y_new[1,48] 12.8 0.0 2.1 8.9 12.8 16.9 4073 1
## y_new[1,49] 12.9 0.0 2.0 8.9 12.8 16.9 3628 1
## y_new[1,50] 12.9 0.0 2.1 8.8 12.9 17.0 4035 1
## y_new[1,51] 12.9 0.0 2.1 8.8 12.9 17.1 4295 1
## y_new[1,52] 12.9 0.0 2.1 8.8 12.9 17.0 4238 1
## y_new[1,53] 12.9 0.0 2.1 8.9 12.8 17.1 4343 1
## y_new[1,54] 12.9 0.0 2.1 8.9 12.9 17.1 4003 1
## y_new[1,55] 12.9 0.0 2.1 9.0 12.9 17.0 4167 1
## y_new[1,56] 12.9 0.0 2.1 8.8 12.8 17.1 4229 1
## y_new[1,57] 13.0 0.0 2.1 8.9 13.0 17.1 4151 1
## y_new[1,58] 12.9 0.0 2.1 8.8 12.9 17.0 4147 1
## y_new[1,59] 12.9 0.0 2.1 8.9 12.9 17.0 4033 1
## y_new[1,60] 12.9 0.0 2.1 8.8 12.9 17.2 3980 1
## y_new[2,1] 0.0 0.0 1.7 -3.4 0.0 3.4 4064 1
## y_new[2,2] 0.8 0.0 1.7 -2.7 0.8 4.2 3978 1
## y_new[2,3] 1.6 0.0 1.8 -1.9 1.6 5.1 3829 1
## y_new[2,4] 2.3 0.0 1.8 -1.2 2.3 5.9 4066 1
## y_new[2,5] 2.8 0.0 1.8 -0.7 2.8 6.5 3862 1
## y_new[2,6] 3.4 0.0 1.9 -0.4 3.4 7.2 4006 1
## y_new[2,7] 3.9 0.0 1.9 0.2 3.9 7.7 4051 1
## y_new[2,8] 4.3 0.0 1.9 0.6 4.2 8.1 3629 1
## y_new[2,9] 4.6 0.0 1.9 0.9 4.6 8.3 4184 1
## y_new[2,10] 5.0 0.0 1.9 1.2 5.0 8.7 4165 1
## y_new[2,11] 5.3 0.0 2.0 1.5 5.4 9.3 4284 1
## y_new[2,12] 5.6 0.0 1.9 1.8 5.6 9.3 3624 1
## y_new[2,13] 5.8 0.0 1.9 2.0 5.8 9.6 3632 1
## y_new[2,14] 6.1 0.0 1.9 2.3 6.1 9.8 3696 1
## y_new[2,15] 6.3 0.0 1.9 2.5 6.3 10.0 4007 1
## y_new[2,16] 6.5 0.0 1.9 2.7 6.5 10.3 4230 1
## y_new[2,17] 6.6 0.0 1.9 2.9 6.6 10.5 3719 1
## y_new[2,18] 6.7 0.0 1.9 2.9 6.7 10.6 4386 1
## y_new[2,19] 6.9 0.0 1.9 3.2 6.9 10.7 3793 1
## y_new[2,20] 7.0 0.0 1.9 3.2 7.0 10.9 3723 1
## y_new[2,21] 7.1 0.0 1.9 3.3 7.2 10.8 4009 1
## y_new[2,22] 7.3 0.0 2.0 3.3 7.3 11.3 4259 1
## y_new[2,23] 7.2 0.0 1.9 3.3 7.3 11.0 4140 1
## y_new[2,24] 7.4 0.0 1.9 3.6 7.4 11.1 3960 1
## y_new[2,25] 7.5 0.0 1.9 3.7 7.4 11.3 4049 1
## y_new[2,26] 7.6 0.0 2.0 3.7 7.6 11.4 4087 1
## y_new[2,27] 7.6 0.0 1.9 3.8 7.6 11.4 3755 1
## y_new[2,28] 7.7 0.0 1.9 3.8 7.7 11.3 4383 1
## y_new[2,29] 7.7 0.0 2.0 3.8 7.7 11.5 4412 1
## y_new[2,30] 7.8 0.0 1.9 4.0 7.7 11.5 4189 1
## y_new[2,31] 7.8 0.0 1.9 3.9 7.8 11.5 3526 1
## y_new[2,32] 7.8 0.0 2.0 3.9 7.8 11.7 4128 1
## y_new[2,33] 7.9 0.0 1.9 4.1 7.9 11.7 4106 1
## y_new[2,34] 7.9 0.0 1.9 4.1 7.9 11.7 4236 1
## y_new[2,35] 7.9 0.0 2.0 4.0 7.9 11.8 4285 1
## y_new[2,36] 7.9 0.0 2.0 4.1 7.9 11.8 4166 1
## y_new[2,37] 8.0 0.0 2.0 4.1 8.0 11.8 4001 1
## y_new[2,38] 8.0 0.0 2.0 4.2 8.0 12.0 4187 1
## y_new[2,39] 8.0 0.0 2.0 4.2 8.0 12.0 3497 1
## y_new[2,40] 8.0 0.0 2.0 4.0 8.1 12.0 4535 1
## y_new[2,41] 8.1 0.0 2.0 4.2 8.1 12.0 3916 1
## y_new[2,42] 8.1 0.0 2.0 4.3 8.1 11.9 4192 1
## y_new[2,43] 8.1 0.0 2.0 4.1 8.1 11.9 3861 1
## y_new[2,44] 8.2 0.0 1.9 4.3 8.2 12.0 4119 1
## y_new[2,45] 8.2 0.0 1.9 4.4 8.2 12.0 3986 1
## y_new[2,46] 8.2 0.0 2.0 4.4 8.1 12.2 4036 1
## y_new[2,47] 8.2 0.0 2.0 4.2 8.1 12.2 4097 1
## y_new[2,48] 8.2 0.0 2.0 4.2 8.1 12.1 4376 1
## y_new[2,49] 8.2 0.0 2.0 4.2 8.1 12.2 4216 1
## y_new[2,50] 8.2 0.0 2.0 4.2 8.1 12.2 4268 1
## y_new[2,51] 8.2 0.0 2.0 4.3 8.2 12.1 4344 1
## y_new[2,52] 8.3 0.0 2.0 4.3 8.2 12.2 4191 1
## y_new[2,53] 8.2 0.0 2.0 4.2 8.2 12.3 4369 1
## y_new[2,54] 8.2 0.0 2.0 4.3 8.2 12.2 4359 1
## y_new[2,55] 8.2 0.0 2.0 4.3 8.2 12.1 4357 1
## y_new[2,56] 8.3 0.0 2.0 4.4 8.2 12.3 4065 1
## y_new[2,57] 8.2 0.0 2.0 4.3 8.2 12.4 4245 1
## y_new[2,58] 8.2 0.0 2.0 4.4 8.2 12.2 3984 1
## y_new[2,59] 8.2 0.0 2.0 4.3 8.2 12.3 3817 1
## y_new[2,60] 8.3 0.0 2.1 4.3 8.3 12.5 4173 1
## y_new[3,1] 0.0 0.0 1.7 -3.4 0.0 3.4 4032 1
## y_new[3,2] 2.7 0.0 1.8 -0.7 2.8 6.2 3473 1
## y_new[3,3] 5.2 0.0 1.8 1.6 5.2 8.7 3579 1
## y_new[3,4] 7.4 0.0 1.9 3.8 7.4 11.0 3889 1
## y_new[3,5] 9.2 0.0 1.9 5.6 9.2 13.0 4230 1
## y_new[3,6] 10.9 0.0 2.0 6.9 10.8 14.7 4115 1
## y_new[3,7] 12.4 0.0 2.0 8.6 12.4 16.4 4070 1
## y_new[3,8] 13.6 0.0 2.0 9.7 13.6 17.6 4273 1
## y_new[3,9] 14.8 0.0 2.0 10.9 14.9 18.8 4001 1
## y_new[3,10] 15.8 0.0 2.0 12.0 15.8 19.7 4161 1
## y_new[3,11] 16.7 0.0 2.0 12.9 16.7 20.6 3985 1
## y_new[3,12] 17.5 0.0 2.0 13.6 17.5 21.5 4172 1
## y_new[3,13] 18.3 0.0 2.0 14.3 18.3 22.1 4325 1
## y_new[3,14] 18.9 0.0 1.9 15.0 18.9 22.7 4115 1
## y_new[3,15] 19.4 0.0 2.0 15.5 19.5 23.2 4433 1
## y_new[3,16] 19.9 0.0 2.0 16.0 19.9 23.6 4212 1
## y_new[3,17] 20.4 0.0 1.9 16.5 20.4 24.0 3954 1
## y_new[3,18] 20.8 0.0 1.9 17.0 20.8 24.6 3600 1
## y_new[3,19] 21.1 0.0 1.9 17.3 21.1 24.9 3794 1
## y_new[3,20] 21.4 0.0 1.9 17.7 21.4 25.1 3785 1
## y_new[3,21] 21.7 0.0 1.9 17.9 21.7 25.4 3976 1
## y_new[3,22] 21.9 0.0 1.9 18.2 21.9 25.8 4234 1
## y_new[3,23] 22.1 0.0 1.9 18.3 22.1 25.9 4264 1
## y_new[3,24] 22.3 0.0 1.9 18.4 22.3 26.1 4077 1
## y_new[3,25] 22.5 0.0 1.9 18.7 22.5 26.2 4219 1
## y_new[3,26] 22.6 0.0 1.9 18.7 22.7 26.4 4343 1
## y_new[3,27] 22.8 0.0 2.0 18.9 22.8 26.7 4311 1
## y_new[3,28] 22.9 0.0 2.0 18.9 22.9 26.8 4167 1
## y_new[3,29] 23.0 0.0 2.0 19.0 23.0 26.9 4348 1
## y_new[3,30] 23.1 0.0 2.0 19.2 23.1 27.0 3947 1
## y_new[3,31] 23.1 0.0 2.0 19.2 23.1 27.1 4305 1
## y_new[3,32] 23.3 0.0 2.0 19.4 23.3 27.1 4408 1
## y_new[3,33] 23.3 0.0 2.0 19.4 23.4 27.2 4571 1
## y_new[3,34] 23.3 0.0 2.1 19.2 23.3 27.4 3964 1
## y_new[3,35] 23.5 0.0 2.0 19.5 23.4 27.4 4068 1
## y_new[3,36] 23.4 0.0 2.0 19.4 23.4 27.3 4126 1
## y_new[3,37] 23.5 0.0 2.0 19.4 23.5 27.5 4439 1
## y_new[3,38] 23.5 0.0 2.1 19.5 23.5 27.4 4437 1
## y_new[3,39] 23.6 0.0 2.0 19.6 23.6 27.6 3356 1
## y_new[3,40] 23.6 0.0 2.0 19.6 23.6 27.7 4096 1
## y_new[3,41] 23.6 0.0 2.0 19.6 23.7 27.6 4169 1
## y_new[3,42] 23.6 0.0 2.1 19.7 23.6 27.8 4169 1
## y_new[3,43] 23.7 0.0 2.0 19.7 23.7 27.7 4341 1
## y_new[3,44] 23.7 0.0 2.0 19.7 23.7 27.6 4151 1
## y_new[3,45] 23.7 0.0 2.0 19.8 23.7 27.8 4335 1
## y_new[3,46] 23.7 0.0 2.1 19.7 23.7 27.7 4185 1
## y_new[3,47] 23.7 0.0 2.1 19.7 23.7 27.8 4486 1
## y_new[3,48] 23.8 0.0 2.1 19.6 23.8 27.9 4178 1
## y_new[3,49] 23.8 0.0 2.0 19.9 23.7 27.8 4319 1
## y_new[3,50] 23.7 0.0 2.1 19.6 23.7 27.8 4453 1
## y_new[3,51] 23.8 0.0 2.1 19.8 23.8 27.9 4214 1
## y_new[3,52] 23.8 0.0 2.1 19.7 23.8 27.8 4200 1
## y_new[3,53] 23.8 0.0 2.1 19.7 23.8 27.9 4135 1
## y_new[3,54] 23.8 0.0 2.0 19.7 23.8 27.7 4596 1
## y_new[3,55] 23.8 0.0 2.1 19.7 23.8 28.0 4142 1
## y_new[3,56] 23.8 0.0 2.1 19.7 23.7 27.9 4370 1
## y_new[3,57] 23.8 0.0 2.1 19.6 23.8 27.9 4399 1
## y_new[3,58] 23.8 0.0 2.1 19.8 23.8 27.8 3695 1
## y_new[3,59] 23.8 0.0 2.1 19.8 23.8 27.9 3949 1
## y_new[3,60] 23.8 0.0 2.1 19.7 23.9 27.9 4226 1
## y_new[4,1] 0.0 0.0 1.7 -3.3 0.0 3.3 3891 1
## y_new[4,2] 3.2 0.0 1.7 -0.2 3.2 6.7 3914 1
## y_new[4,3] 6.1 0.0 1.8 2.5 6.1 9.6 3690 1
## y_new[4,4] 8.5 0.0 1.9 4.8 8.5 12.2 4112 1
## y_new[4,5] 10.6 0.0 2.0 6.7 10.6 14.4 3845 1
## y_new[4,6] 12.5 0.0 2.0 8.7 12.5 16.4 4285 1
## y_new[4,7] 14.1 0.0 2.0 10.3 14.1 18.1 4145 1
## y_new[4,8] 15.6 0.0 2.0 11.8 15.6 19.6 4116 1
## y_new[4,9] 16.8 0.0 2.0 12.9 16.8 20.6 4441 1
## y_new[4,10] 17.9 0.0 2.0 14.0 18.0 21.9 4199 1
## y_new[4,11] 18.9 0.0 1.9 15.1 18.9 22.7 4139 1
## y_new[4,12] 19.7 0.0 2.0 15.8 19.7 23.6 3954 1
## y_new[4,13] 20.5 0.0 1.9 16.7 20.5 24.3 3920 1
## y_new[4,14] 21.1 0.0 1.9 17.3 21.1 24.9 4126 1
## y_new[4,15] 21.7 0.0 1.9 18.0 21.7 25.6 4243 1
## y_new[4,16] 22.2 0.0 1.9 18.5 22.2 26.1 4073 1
## y_new[4,17] 22.6 0.0 1.9 18.8 22.6 26.3 3951 1
## y_new[4,18] 23.1 0.0 1.9 19.4 23.0 26.8 4200 1
## y_new[4,19] 23.4 0.0 2.0 19.5 23.4 27.3 4193 1
## y_new[4,20] 23.7 0.0 1.9 20.0 23.7 27.4 3789 1
## y_new[4,21] 23.9 0.0 1.9 20.2 24.0 27.6 4068 1
## y_new[4,22] 24.2 0.0 1.9 20.4 24.2 27.8 4304 1
## y_new[4,23] 24.4 0.0 1.9 20.7 24.4 28.1 4322 1
## y_new[4,24] 24.6 0.0 1.9 20.8 24.6 28.3 3998 1
## y_new[4,25] 24.7 0.0 1.9 20.9 24.7 28.5 4037 1
## y_new[4,26] 24.9 0.0 1.9 21.1 24.9 28.7 4066 1
## y_new[4,27] 25.0 0.0 2.0 21.2 25.0 28.9 3494 1
## y_new[4,28] 25.1 0.0 2.0 21.2 25.1 29.1 4164 1
## y_new[4,29] 25.2 0.0 2.0 21.2 25.2 29.0 3594 1
## y_new[4,30] 25.3 0.0 2.0 21.2 25.3 29.2 4189 1
## y_new[4,31] 25.3 0.0 2.0 21.2 25.3 29.2 4013 1
## y_new[4,32] 25.4 0.0 2.0 21.6 25.4 29.2 4040 1
## y_new[4,33] 25.5 0.0 2.0 21.6 25.5 29.4 3991 1
## y_new[4,34] 25.5 0.0 2.0 21.5 25.5 29.5 4051 1
## y_new[4,35] 25.6 0.0 2.0 21.6 25.5 29.5 4046 1
## y_new[4,36] 25.5 0.0 2.1 21.3 25.5 29.5 3818 1
## y_new[4,37] 25.6 0.0 2.1 21.6 25.6 29.6 3618 1
## y_new[4,38] 25.7 0.0 2.0 21.7 25.6 29.8 3988 1
## y_new[4,39] 25.6 0.0 2.0 21.6 25.7 29.6 4196 1
## y_new[4,40] 25.7 0.0 2.1 21.6 25.7 29.9 3993 1
## y_new[4,41] 25.8 0.0 2.1 21.8 25.8 29.7 4070 1
## y_new[4,42] 25.7 0.0 2.0 21.7 25.7 29.7 4217 1
## y_new[4,43] 25.8 0.0 2.0 21.8 25.8 29.7 4224 1
## y_new[4,44] 25.8 0.0 2.0 21.9 25.8 29.8 4416 1
## y_new[4,45] 25.8 0.0 2.0 21.9 25.8 29.9 4072 1
## y_new[4,46] 25.8 0.0 2.1 21.8 25.7 30.0 3647 1
## y_new[4,47] 25.8 0.0 2.1 21.8 25.8 30.0 4045 1
## y_new[4,48] 25.8 0.0 2.1 21.7 25.9 30.0 3753 1
## y_new[4,49] 25.8 0.0 2.1 21.8 25.8 29.8 3933 1
## y_new[4,50] 25.8 0.0 2.1 21.7 25.9 29.9 4443 1
## y_new[4,51] 25.8 0.0 2.1 21.9 25.8 29.8 3981 1
## y_new[4,52] 25.8 0.0 2.1 21.6 25.8 30.0 4206 1
## y_new[4,53] 25.8 0.0 2.1 21.7 25.8 29.9 3584 1
## y_new[4,54] 25.8 0.0 2.1 21.7 25.8 29.8 4534 1
## y_new[4,55] 25.8 0.0 2.1 21.8 25.9 29.9 4266 1
## y_new[4,56] 25.9 0.0 2.1 21.8 25.9 30.0 4126 1
## y_new[4,57] 25.9 0.0 2.1 21.7 25.8 30.1 4193 1
## y_new[4,58] 25.9 0.0 2.1 21.8 25.9 30.0 3898 1
## y_new[4,59] 25.9 0.0 2.1 21.9 25.9 29.8 3995 1
## y_new[4,60] 25.9 0.0 2.1 21.7 25.9 30.2 4002 1
## y_new[5,1] 0.0 0.0 1.7 -3.3 0.0 3.3 4163 1
## y_new[5,2] 1.1 0.0 1.7 -2.1 1.1 4.6 4026 1
## y_new[5,3] 2.1 0.0 1.8 -1.4 2.1 5.6 4009 1
## y_new[5,4] 3.0 0.0 1.8 -0.4 3.0 6.6 3312 1
## y_new[5,5] 3.8 0.0 1.8 0.2 3.9 7.5 3935 1
## y_new[5,6] 4.6 0.0 1.9 0.9 4.6 8.4 4055 1
## y_new[5,7] 5.4 0.0 1.9 1.8 5.3 9.0 4006 1
## y_new[5,8] 6.0 0.0 1.9 2.3 6.0 9.8 3672 1
## y_new[5,9] 6.6 0.0 2.0 2.8 6.6 10.5 3952 1
## y_new[5,10] 7.2 0.0 2.0 3.3 7.2 11.1 3799 1
## y_new[5,11] 7.7 0.0 1.9 3.8 7.7 11.6 3750 1
## y_new[5,12] 8.1 0.0 2.0 4.3 8.0 12.0 4049 1
## y_new[5,13] 8.6 0.0 2.0 4.7 8.6 12.5 3873 1
## y_new[5,14] 9.0 0.0 2.0 5.2 8.9 12.9 3994 1
## y_new[5,15] 9.3 0.0 2.0 5.5 9.3 13.1 3952 1
## y_new[5,16] 9.7 0.0 2.0 5.9 9.7 13.7 3873 1
## y_new[5,17] 10.0 0.0 1.9 6.2 10.0 13.9 3775 1
## y_new[5,18] 10.3 0.0 1.9 6.4 10.2 13.9 3925 1
## y_new[5,19] 10.6 0.0 2.0 6.7 10.6 14.4 4011 1
## y_new[5,20] 10.7 0.0 1.9 6.9 10.7 14.6 4083 1
## y_new[5,21] 10.9 0.0 1.9 7.2 10.9 14.7 3971 1
## y_new[5,22] 11.2 0.0 1.9 7.5 11.2 15.0 4269 1
## y_new[5,23] 11.4 0.0 1.9 7.6 11.4 15.2 4076 1
## y_new[5,24] 11.6 0.0 2.0 7.7 11.5 15.4 3915 1
## y_new[5,25] 11.8 0.0 2.0 7.8 11.8 15.6 3702 1
## y_new[5,26] 11.9 0.0 1.9 8.0 11.9 15.7 4125 1
## y_new[5,27] 12.1 0.0 1.9 8.4 12.1 16.0 4041 1
## y_new[5,28] 12.2 0.0 1.9 8.3 12.3 16.1 4235 1
## y_new[5,29] 12.4 0.0 1.9 8.5 12.4 16.1 4333 1
## y_new[5,30] 12.5 0.0 2.0 8.7 12.5 16.4 3922 1
## y_new[5,31] 12.5 0.0 2.0 8.6 12.5 16.3 4076 1
## y_new[5,32] 12.7 0.0 2.0 8.9 12.7 16.6 3765 1
## y_new[5,33] 12.8 0.0 1.9 8.9 12.8 16.6 4109 1
## y_new[5,34] 12.9 0.0 2.0 9.0 12.9 16.8 4032 1
## y_new[5,35] 12.9 0.0 2.0 8.9 12.9 16.9 4203 1
## y_new[5,36] 13.0 0.0 2.0 9.0 13.0 16.9 4294 1
## y_new[5,37] 13.1 0.0 2.0 9.0 13.1 17.0 4122 1
## y_new[5,38] 13.1 0.0 2.0 9.1 13.1 17.1 3870 1
## y_new[5,39] 13.2 0.0 2.0 9.1 13.2 17.1 4231 1
## y_new[5,40] 13.3 0.0 2.0 9.3 13.3 17.2 3965 1
## y_new[5,41] 13.3 0.0 2.1 9.3 13.3 17.3 4297 1
## y_new[5,42] 13.3 0.0 2.1 9.1 13.3 17.3 3859 1
## y_new[5,43] 13.4 0.0 2.0 9.5 13.4 17.4 3870 1
## y_new[5,44] 13.4 0.0 2.1 9.4 13.4 17.6 4390 1
## y_new[5,45] 13.5 0.0 2.0 9.6 13.5 17.4 4088 1
## y_new[5,46] 13.5 0.0 2.1 9.4 13.5 17.7 4061 1
## y_new[5,47] 13.6 0.0 2.1 9.4 13.6 17.6 4511 1
## y_new[5,48] 13.6 0.0 2.1 9.6 13.6 17.6 4227 1
## y_new[5,49] 13.7 0.0 2.1 9.7 13.7 17.8 4006 1
## y_new[5,50] 13.7 0.0 2.1 9.5 13.7 17.8 3886 1
## y_new[5,51] 13.7 0.0 2.2 9.4 13.7 18.0 4588 1
## y_new[5,52] 13.7 0.0 2.1 9.6 13.8 17.9 4116 1
## y_new[5,53] 13.7 0.0 2.2 9.6 13.7 18.0 3944 1
## y_new[5,54] 13.8 0.0 2.2 9.5 13.8 17.9 4086 1
## y_new[5,55] 13.8 0.0 2.2 9.6 13.8 18.1 3912 1
## y_new[5,56] 13.8 0.0 2.2 9.6 13.8 17.9 4186 1
## y_new[5,57] 13.8 0.0 2.2 9.5 13.8 18.0 4464 1
## y_new[5,58] 13.8 0.0 2.2 9.6 13.8 18.2 3932 1
## y_new[5,59] 13.9 0.0 2.2 9.6 13.8 18.1 4303 1
## y_new[5,60] 13.8 0.0 2.2 9.7 13.8 18.1 3109 1
## y_new[6,1] 0.0 0.0 1.7 -3.4 0.0 3.5 3593 1
## y_new[6,2] 1.5 0.0 1.7 -1.8 1.4 4.9 3870 1
## y_new[6,3] 2.8 0.0 1.8 -0.8 2.8 6.2 3844 1
## y_new[6,4] 3.9 0.0 1.8 0.3 3.9 7.5 4065 1
## y_new[6,5] 5.0 0.0 1.9 1.3 5.0 8.7 4231 1
## y_new[6,6] 6.0 0.0 1.9 2.1 6.0 9.9 3647 1
## y_new[6,7] 6.8 0.0 2.0 3.0 6.8 10.6 4000 1
## y_new[6,8] 7.6 0.0 2.0 3.8 7.6 11.8 3447 1
## y_new[6,9] 8.4 0.0 2.0 4.4 8.4 12.3 3479 1
## y_new[6,10] 8.9 0.0 2.0 4.9 8.9 13.0 3869 1
## y_new[6,11] 9.6 0.0 2.0 5.6 9.5 13.6 3911 1
## y_new[6,12] 10.0 0.0 2.0 6.0 10.0 14.0 3987 1
## y_new[6,13] 10.5 0.0 2.0 6.6 10.5 14.5 4149 1
## y_new[6,14] 11.0 0.0 2.0 7.1 11.0 15.0 4170 1
## y_new[6,15] 11.3 0.0 2.0 7.3 11.4 15.2 4113 1
## y_new[6,16] 11.7 0.0 1.9 7.9 11.7 15.5 4418 1
## y_new[6,17] 12.0 0.0 2.0 8.1 12.0 15.9 3606 1
## y_new[6,18] 12.4 0.0 2.0 8.5 12.4 16.2 3376 1
## y_new[6,19] 12.7 0.0 1.9 8.9 12.6 16.4 3955 1
## y_new[6,20] 12.8 0.0 1.9 9.0 12.9 16.7 4147 1
## y_new[6,21] 13.1 0.0 1.9 9.4 13.1 16.9 3978 1
## y_new[6,22] 13.3 0.0 1.9 9.5 13.3 17.1 3732 1
## y_new[6,23] 13.4 0.0 1.9 9.7 13.5 17.2 3767 1
## y_new[6,24] 13.7 0.0 1.9 9.9 13.7 17.5 3774 1
## y_new[6,25] 13.8 0.0 1.9 10.0 13.8 17.7 3825 1
## y_new[6,26] 13.9 0.0 2.0 9.9 14.0 17.7 4001 1
## y_new[6,27] 14.1 0.0 1.9 10.2 14.1 18.0 4061 1
## y_new[6,28] 14.2 0.0 2.0 10.4 14.2 18.1 4014 1
## y_new[6,29] 14.3 0.0 1.9 10.6 14.3 18.2 4298 1
## y_new[6,30] 14.4 0.0 2.0 10.5 14.5 18.2 4189 1
## y_new[6,31] 14.5 0.0 2.0 10.6 14.5 18.4 3899 1
## y_new[6,32] 14.6 0.0 2.0 10.7 14.6 18.4 4355 1
## y_new[6,33] 14.7 0.0 2.0 10.9 14.7 18.6 4003 1
## y_new[6,34] 14.8 0.0 2.0 10.8 14.7 18.8 3972 1
## y_new[6,35] 14.8 0.0 2.0 10.9 14.9 18.7 3895 1
## y_new[6,36] 14.9 0.0 2.0 11.0 14.8 18.7 3864 1
## y_new[6,37] 14.9 0.0 2.0 11.0 14.9 18.9 4096 1
## y_new[6,38] 15.0 0.0 2.0 11.0 15.1 18.8 4140 1
## y_new[6,39] 15.1 0.0 2.0 11.1 15.1 19.0 3848 1
## y_new[6,40] 15.1 0.0 2.1 11.1 15.1 19.1 3994 1
## y_new[6,41] 15.1 0.0 2.0 11.1 15.1 19.1 4073 1
## y_new[6,42] 15.1 0.0 2.1 11.1 15.1 19.2 4196 1
## y_new[6,43] 15.2 0.0 2.1 11.2 15.2 19.2 3525 1
## y_new[6,44] 15.2 0.0 2.1 11.1 15.2 19.4 3264 1
## y_new[6,45] 15.3 0.0 2.1 11.1 15.3 19.4 4186 1
## y_new[6,46] 15.3 0.0 2.1 11.3 15.3 19.5 3133 1
## y_new[6,47] 15.3 0.0 2.2 11.0 15.3 19.5 4330 1
## y_new[6,48] 15.4 0.0 2.1 11.2 15.4 19.7 3956 1
## y_new[6,49] 15.4 0.0 2.1 11.1 15.4 19.5 4145 1
## y_new[6,50] 15.4 0.0 2.2 11.1 15.3 19.6 3444 1
## y_new[6,51] 15.4 0.0 2.1 11.4 15.4 19.6 3839 1
## y_new[6,52] 15.4 0.0 2.2 11.1 15.4 19.6 4251 1
## y_new[6,53] 15.4 0.0 2.2 11.2 15.4 19.7 3813 1
## y_new[6,54] 15.5 0.0 2.2 11.3 15.4 19.9 4122 1
## y_new[6,55] 15.5 0.0 2.2 11.2 15.5 19.8 4103 1
## y_new[6,56] 15.4 0.0 2.2 11.3 15.4 19.8 3548 1
## y_new[6,57] 15.5 0.0 2.2 11.1 15.5 20.0 3855 1
## y_new[6,58] 15.5 0.0 2.2 11.3 15.5 19.7 3972 1
## y_new[6,59] 15.5 0.0 2.2 11.3 15.5 19.9 3615 1
## y_new[6,60] 15.5 0.0 2.2 11.2 15.5 20.0 3020 1
## y_new[7,1] 0.0 0.0 1.7 -3.3 -0.1 3.3 4056 1
## y_new[7,2] 1.4 0.0 1.8 -2.0 1.4 4.9 3945 1
## y_new[7,3] 2.7 0.0 1.8 -0.9 2.7 6.4 3877 1
## y_new[7,4] 3.8 0.0 1.8 0.2 3.8 7.4 4101 1
## y_new[7,5] 4.8 0.0 1.9 1.1 4.8 8.5 3775 1
## y_new[7,6] 5.8 0.0 1.9 2.2 5.8 9.5 3565 1
## y_new[7,7] 6.6 0.0 1.9 3.0 6.6 10.4 4041 1
## y_new[7,8] 7.4 0.0 1.9 3.6 7.4 11.3 4252 1
## y_new[7,9] 8.0 0.0 1.9 4.2 8.0 11.8 4237 1
## y_new[7,10] 8.7 0.0 1.9 4.9 8.7 12.6 4302 1
## y_new[7,11] 9.2 0.0 2.0 5.4 9.2 13.1 3653 1
## y_new[7,12] 9.8 0.0 1.9 6.0 9.7 13.6 4033 1
## y_new[7,13] 10.2 0.0 2.0 6.4 10.2 14.0 4205 1
## y_new[7,14] 10.6 0.0 1.9 6.8 10.7 14.4 4342 1
## y_new[7,15] 10.9 0.0 2.0 7.1 10.9 14.7 3931 1
## y_new[7,16] 11.4 0.0 1.9 7.6 11.4 15.2 4070 1
## y_new[7,17] 11.7 0.0 1.9 7.9 11.6 15.4 3773 1
## y_new[7,18] 11.9 0.0 1.9 8.0 11.9 15.8 4217 1
## y_new[7,19] 12.2 0.0 1.9 8.4 12.2 16.1 4298 1
## y_new[7,20] 12.4 0.0 1.9 8.6 12.5 16.2 4259 1
## y_new[7,21] 12.7 0.0 1.9 8.8 12.7 16.3 3952 1
## y_new[7,22] 12.8 0.0 1.9 9.0 12.8 16.4 3894 1
## y_new[7,23] 13.0 0.0 1.9 9.2 13.0 16.7 4376 1
## y_new[7,24] 13.1 0.0 1.9 9.4 13.1 17.0 4224 1
## y_new[7,25] 13.3 0.0 1.9 9.6 13.2 17.1 3943 1
## y_new[7,26] 13.4 0.0 1.9 9.6 13.4 17.3 4396 1
## y_new[7,27] 13.5 0.0 1.9 9.7 13.5 17.2 4141 1
## y_new[7,28] 13.6 0.0 2.0 9.8 13.6 17.6 4282 1
## y_new[7,29] 13.7 0.0 2.0 9.9 13.7 17.5 4148 1
## y_new[7,30] 13.9 0.0 1.9 10.1 13.9 17.6 4080 1
## y_new[7,31] 13.9 0.0 1.9 10.1 13.9 17.8 4181 1
## y_new[7,32] 14.0 0.0 2.0 10.0 14.0 18.0 4254 1
## y_new[7,33] 14.1 0.0 2.0 10.1 14.1 18.0 4122 1
## y_new[7,34] 14.1 0.0 2.0 10.2 14.1 18.0 4414 1
## y_new[7,35] 14.2 0.0 2.0 10.4 14.2 18.1 4524 1
## y_new[7,36] 14.2 0.0 2.1 10.1 14.2 18.1 4378 1
## y_new[7,37] 14.3 0.0 2.0 10.4 14.3 18.1 4280 1
## y_new[7,38] 14.3 0.0 2.0 10.5 14.3 18.2 4348 1
## y_new[7,39] 14.3 0.0 2.0 10.3 14.4 18.2 4044 1
## y_new[7,40] 14.4 0.0 2.0 10.5 14.3 18.4 4365 1
## y_new[7,41] 14.4 0.0 2.0 10.3 14.4 18.5 4122 1
## y_new[7,42] 14.5 0.0 2.0 10.6 14.5 18.3 4250 1
## y_new[7,43] 14.5 0.0 2.0 10.6 14.5 18.4 4420 1
## y_new[7,44] 14.5 0.0 2.0 10.6 14.5 18.5 4225 1
## y_new[7,45] 14.6 0.0 2.0 10.7 14.6 18.6 4133 1
## y_new[7,46] 14.6 0.0 2.1 10.6 14.6 18.5 4173 1
## y_new[7,47] 14.6 0.0 2.1 10.6 14.6 18.6 4619 1
## y_new[7,48] 14.6 0.0 2.1 10.6 14.6 18.6 4176 1
## y_new[7,49] 14.6 0.0 2.1 10.5 14.6 18.8 4392 1
## y_new[7,50] 14.6 0.0 2.1 10.4 14.6 18.5 4541 1
## y_new[7,51] 14.7 0.0 2.1 10.6 14.7 18.7 4073 1
## y_new[7,52] 14.7 0.0 2.1 10.4 14.7 18.8 4206 1
## y_new[7,53] 14.7 0.0 2.1 10.6 14.7 18.9 4303 1
## y_new[7,54] 14.6 0.0 2.1 10.5 14.6 18.7 4564 1
## y_new[7,55] 14.7 0.0 2.1 10.5 14.6 18.8 4271 1
## y_new[7,56] 14.7 0.0 2.1 10.6 14.8 18.8 4424 1
## y_new[7,57] 14.7 0.0 2.1 10.6 14.7 18.9 4353 1
## y_new[7,58] 14.7 0.0 2.1 10.6 14.7 18.8 4364 1
## y_new[7,59] 14.7 0.0 2.2 10.4 14.7 18.9 4236 1
## y_new[7,60] 14.7 0.0 2.1 10.7 14.7 18.7 4023 1
## y_new[8,1] 0.0 0.0 1.7 -3.5 0.0 3.4 3995 1
## y_new[8,2] 1.7 0.0 1.8 -1.7 1.7 5.2 3885 1
## y_new[8,3] 3.3 0.0 1.9 -0.4 3.3 7.1 4248 1
## y_new[8,4] 4.6 0.0 1.9 0.8 4.6 8.4 4159 1
## y_new[8,5] 5.8 0.0 1.9 2.0 5.7 9.6 4411 1
## y_new[8,6] 6.7 0.0 2.0 2.9 6.7 10.7 4159 1
## y_new[8,7] 7.6 0.0 2.0 3.8 7.5 11.6 3895 1
## y_new[8,8] 8.3 0.0 2.0 4.4 8.3 12.3 4133 1
## y_new[8,9] 8.9 0.0 2.0 4.9 8.9 12.9 3816 1
## y_new[8,10] 9.5 0.0 2.0 5.6 9.5 13.4 4502 1
## y_new[8,11] 9.9 0.0 2.0 6.0 9.9 13.8 4400 1
## y_new[8,12] 10.4 0.0 2.0 6.4 10.4 14.4 4160 1
## y_new[8,13] 10.7 0.0 1.9 7.0 10.7 14.4 4395 1
## y_new[8,14] 11.0 0.0 1.9 7.2 11.0 14.8 4010 1
## y_new[8,15] 11.3 0.0 1.9 7.6 11.3 15.0 3981 1
## y_new[8,16] 11.6 0.0 1.9 7.8 11.6 15.4 4328 1
## y_new[8,17] 11.8 0.0 1.9 8.0 11.8 15.5 3975 1
## y_new[8,18] 12.0 0.0 1.9 8.3 12.0 15.8 3998 1
## y_new[8,19] 12.1 0.0 1.9 8.4 12.1 16.0 4258 1
## y_new[8,20] 12.3 0.0 1.9 8.7 12.3 16.0 3579 1
## y_new[8,21] 12.4 0.0 1.9 8.7 12.4 16.1 4218 1
## y_new[8,22] 12.5 0.0 1.9 8.7 12.6 16.2 4085 1
## y_new[8,23] 12.6 0.0 1.9 8.9 12.6 16.5 4264 1
## y_new[8,24] 12.7 0.0 1.9 9.0 12.7 16.6 4296 1
## y_new[8,25] 12.8 0.0 1.9 9.0 12.8 16.7 4022 1
## y_new[8,26] 12.9 0.0 1.9 9.0 12.9 16.7 4642 1
## y_new[8,27] 12.9 0.0 1.9 9.1 12.9 16.7 3982 1
## y_new[8,28] 13.0 0.0 1.9 9.2 13.0 16.7 4162 1
## y_new[8,29] 13.0 0.0 2.0 9.3 13.0 16.9 3753 1
## y_new[8,30] 13.1 0.0 2.0 9.2 13.0 16.8 3877 1
## y_new[8,31] 13.1 0.0 2.0 9.2 13.1 17.0 4239 1
## y_new[8,32] 13.1 0.0 2.0 9.2 13.1 17.0 4348 1
## y_new[8,33] 13.2 0.0 2.0 9.4 13.1 17.1 4357 1
## y_new[8,34] 13.2 0.0 2.0 9.3 13.2 17.1 4034 1
## y_new[8,35] 13.3 0.0 2.0 9.3 13.3 17.1 4419 1
## y_new[8,36] 13.2 0.0 2.0 9.3 13.2 17.2 3975 1
## y_new[8,37] 13.3 0.0 2.0 9.4 13.2 17.2 3987 1
## y_new[8,38] 13.3 0.0 2.0 9.4 13.3 17.2 4310 1
## y_new[8,39] 13.3 0.0 2.0 9.3 13.3 17.3 4085 1
## y_new[8,40] 13.3 0.0 2.0 9.4 13.3 17.4 3981 1
## y_new[8,41] 13.3 0.0 2.0 9.5 13.3 17.2 4249 1
## y_new[8,42] 13.3 0.0 2.0 9.3 13.3 17.3 4282 1
## y_new[8,43] 13.3 0.0 2.0 9.4 13.3 17.3 3791 1
## y_new[8,44] 13.3 0.0 2.0 9.4 13.3 17.5 4024 1
## y_new[8,45] 13.3 0.0 2.0 9.4 13.3 17.2 3796 1
## y_new[8,46] 13.4 0.0 2.1 9.4 13.4 17.4 4019 1
## y_new[8,47] 13.3 0.0 2.1 9.3 13.4 17.3 4435 1
## y_new[8,48] 13.4 0.0 2.0 9.5 13.4 17.3 3900 1
## y_new[8,49] 13.4 0.0 2.1 9.4 13.4 17.4 4341 1
## y_new[8,50] 13.4 0.0 2.0 9.4 13.4 17.3 4127 1
## y_new[8,51] 13.4 0.0 2.1 9.4 13.4 17.5 4363 1
## y_new[8,52] 13.4 0.0 2.0 9.4 13.3 17.4 3938 1
## y_new[8,53] 13.4 0.0 2.0 9.3 13.4 17.4 4563 1
## y_new[8,54] 13.4 0.0 2.1 9.3 13.4 17.6 4389 1
## y_new[8,55] 13.4 0.0 2.0 9.4 13.3 17.3 4200 1
## y_new[8,56] 13.4 0.0 2.1 9.4 13.4 17.5 3710 1
## y_new[8,57] 13.4 0.0 2.0 9.5 13.3 17.3 4540 1
## y_new[8,58] 13.4 0.0 2.1 9.3 13.4 17.4 4206 1
## y_new[8,59] 13.5 0.0 2.0 9.5 13.5 17.4 3667 1
## y_new[8,60] 13.4 0.0 2.0 9.4 13.4 17.5 4224 1
## y_new[9,1] 0.0 0.0 1.7 -3.4 0.0 3.3 4043 1
## y_new[9,2] 4.7 0.0 1.8 1.1 4.7 8.3 4137 1
## y_new[9,3] 8.7 0.0 1.9 5.0 8.7 12.5 4216 1
## y_new[9,4] 12.1 0.0 2.0 8.3 12.1 15.9 4350 1
## y_new[9,5] 15.0 0.0 2.0 11.0 15.0 18.8 4002 1
## y_new[9,6] 17.4 0.0 2.0 13.3 17.4 21.4 4241 1
## y_new[9,7] 19.5 0.0 2.0 15.5 19.5 23.4 4403 1
## y_new[9,8] 21.3 0.0 2.0 17.3 21.3 25.4 3682 1
## y_new[9,9] 22.8 0.0 2.0 18.8 22.8 26.9 4051 1
## y_new[9,10] 24.2 0.0 2.0 20.3 24.2 28.1 4195 1
## y_new[9,11] 25.2 0.0 2.0 21.3 25.2 29.1 4405 1
## y_new[9,12] 26.2 0.0 2.0 22.4 26.2 30.1 4473 1
## y_new[9,13] 27.0 0.0 1.9 23.2 27.0 30.8 4450 1
## y_new[9,14] 27.7 0.0 1.9 23.9 27.8 31.4 4150 1
## y_new[9,15] 28.3 0.0 1.9 24.5 28.3 31.9 4349 1
## y_new[9,16] 28.8 0.0 1.9 25.0 28.9 32.6 4262 1
## y_new[9,17] 29.3 0.0 1.9 25.5 29.3 33.1 3662 1
## y_new[9,18] 29.6 0.0 1.9 25.9 29.6 33.3 4035 1
## y_new[9,19] 29.9 0.0 1.9 26.3 29.9 33.7 3993 1
## y_new[9,20] 30.3 0.0 1.9 26.4 30.3 34.0 3779 1
## y_new[9,21] 30.5 0.0 1.9 26.8 30.5 34.2 4213 1
## y_new[9,22] 30.7 0.0 1.9 26.9 30.7 34.5 4367 1
## y_new[9,23] 30.8 0.0 1.9 27.1 30.8 34.5 3978 1
## y_new[9,24] 30.9 0.0 1.9 27.2 30.9 34.7 4235 1
## y_new[9,25] 31.1 0.0 2.0 27.2 31.1 35.0 3949 1
## y_new[9,26] 31.2 0.0 1.9 27.3 31.2 35.0 3909 1
## y_new[9,27] 31.3 0.0 2.0 27.4 31.4 35.0 4234 1
## y_new[9,28] 31.4 0.0 2.0 27.7 31.4 35.3 4012 1
## y_new[9,29] 31.5 0.0 2.0 27.7 31.5 35.5 4189 1
## y_new[9,30] 31.5 0.0 2.0 27.6 31.5 35.4 3911 1
## y_new[9,31] 31.5 0.0 2.0 27.5 31.6 35.3 4236 1
## y_new[9,32] 31.6 0.0 2.0 27.8 31.6 35.5 4122 1
## y_new[9,33] 31.6 0.0 2.0 27.7 31.6 35.5 4277 1
## y_new[9,34] 31.7 0.0 2.0 27.8 31.7 35.4 4390 1
## y_new[9,35] 31.7 0.0 2.0 27.6 31.7 35.5 4233 1
## y_new[9,36] 31.7 0.0 2.0 27.8 31.6 35.7 4394 1
## y_new[9,37] 31.7 0.0 2.0 27.8 31.8 35.7 4167 1
## y_new[9,38] 31.8 0.0 2.0 27.9 31.8 35.6 4267 1
## y_new[9,39] 31.8 0.0 2.0 27.8 31.7 35.8 4337 1
## y_new[9,40] 31.8 0.0 2.0 27.9 31.8 35.8 4270 1
## y_new[9,41] 31.8 0.0 2.0 27.8 31.8 35.7 4172 1
## y_new[9,42] 31.8 0.0 2.0 27.7 31.8 35.9 3932 1
## y_new[9,43] 31.8 0.0 2.1 27.8 31.8 35.9 3855 1
## y_new[9,44] 31.8 0.0 2.0 27.8 31.8 35.7 4215 1
## y_new[9,45] 31.8 0.0 2.0 27.8 31.8 35.8 4289 1
## y_new[9,46] 31.8 0.0 2.1 27.8 31.8 35.9 4272 1
## y_new[9,47] 31.8 0.0 2.1 27.6 31.8 35.8 4350 1
## y_new[9,48] 31.8 0.0 2.0 27.8 31.8 35.9 4108 1
## y_new[9,49] 31.8 0.0 2.1 27.8 31.8 35.9 3945 1
## y_new[9,50] 31.8 0.0 2.1 27.8 31.8 35.8 4232 1
## y_new[9,51] 31.9 0.0 2.1 27.9 31.9 36.0 4313 1
## y_new[9,52] 31.8 0.0 2.1 27.8 31.8 36.0 4110 1
## y_new[9,53] 31.8 0.0 2.0 27.9 31.8 35.9 4186 1
## y_new[9,54] 31.8 0.0 2.0 27.9 31.8 35.9 4317 1
## y_new[9,55] 31.9 0.0 2.1 27.8 31.9 36.0 4172 1
## y_new[9,56] 31.8 0.0 2.1 27.8 31.8 35.9 4372 1
## y_new[9,57] 31.9 0.0 2.0 27.9 31.9 35.9 4029 1
## y_new[9,58] 31.9 0.0 2.1 27.9 31.8 35.9 4412 1
## y_new[9,59] 31.8 0.0 2.1 27.7 31.8 35.9 4251 1
## y_new[9,60] 31.9 0.0 2.1 27.9 31.9 36.0 4096 1
## y_new[10,1] 0.0 0.0 1.7 -3.2 0.1 3.3 4051 1
## y_new[10,2] 2.8 0.0 1.7 -0.6 2.8 6.2 4051 1
## y_new[10,3] 5.1 0.0 1.9 1.4 5.1 8.7 4202 1
## y_new[10,4] 7.0 0.0 2.0 3.1 7.0 10.9 3940 1
## y_new[10,5] 8.7 0.0 2.0 4.8 8.7 12.7 4101 1
## y_new[10,6] 10.2 0.0 2.1 6.2 10.2 14.3 3803 1
## y_new[10,7] 11.3 0.0 2.1 7.3 11.3 15.3 4009 1
## y_new[10,8] 12.2 0.0 2.0 8.2 12.2 16.1 3965 1
## y_new[10,9] 13.1 0.0 2.0 9.2 13.1 17.1 4368 1
## y_new[10,10] 13.9 0.0 2.0 9.8 13.9 17.7 4292 1
## y_new[10,11] 14.4 0.0 2.0 10.4 14.4 18.2 4375 1
## y_new[10,12] 14.9 0.0 2.0 11.2 14.9 18.7 4202 1
## y_new[10,13] 15.3 0.0 1.9 11.5 15.3 19.0 4457 1
## y_new[10,14] 15.7 0.0 1.9 11.9 15.7 19.4 4320 1
## y_new[10,15] 16.0 0.0 1.9 12.3 16.0 19.8 4136 1
## y_new[10,16] 16.3 0.0 1.9 12.4 16.3 19.9 4355 1
## y_new[10,17] 16.5 0.0 1.9 12.7 16.5 20.2 4208 1
## y_new[10,18] 16.7 0.0 1.9 12.9 16.7 20.4 4200 1
## y_new[10,19] 16.9 0.0 1.9 13.2 16.9 20.6 4282 1
## y_new[10,20] 17.0 0.0 1.9 13.2 17.0 20.7 4201 1
## y_new[10,21] 17.1 0.0 2.0 13.3 17.1 21.0 3677 1
## y_new[10,22] 17.3 0.0 2.0 13.5 17.2 21.1 4212 1
## y_new[10,23] 17.4 0.0 1.9 13.6 17.4 21.2 4082 1
## y_new[10,24] 17.4 0.0 1.9 13.6 17.4 21.3 4333 1
## y_new[10,25] 17.4 0.0 2.0 13.6 17.4 21.3 4187 1
## y_new[10,26] 17.5 0.0 2.0 13.8 17.5 21.5 3818 1
## y_new[10,27] 17.5 0.0 2.0 13.7 17.5 21.5 4216 1
## y_new[10,28] 17.6 0.0 2.0 13.9 17.6 21.5 4107 1
## y_new[10,29] 17.7 0.0 1.9 13.9 17.7 21.5 3911 1
## y_new[10,30] 17.7 0.0 2.0 13.9 17.6 21.6 3926 1
## y_new[10,31] 17.7 0.0 2.0 13.8 17.7 21.7 4163 1
## y_new[10,32] 17.7 0.0 2.0 13.9 17.7 21.6 3686 1
## y_new[10,33] 17.7 0.0 2.0 14.0 17.7 21.7 4562 1
## y_new[10,34] 17.8 0.0 2.0 13.9 17.8 21.7 4062 1
## y_new[10,35] 17.8 0.0 2.0 14.1 17.7 21.7 3816 1
## y_new[10,36] 17.8 0.0 2.0 13.9 17.8 21.9 4196 1
## y_new[10,37] 17.8 0.0 2.0 14.0 17.8 21.8 4299 1
## y_new[10,38] 17.8 0.0 2.0 14.0 17.8 21.7 4173 1
## y_new[10,39] 17.8 0.0 2.0 13.9 17.8 21.9 4192 1
## y_new[10,40] 17.9 0.0 2.0 13.9 17.9 21.9 4042 1
## y_new[10,41] 17.9 0.0 2.0 14.0 17.8 21.8 3977 1
## y_new[10,42] 17.9 0.0 2.0 14.0 17.9 21.9 4251 1
## y_new[10,43] 17.8 0.0 2.0 13.8 17.7 21.9 4094 1
## y_new[10,44] 17.8 0.0 2.0 13.9 17.8 21.9 4634 1
## y_new[10,45] 17.9 0.0 2.1 13.8 17.8 21.9 4176 1
## y_new[10,46] 17.9 0.0 2.0 14.1 17.9 21.9 3954 1
## y_new[10,47] 17.8 0.0 2.1 13.8 17.8 22.0 4444 1
## y_new[10,48] 17.9 0.0 2.0 14.0 17.8 21.8 3905 1
## y_new[10,49] 17.8 0.0 2.0 13.9 17.8 21.9 4026 1
## y_new[10,50] 17.9 0.0 2.0 13.9 17.8 21.9 4384 1
## y_new[10,51] 17.9 0.0 2.0 13.8 17.8 21.8 4278 1
## y_new[10,52] 17.9 0.0 2.0 14.0 17.9 22.0 3890 1
## y_new[10,53] 17.9 0.0 2.0 14.1 17.9 21.7 4020 1
## y_new[10,54] 17.9 0.0 2.0 13.9 17.8 21.8 4303 1
## y_new[10,55] 17.9 0.0 2.0 14.1 17.9 21.9 4140 1
## y_new[10,56] 17.9 0.0 2.0 13.9 17.9 21.8 4333 1
## y_new[10,57] 17.9 0.0 2.0 14.0 17.9 22.0 4044 1
## y_new[10,58] 17.9 0.0 2.1 13.8 17.9 22.0 4256 1
## y_new[10,59] 17.9 0.0 2.0 13.8 17.9 21.9 4448 1
## y_new[10,60] 17.9 0.0 2.0 14.0 17.9 22.0 3887 1
## y_new[11,1] 0.0 0.0 1.7 -3.4 0.0 3.4 3867 1
## y_new[11,2] 2.8 0.0 1.8 -0.6 2.9 6.3 3994 1
## y_new[11,3] 5.3 0.0 1.9 1.5 5.3 9.1 4178 1
## y_new[11,4] 7.3 0.0 2.0 3.4 7.3 11.3 4404 1
## y_new[11,5] 9.1 0.0 2.0 5.2 9.1 13.1 4205 1
## y_new[11,6] 10.6 0.0 2.0 6.7 10.6 14.7 4215 1
## y_new[11,7] 11.9 0.0 2.1 7.9 11.9 15.9 4158 1
## y_new[11,8] 12.9 0.0 2.0 9.0 12.9 16.9 4169 1
## y_new[11,9] 13.9 0.0 2.0 9.8 13.9 17.9 4332 1
## y_new[11,10] 14.6 0.0 2.0 10.8 14.6 18.6 4314 1
## y_new[11,11] 15.3 0.0 1.9 11.5 15.3 19.1 4068 1
## y_new[11,12] 16.0 0.0 2.0 12.0 16.0 19.7 4033 1
## y_new[11,13] 16.5 0.0 2.0 12.7 16.5 20.4 4524 1
## y_new[11,14] 17.0 0.0 1.9 13.1 17.0 20.7 4252 1
## y_new[11,15] 17.2 0.0 1.9 13.6 17.3 21.0 3690 1
## y_new[11,16] 17.6 0.0 1.9 13.6 17.6 21.4 3934 1
## y_new[11,17] 17.9 0.0 1.9 14.2 17.9 21.7 3887 1
## y_new[11,18] 18.1 0.0 1.9 14.3 18.1 21.8 4358 1
## y_new[11,19] 18.3 0.0 1.9 14.6 18.4 22.2 4119 1
## y_new[11,20] 18.5 0.0 1.9 14.8 18.5 22.3 4138 1
## y_new[11,21] 18.7 0.0 1.9 14.9 18.7 22.4 3973 1
## y_new[11,22] 18.8 0.0 1.9 15.0 18.7 22.5 4240 1
## y_new[11,23] 18.9 0.0 2.0 15.1 18.9 22.6 4465 1
## y_new[11,24] 19.0 0.0 1.9 15.3 19.0 22.7 4506 1
## y_new[11,25] 19.1 0.0 1.9 15.5 19.1 23.0 4329 1
## y_new[11,26] 19.1 0.0 2.0 15.3 19.1 22.9 4160 1
## y_new[11,27] 19.2 0.0 2.0 15.4 19.3 23.1 3974 1
## y_new[11,28] 19.3 0.0 2.0 15.4 19.3 23.1 4565 1
## y_new[11,29] 19.3 0.0 2.0 15.5 19.3 23.2 4532 1
## y_new[11,30] 19.4 0.0 2.0 15.5 19.3 23.3 4534 1
## y_new[11,31] 19.4 0.0 2.0 15.4 19.4 23.2 4479 1
## y_new[11,32] 19.4 0.0 2.0 15.6 19.4 23.4 4017 1
## y_new[11,33] 19.5 0.0 2.0 15.6 19.5 23.6 4130 1
## y_new[11,34] 19.5 0.0 2.0 15.5 19.5 23.5 4200 1
## y_new[11,35] 19.5 0.0 2.0 15.6 19.5 23.5 3964 1
## y_new[11,36] 19.5 0.0 2.0 15.6 19.5 23.5 4354 1
## y_new[11,37] 19.5 0.0 2.0 15.6 19.5 23.6 4033 1
## y_new[11,38] 19.5 0.0 2.0 15.6 19.5 23.4 4198 1
## y_new[11,39] 19.6 0.0 2.0 15.5 19.5 23.6 4498 1
## y_new[11,40] 19.6 0.0 2.0 15.7 19.5 23.6 4485 1
## y_new[11,41] 19.6 0.0 2.0 15.5 19.6 23.5 4427 1
## y_new[11,42] 19.6 0.0 2.1 15.5 19.6 23.8 4191 1
## y_new[11,43] 19.6 0.0 2.1 15.6 19.6 23.6 4210 1
## y_new[11,44] 19.6 0.0 2.1 15.5 19.6 23.7 4310 1
## y_new[11,45] 19.7 0.0 2.1 15.6 19.6 23.7 3613 1
## y_new[11,46] 19.6 0.0 2.0 15.7 19.6 23.5 4276 1
## y_new[11,47] 19.6 0.0 2.0 15.6 19.7 23.4 4161 1
## y_new[11,48] 19.6 0.0 2.1 15.5 19.6 23.7 4572 1
## y_new[11,49] 19.7 0.0 2.0 15.8 19.7 23.6 4341 1
## y_new[11,50] 19.6 0.0 2.0 15.7 19.6 23.7 4755 1
## y_new[11,51] 19.7 0.0 2.1 15.7 19.6 23.7 4070 1
## y_new[11,52] 19.7 0.0 2.0 15.7 19.7 23.7 4258 1
## y_new[11,53] 19.7 0.0 2.0 15.7 19.7 23.7 4331 1
## y_new[11,54] 19.7 0.0 2.0 15.7 19.7 23.7 4390 1
## y_new[11,55] 19.7 0.0 2.1 15.5 19.7 23.7 4334 1
## y_new[11,56] 19.7 0.0 2.1 15.7 19.7 23.9 4092 1
## y_new[11,57] 19.7 0.0 2.1 15.7 19.6 23.9 4345 1
## y_new[11,58] 19.7 0.0 2.1 15.8 19.7 23.9 4604 1
## y_new[11,59] 19.6 0.0 2.1 15.6 19.6 23.6 4212 1
## y_new[11,60] 19.7 0.0 2.1 15.6 19.6 23.8 4315 1
## y_new[12,1] 0.0 0.0 1.7 -3.3 0.0 3.3 4240 1
## y_new[12,2] 3.1 0.0 1.8 -0.5 3.1 6.7 3929 1
## y_new[12,3] 5.6 0.0 1.9 1.7 5.5 9.3 4032 1
## y_new[12,4] 7.5 0.0 2.1 3.6 7.5 11.7 3835 1
## y_new[12,5] 9.1 0.0 2.1 4.9 9.1 13.2 4404 1
## y_new[12,6] 10.4 0.0 2.1 6.4 10.4 14.5 4607 1
## y_new[12,7] 11.4 0.0 2.0 7.2 11.4 15.3 3837 1
## y_new[12,8] 12.3 0.0 2.0 8.4 12.3 16.3 4278 1
## y_new[12,9] 13.1 0.0 2.0 9.1 13.1 16.9 4205 1
## y_new[12,10] 13.6 0.0 2.0 9.7 13.6 17.5 4146 1
## y_new[12,11] 14.1 0.0 1.9 10.3 14.1 17.7 3892 1
## y_new[12,12] 14.5 0.0 1.9 10.7 14.4 18.3 4152 1
## y_new[12,13] 14.8 0.0 1.9 11.1 14.8 18.5 4369 1
## y_new[12,14] 15.1 0.0 1.9 11.2 15.1 18.8 4267 1
## y_new[12,15] 15.3 0.0 1.9 11.5 15.3 19.0 4037 1
## y_new[12,16] 15.4 0.0 1.9 11.8 15.4 19.1 4046 1
## y_new[12,17] 15.6 0.0 1.9 11.8 15.6 19.3 3649 1
## y_new[12,18] 15.7 0.0 1.9 12.0 15.8 19.5 3738 1
## y_new[12,19] 15.8 0.0 1.9 12.0 15.8 19.5 4170 1
## y_new[12,20] 15.9 0.0 1.9 12.2 15.9 19.7 4130 1
## y_new[12,21] 16.0 0.0 1.9 12.3 16.0 19.7 3839 1
## y_new[12,22] 16.1 0.0 1.9 12.3 16.1 19.8 4272 1
## y_new[12,23] 16.0 0.0 1.9 12.3 16.0 20.0 4393 1
## y_new[12,24] 16.1 0.0 2.0 12.3 16.1 20.0 4182 1
## y_new[12,25] 16.1 0.0 2.0 12.3 16.1 19.9 3780 1
## y_new[12,26] 16.1 0.0 1.9 12.3 16.1 19.9 4202 1
## y_new[12,27] 16.2 0.0 2.0 12.4 16.2 20.1 4320 1
## y_new[12,28] 16.2 0.0 2.0 12.5 16.2 20.1 4109 1
## y_new[12,29] 16.2 0.0 2.0 12.3 16.2 20.2 4451 1
## y_new[12,30] 16.2 0.0 2.0 12.4 16.2 20.1 4131 1
## y_new[12,31] 16.3 0.0 1.9 12.3 16.2 20.1 4092 1
## y_new[12,32] 16.2 0.0 2.0 12.5 16.2 20.2 4122 1
## y_new[12,33] 16.3 0.0 2.0 12.6 16.3 20.2 4104 1
## y_new[12,34] 16.3 0.0 2.0 12.3 16.3 20.2 4134 1
## y_new[12,35] 16.3 0.0 2.0 12.5 16.3 20.3 4291 1
## y_new[12,36] 16.3 0.0 2.0 12.5 16.3 20.3 4007 1
## y_new[12,37] 16.2 0.0 2.0 12.3 16.3 20.0 4346 1
## y_new[12,38] 16.3 0.0 2.0 12.5 16.3 20.3 4051 1
## y_new[12,39] 16.4 0.0 2.0 12.5 16.4 20.1 4538 1
## y_new[12,40] 16.3 0.0 2.0 12.4 16.3 20.1 4087 1
## y_new[12,41] 16.3 0.0 2.0 12.3 16.3 20.3 4004 1
## y_new[12,42] 16.3 0.0 2.0 12.3 16.3 20.3 4460 1
## y_new[12,43] 16.4 0.0 2.0 12.5 16.4 20.4 4092 1
## y_new[12,44] 16.3 0.0 2.0 12.3 16.3 20.1 3903 1
## y_new[12,45] 16.3 0.0 2.0 12.5 16.4 20.2 4279 1
## y_new[12,46] 16.3 0.0 2.0 12.5 16.3 20.3 3831 1
## y_new[12,47] 16.3 0.0 2.0 12.5 16.4 20.3 4546 1
## y_new[12,48] 16.3 0.0 2.0 12.4 16.3 20.3 4207 1
## y_new[12,49] 16.3 0.0 2.0 12.6 16.3 20.4 4633 1
## y_new[12,50] 16.4 0.0 2.0 12.5 16.3 20.3 4269 1
## y_new[12,51] 16.3 0.0 2.0 12.4 16.3 20.3 4348 1
## y_new[12,52] 16.3 0.0 2.0 12.5 16.3 20.4 4142 1
## y_new[12,53] 16.3 0.0 2.0 12.4 16.3 20.3 4018 1
## y_new[12,54] 16.3 0.0 2.0 12.4 16.3 20.4 4342 1
## y_new[12,55] 16.3 0.0 2.0 12.3 16.3 20.3 4424 1
## y_new[12,56] 16.3 0.0 2.0 12.4 16.3 20.2 4267 1
## y_new[12,57] 16.3 0.0 2.0 12.5 16.3 20.2 4043 1
## y_new[12,58] 16.3 0.0 2.0 12.3 16.3 20.2 4166 1
## y_new[12,59] 16.3 0.0 2.0 12.5 16.3 20.3 3971 1
## y_new[12,60] 16.3 0.0 2.0 12.5 16.3 20.3 4174 1
## y_new[13,1] 0.0 0.0 1.7 -3.3 0.0 3.3 3879 1
## y_new[13,2] 1.0 0.0 1.7 -2.3 1.0 4.5 4170 1
## y_new[13,3] 1.9 0.0 1.7 -1.5 1.9 5.2 3784 1
## y_new[13,4] 2.8 0.0 1.8 -0.7 2.8 6.4 3657 1
## y_new[13,5] 3.5 0.0 1.8 0.0 3.5 7.3 4125 1
## y_new[13,6] 4.3 0.0 1.8 0.7 4.3 7.9 4163 1
## y_new[13,7] 4.9 0.0 1.9 1.3 4.8 8.6 3975 1
## y_new[13,8] 5.4 0.0 1.9 1.8 5.4 9.2 4117 1
## y_new[13,9] 6.0 0.0 1.9 2.2 6.0 9.9 4172 1
## y_new[13,10] 6.4 0.0 2.0 2.4 6.4 10.2 3780 1
## y_new[13,11] 6.9 0.0 1.9 3.1 6.9 10.6 4214 1
## y_new[13,12] 7.2 0.0 1.9 3.4 7.2 11.0 3947 1
## y_new[13,13] 7.6 0.0 2.0 3.9 7.6 11.6 3829 1
## y_new[13,14] 7.9 0.0 1.9 4.1 8.0 11.7 3884 1
## y_new[13,15] 8.2 0.0 2.0 4.5 8.2 12.0 4151 1
## y_new[13,16] 8.5 0.0 1.9 4.6 8.5 12.3 3334 1
## y_new[13,17] 8.7 0.0 1.9 4.9 8.7 12.5 4020 1
## y_new[13,18] 9.0 0.0 1.9 5.4 8.9 12.6 3864 1
## y_new[13,19] 9.2 0.0 1.9 5.5 9.2 12.9 4094 1
## y_new[13,20] 9.4 0.0 2.0 5.5 9.4 13.2 3827 1
## y_new[13,21] 9.5 0.0 1.9 5.7 9.5 13.3 4063 1
## y_new[13,22] 9.7 0.0 1.9 5.9 9.7 13.5 3932 1
## y_new[13,23] 9.8 0.0 1.9 6.0 9.8 13.6 3950 1
## y_new[13,24] 10.0 0.0 1.9 6.2 10.0 13.7 3881 1
## y_new[13,25] 10.1 0.0 1.9 6.4 10.1 13.9 4248 1
## y_new[13,26] 10.2 0.0 2.0 6.3 10.1 14.2 3867 1
## y_new[13,27] 10.3 0.0 1.9 6.4 10.3 14.0 3925 1
## y_new[13,28] 10.4 0.0 1.9 6.7 10.5 14.2 3757 1
## y_new[13,29] 10.5 0.0 2.0 6.6 10.5 14.4 4176 1
## y_new[13,30] 10.6 0.0 1.9 6.8 10.6 14.3 4165 1
## y_new[13,31] 10.6 0.0 1.9 6.9 10.6 14.3 4096 1
## y_new[13,32] 10.7 0.0 2.0 6.9 10.7 14.6 4449 1
## y_new[13,33] 10.8 0.0 2.0 6.9 10.8 14.6 3828 1
## y_new[13,34] 10.9 0.0 2.0 7.1 10.8 14.7 3523 1
## y_new[13,35] 10.9 0.0 2.0 7.1 10.9 14.8 4054 1
## y_new[13,36] 11.0 0.0 2.0 6.9 11.0 14.9 4045 1
## y_new[13,37] 11.0 0.0 2.0 7.1 11.0 14.9 3841 1
## y_new[13,38] 11.0 0.0 2.0 6.9 11.1 15.1 3926 1
## y_new[13,39] 11.1 0.0 2.0 7.1 11.1 14.9 4086 1
## y_new[13,40] 11.1 0.0 2.0 7.2 11.0 15.1 4024 1
## y_new[13,41] 11.2 0.0 2.0 7.2 11.1 15.1 4490 1
## y_new[13,42] 11.2 0.0 2.0 7.4 11.2 15.2 3931 1
## y_new[13,43] 11.2 0.0 2.1 7.1 11.2 15.2 4010 1
## y_new[13,44] 11.2 0.0 2.1 7.1 11.3 15.2 4269 1
## y_new[13,45] 11.3 0.0 2.1 7.3 11.3 15.4 3969 1
## y_new[13,46] 11.3 0.0 2.1 7.4 11.3 15.5 4157 1
## y_new[13,47] 11.3 0.0 2.0 7.3 11.3 15.3 3966 1
## y_new[13,48] 11.3 0.0 2.1 7.2 11.3 15.5 4364 1
## y_new[13,49] 11.3 0.0 2.0 7.3 11.3 15.4 3718 1
## y_new[13,50] 11.3 0.0 2.1 7.3 11.3 15.5 4085 1
## y_new[13,51] 11.4 0.0 2.1 7.3 11.4 15.3 3672 1
## y_new[13,52] 11.4 0.0 2.1 7.3 11.4 15.5 4026 1
## y_new[13,53] 11.4 0.0 2.1 7.5 11.4 15.4 3746 1
## y_new[13,54] 11.4 0.0 2.1 7.3 11.4 15.6 4111 1
## y_new[13,55] 11.4 0.0 2.1 7.3 11.3 15.6 4377 1
## y_new[13,56] 11.4 0.0 2.1 7.2 11.4 15.7 3855 1
## y_new[13,57] 11.4 0.0 2.1 7.3 11.4 15.6 4306 1
## y_new[13,58] 11.4 0.0 2.1 7.4 11.4 15.5 4378 1
## y_new[13,59] 11.5 0.0 2.1 7.4 11.4 15.6 4166 1
## y_new[13,60] 11.5 0.0 2.1 7.3 11.5 15.5 4104 1
## y_new[14,1] 0.0 0.0 1.7 -3.5 0.0 3.3 3995 1
## y_new[14,2] 2.4 0.0 1.7 -0.9 2.4 5.9 4075 1
## y_new[14,3] 4.6 0.0 1.8 1.1 4.6 8.2 4047 1
## y_new[14,4] 6.6 0.0 1.8 3.0 6.6 10.2 4017 1
## y_new[14,5] 8.3 0.0 1.9 4.7 8.4 12.0 4220 1
## y_new[14,6] 9.9 0.0 1.9 6.1 9.9 13.7 4317 1
## y_new[14,7] 11.4 0.0 2.0 7.5 11.3 15.2 4139 1
## y_new[14,8] 12.7 0.0 2.0 8.8 12.6 16.7 3899 1
## y_new[14,9] 13.8 0.0 2.0 10.0 13.8 17.6 3918 1
## y_new[14,10] 14.9 0.0 2.0 11.1 14.9 18.9 3602 1
## y_new[14,11] 15.8 0.0 2.0 11.9 15.8 19.7 4197 1
## y_new[14,12] 16.7 0.0 2.0 12.6 16.7 20.5 4267 1
## y_new[14,13] 17.5 0.0 2.0 13.6 17.5 21.3 4178 1
## y_new[14,14] 18.1 0.0 2.0 14.3 18.1 22.0 3988 1
## y_new[14,15] 18.8 0.0 2.0 15.1 18.8 22.7 3947 1
## y_new[14,16] 19.3 0.0 1.9 15.5 19.3 23.2 3990 1
## y_new[14,17] 19.9 0.0 2.0 16.1 19.8 23.8 4175 1
## y_new[14,18] 20.3 0.0 1.9 16.6 20.3 24.2 3859 1
## y_new[14,19] 20.8 0.0 1.9 17.0 20.8 24.5 4098 1
## y_new[14,20] 21.1 0.0 1.9 17.3 21.1 24.8 4155 1
## y_new[14,21] 21.5 0.0 1.9 17.8 21.5 25.2 4167 1
## y_new[14,22] 21.8 0.0 1.9 18.0 21.8 25.4 4081 1
## y_new[14,23] 22.1 0.0 1.9 18.3 22.0 25.9 4280 1
## y_new[14,24] 22.2 0.0 1.9 18.6 22.2 26.1 4293 1
## y_new[14,25] 22.5 0.0 1.9 18.7 22.5 26.2 4049 1
## y_new[14,26] 22.8 0.0 1.9 19.1 22.8 26.5 4205 1
## y_new[14,27] 22.9 0.0 1.9 19.2 22.9 26.6 4077 1
## y_new[14,28] 23.1 0.0 1.9 19.3 23.1 26.9 3911 1
## y_new[14,29] 23.3 0.0 2.0 19.4 23.3 27.1 4181 1
## y_new[14,30] 23.5 0.0 2.0 19.6 23.5 27.2 4145 1
## y_new[14,31] 23.5 0.0 2.0 19.7 23.5 27.4 4033 1
## y_new[14,32] 23.6 0.0 2.0 19.6 23.6 27.6 3833 1
## y_new[14,33] 23.7 0.0 2.0 19.7 23.8 27.6 4179 1
## y_new[14,34] 23.9 0.0 2.0 20.0 23.9 27.9 4163 1
## y_new[14,35] 23.9 0.0 2.0 19.9 23.9 27.8 4533 1
## y_new[14,36] 24.0 0.0 2.0 20.2 24.0 28.0 4432 1
## y_new[14,37] 24.0 0.0 2.0 20.1 24.1 27.9 4291 1
## y_new[14,38] 24.1 0.0 2.0 20.1 24.1 28.0 4434 1
## y_new[14,39] 24.2 0.0 2.1 20.1 24.2 28.2 4208 1
## y_new[14,40] 24.2 0.0 2.0 20.3 24.2 28.2 4309 1
## y_new[14,41] 24.3 0.0 2.0 20.3 24.4 28.3 3877 1
## y_new[14,42] 24.4 0.0 2.0 20.3 24.4 28.3 4013 1
## y_new[14,43] 24.4 0.0 2.1 20.3 24.4 28.4 4454 1
## y_new[14,44] 24.4 0.0 2.1 20.3 24.4 28.4 4036 1
## y_new[14,45] 24.5 0.0 2.1 20.4 24.5 28.5 4163 1
## y_new[14,46] 24.5 0.0 2.1 20.4 24.5 28.5 4337 1
## y_new[14,47] 24.4 0.0 2.1 20.2 24.5 28.5 4594 1
## y_new[14,48] 24.5 0.0 2.1 20.5 24.5 28.5 4146 1
## y_new[14,49] 24.5 0.0 2.1 20.4 24.6 28.8 4349 1
## y_new[14,50] 24.6 0.0 2.1 20.4 24.6 28.6 4352 1
## y_new[14,51] 24.6 0.0 2.1 20.3 24.6 28.8 4302 1
## y_new[14,52] 24.6 0.0 2.1 20.6 24.6 28.8 3758 1
## y_new[14,53] 24.6 0.0 2.1 20.4 24.6 28.8 4289 1
## y_new[14,54] 24.7 0.0 2.1 20.4 24.7 28.9 4145 1
## y_new[14,55] 24.7 0.0 2.1 20.5 24.7 28.8 4360 1
## y_new[14,56] 24.7 0.0 2.1 20.6 24.7 28.9 4234 1
## y_new[14,57] 24.6 0.0 2.1 20.5 24.6 28.9 4385 1
## y_new[14,58] 24.7 0.0 2.1 20.5 24.6 28.9 4235 1
## y_new[14,59] 24.7 0.0 2.1 20.5 24.7 28.9 4317 1
## y_new[14,60] 24.7 0.0 2.1 20.5 24.7 28.8 4054 1
## y_new[15,1] 0.0 0.0 1.7 -3.4 0.0 3.4 3664 1
## y_new[15,2] 2.0 0.0 1.8 -1.4 2.0 5.4 3885 1
## y_new[15,3] 3.8 0.0 1.8 0.4 3.7 7.4 3825 1
## y_new[15,4] 5.3 0.0 1.8 1.7 5.3 8.9 3709 1
## y_new[15,5] 6.6 0.0 1.9 2.9 6.7 10.4 4416 1
## y_new[15,6] 7.8 0.0 1.9 4.1 7.8 11.6 4711 1
## y_new[15,7] 8.8 0.0 2.0 5.0 8.8 12.8 4016 1
## y_new[15,8] 9.7 0.0 1.9 6.0 9.7 13.7 4345 1
## y_new[15,9] 10.6 0.0 1.9 6.9 10.5 14.3 4166 1
## y_new[15,10] 11.3 0.0 2.0 7.5 11.3 15.2 4490 1
## y_new[15,11] 11.9 0.0 1.9 8.1 11.9 15.7 4168 1
## y_new[15,12] 12.4 0.0 1.9 8.7 12.4 16.3 4456 1
## y_new[15,13] 12.9 0.0 2.0 9.0 12.9 16.8 4398 1
## y_new[15,14] 13.4 0.0 1.9 9.5 13.4 17.2 4347 1
## y_new[15,15] 13.8 0.0 1.9 10.0 13.8 17.5 3982 1
## y_new[15,16] 14.1 0.0 1.9 10.2 14.1 17.8 4246 1
## y_new[15,17] 14.4 0.0 1.9 10.6 14.4 18.0 4076 1
## y_new[15,18] 14.7 0.0 1.9 10.9 14.6 18.5 4032 1
## y_new[15,19] 14.9 0.0 1.9 11.0 14.9 18.6 4200 1
## y_new[15,20] 15.1 0.0 1.9 11.2 15.1 18.7 4270 1
## y_new[15,21] 15.3 0.0 1.9 11.4 15.3 19.1 3729 1
## y_new[15,22] 15.4 0.0 1.9 11.8 15.4 19.2 3863 1
## y_new[15,23] 15.5 0.0 2.0 11.7 15.5 19.5 4265 1
## y_new[15,24] 15.7 0.0 1.9 11.8 15.7 19.5 4196 1
## y_new[15,25] 15.9 0.0 2.0 12.0 15.8 19.9 4152 1
## y_new[15,26] 15.9 0.0 2.0 12.1 15.8 19.8 4430 1
## y_new[15,27] 16.0 0.0 1.9 12.1 16.0 19.7 3999 1
## y_new[15,28] 16.0 0.0 2.0 12.1 16.0 19.9 4200 1
## y_new[15,29] 16.1 0.0 2.0 12.2 16.1 20.0 3739 1
## y_new[15,30] 16.2 0.0 1.9 12.4 16.1 19.9 4242 1
## y_new[15,31] 16.3 0.0 2.0 12.3 16.2 20.1 4367 1
## y_new[15,32] 16.3 0.0 2.0 12.5 16.3 20.1 4483 1
## y_new[15,33] 16.3 0.0 2.0 12.5 16.4 20.2 4040 1
## y_new[15,34] 16.4 0.0 2.0 12.4 16.4 20.3 4035 1
## y_new[15,35] 16.4 0.0 2.0 12.5 16.4 20.3 4615 1
## y_new[15,36] 16.4 0.0 2.0 12.4 16.4 20.4 4495 1
## y_new[15,37] 16.5 0.0 2.0 12.6 16.5 20.5 4087 1
## y_new[15,38] 16.5 0.0 2.0 12.5 16.5 20.5 4320 1
## y_new[15,39] 16.5 0.0 2.1 12.5 16.5 20.4 4492 1
## y_new[15,40] 16.5 0.0 2.0 12.7 16.5 20.4 4374 1
## y_new[15,41] 16.5 0.0 2.0 12.4 16.5 20.5 4435 1
## y_new[15,42] 16.5 0.0 2.1 12.6 16.5 20.6 4045 1
## y_new[15,43] 16.5 0.0 2.0 12.5 16.5 20.6 4446 1
## y_new[15,44] 16.6 0.0 2.0 12.6 16.6 20.5 4230 1
## y_new[15,45] 16.6 0.0 2.1 12.4 16.6 20.6 4262 1
## y_new[15,46] 16.6 0.0 2.0 12.7 16.6 20.8 4466 1
## y_new[15,47] 16.6 0.0 2.0 12.6 16.7 20.6 4594 1
## y_new[15,48] 16.6 0.0 2.0 12.8 16.6 20.6 4544 1
## y_new[15,49] 16.6 0.0 2.1 12.6 16.6 20.6 4701 1
## y_new[15,50] 16.6 0.0 2.0 12.8 16.6 20.6 3985 1
## y_new[15,51] 16.6 0.0 2.1 12.6 16.6 20.5 4238 1
## y_new[15,52] 16.6 0.0 2.1 12.6 16.6 20.7 4305 1
## y_new[15,53] 16.7 0.0 2.1 12.6 16.6 20.7 4320 1
## y_new[15,54] 16.7 0.0 2.0 12.6 16.7 20.6 4756 1
## y_new[15,55] 16.6 0.0 2.1 12.6 16.6 20.7 4422 1
## y_new[15,56] 16.7 0.0 2.1 12.5 16.7 20.8 3658 1
## y_new[15,57] 16.7 0.0 2.1 12.6 16.7 20.8 4992 1
## y_new[15,58] 16.7 0.0 2.1 12.6 16.7 20.8 4288 1
## y_new[15,59] 16.7 0.0 2.1 12.6 16.6 20.8 4217 1
## y_new[15,60] 16.7 0.0 2.1 12.7 16.6 20.7 4485 1
## y_new[16,1] 0.0 0.0 1.7 -3.3 0.0 3.4 4164 1
## y_new[16,2] 6.0 0.0 1.8 2.3 6.0 9.7 4159 1
## y_new[16,3] 10.8 0.0 1.9 6.9 10.7 14.6 3846 1
## y_new[16,4] 14.7 0.0 2.0 10.8 14.7 18.7 4324 1
## y_new[16,5] 18.0 0.0 2.1 14.0 18.0 22.0 4500 1
## y_new[16,6] 20.5 0.0 2.1 16.4 20.5 24.6 4155 1
## y_new[16,7] 22.6 0.0 2.0 18.7 22.6 26.6 4150 1
## y_new[16,8] 24.3 0.0 2.0 20.3 24.3 28.1 4086 1
## y_new[16,9] 25.7 0.0 2.0 21.8 25.7 29.5 3644 1
## y_new[16,10] 26.8 0.0 1.9 23.0 26.9 30.7 4105 1
## y_new[16,11] 27.8 0.0 1.9 23.9 27.8 31.7 4436 1
## y_new[16,12] 28.5 0.0 1.9 24.9 28.5 32.3 4315 1
## y_new[16,13] 29.2 0.0 1.9 25.4 29.2 32.9 4415 1
## y_new[16,14] 29.6 0.0 1.9 25.8 29.6 33.3 4371 1
## y_new[16,15] 30.0 0.0 1.9 26.3 30.1 33.8 4266 1
## y_new[16,16] 30.4 0.0 1.9 26.6 30.4 34.1 4156 1
## y_new[16,17] 30.7 0.0 1.9 26.9 30.7 34.3 4137 1
## y_new[16,18] 30.8 0.0 1.9 27.0 30.8 34.6 3866 1
## y_new[16,19] 31.0 0.0 1.9 27.3 31.0 34.8 4369 1
## y_new[16,20] 31.2 0.0 1.9 27.4 31.2 34.9 4303 1
## y_new[16,21] 31.3 0.0 1.9 27.5 31.3 35.0 4213 1
## y_new[16,22] 31.4 0.0 2.0 27.6 31.4 35.4 4743 1
## y_new[16,23] 31.5 0.0 2.0 27.7 31.5 35.5 4280 1
## y_new[16,24] 31.6 0.0 2.0 27.7 31.6 35.4 4503 1
## y_new[16,25] 31.6 0.0 2.0 27.6 31.6 35.6 4164 1
## y_new[16,26] 31.6 0.0 1.9 27.8 31.6 35.4 3976 1
## y_new[16,27] 31.7 0.0 2.0 27.8 31.7 35.8 4432 1
## y_new[16,28] 31.7 0.0 1.9 28.0 31.7 35.5 3776 1
## y_new[16,29] 31.8 0.0 2.0 27.7 31.8 35.6 4149 1
## y_new[16,30] 31.8 0.0 2.0 27.8 31.7 35.8 4589 1
## y_new[16,31] 31.8 0.0 1.9 28.0 31.8 35.7 4206 1
## y_new[16,32] 31.8 0.0 2.0 27.7 31.8 35.6 4080 1
## y_new[16,33] 31.8 0.0 2.0 27.8 31.8 35.8 4133 1
## y_new[16,34] 31.8 0.0 2.0 28.0 31.8 35.7 4195 1
## y_new[16,35] 31.9 0.0 2.0 28.1 31.9 35.8 4063 1
## y_new[16,36] 31.8 0.0 2.0 27.9 31.8 35.9 4752 1
## y_new[16,37] 31.9 0.0 2.0 28.0 31.8 35.9 4387 1
## y_new[16,38] 31.8 0.0 2.0 27.9 31.9 35.7 4398 1
## y_new[16,39] 31.8 0.0 2.0 28.1 31.8 35.9 3930 1
## y_new[16,40] 31.9 0.0 2.0 27.9 31.9 35.7 4196 1
## y_new[16,41] 31.8 0.0 2.0 27.9 31.8 35.7 4124 1
## y_new[16,42] 31.8 0.0 2.0 27.9 31.8 35.9 3857 1
## y_new[16,43] 31.9 0.0 2.0 28.0 31.9 36.0 4298 1
## y_new[16,44] 31.9 0.0 2.0 28.0 31.9 35.8 4394 1
## y_new[16,45] 31.9 0.0 2.0 28.0 31.8 35.7 4489 1
## y_new[16,46] 31.8 0.0 2.0 27.8 31.9 35.6 4303 1
## y_new[16,47] 31.9 0.0 2.0 27.9 31.8 35.8 4137 1
## y_new[16,48] 31.9 0.0 2.0 28.0 31.9 35.8 4256 1
## y_new[16,49] 31.9 0.0 2.0 28.1 31.9 35.8 4148 1
## y_new[16,50] 31.9 0.0 2.0 27.9 31.9 35.8 3736 1
## y_new[16,51] 31.9 0.0 2.0 28.1 31.9 36.0 4144 1
## y_new[16,52] 31.9 0.0 2.0 27.9 31.9 35.8 4244 1
## y_new[16,53] 31.8 0.0 2.0 27.8 31.8 35.9 4591 1
## y_new[16,54] 31.9 0.0 2.0 28.0 31.8 35.9 4085 1
## y_new[16,55] 31.9 0.0 2.0 28.0 31.9 35.8 4374 1
## y_new[16,56] 31.9 0.0 2.0 28.1 31.9 35.6 4451 1
## y_new[16,57] 31.9 0.0 2.0 28.0 31.8 35.7 4267 1
## y_new[16,58] 31.8 0.0 2.0 27.9 31.9 35.8 4317 1
## y_new[16,59] 31.9 0.0 2.0 28.0 31.9 35.9 4338 1
## y_new[16,60] 31.8 0.0 2.0 27.9 31.8 35.8 4435 1
## lp__ -85.0 0.2 5.3 -96.9 -84.6 -76.0 1100 1
##
## Samples were drawn using NUTS(diag_e) at Tue Dec 26 23:07:23 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).MCMCで得られたデータを利用して予測分布を可視化する。
ms <- rstan::extract(fit)
d_est <- data.frame()
for (n in 1:nrow(d)) {
qua <- apply(ms$y_new[,n,], 2, quantile, prob = c(0.025, 0.5, 0.975))
d_est <- rbind(d_est, data.frame(PersonID = n, Time = Time_new, t(qua), check.names = FALSE))
}
d2 <- d %>%
tidyr::pivot_longer(cols = -PersonID, values_to = 'Y') %>%
mutate(Time = readr::parse_number(name)) %>%
select(-name)
ggplot(data = d_est, aes(x = Time, y = `50%`)) +
theme_bw(base_size = 15) +
facet_wrap(~PersonID) +
geom_ribbon(aes(ymin = `2.5%`, ymax = `97.5%`), fill = 'black', alpha = 1/5) +
geom_line(linewidth = 0.5) +
geom_point(data = d2, aes(x = Time, y = Y), size = 3) +
labs(x = 'Time (hour)', y = 'Y') +
scale_x_continuous(breaks = Time, limit = c(0,24)) +
scale_y_continuous(breaks = seq(0,40,10), limit = c(-3,37))
ガンマ分布を利用したモデル
書籍と同じようなモデルとして、ガンマ分布を利用する方法もある。ガンマ分布は正の値しかとらないので、今回のケースでは都合よい。Stanで使用する際はパラメタを\(\alpha = \frac{\mu^2}{\sigma},\beta=\frac{\mu}{\sigma}\)と指定するので注意。
\(\alpha,\beta\)と\(\mu,\sigma\)の関係は下記の通り。
ガンマ分布を使った場合のStanのモデルは下記のように表現できる。
data {
int N;
int T;
real Time[T];
real Y[N,T];
int T_new;
real Time_new[T_new];
}
parameters {
real mu_a;
real mu_b;
real<lower=0> a[N];
real<lower=0> b[N];
real<lower=0> s_a;
real<lower=0> s_b;
real<lower=0> s_Y;
}
model {
for (n in 1:N) {
a[n] ~ gamma(mu_a^2/s_a, mu_a/s_a);
b[n] ~ gamma(mu_b^2/s_b, mu_b/s_b);
}
for (n in 1:N)
for (t in 1:T)
Y[n,t] ~ normal(a[n]*(1 - exp(-b[n]*Time[t])), s_Y);
}
generated quantities {
real y_new[N,T_new];
for (n in 1:N)
for (t in 1:T_new)
y_new[n,t] = normal_rng(a[n]*(1 - exp(-b[n]*Time_new[t])), s_Y);
}
ここでは、stan_model()関数で最初にコンパイルしておいてから、
sampling()関数でサンプリングする。
パラメタの推定結果はこちら。\(\sigma_{Y}\)以外は対数スケールとなっている。少し混乱するが、a[1],b[1]は通常スケールでexpで変換する前のa0,b0が対数スケールということ(対数変換したものが正規分布に従うと考えている)。
## Inference for Stan model: anon_model.
## 4 chains, each with iter=2000; warmup=1000; thin=1;
## post-warmup draws per chain=1000, total post-warmup draws=4000.
##
## mean se_mean sd 2.5% 50% 97.5% n_eff Rhat
## mu_a 19.8 0.0 2.4 15.7 19.5 25.2 2831 1
## mu_b 0.3 0.0 0.0 0.3 0.3 0.5 2621 1
## a[1] 13.0 0.0 1.3 10.7 12.9 15.7 5059 1
## a[2] 8.2 0.0 1.3 6.0 8.1 10.9 3736 1
## a[3] 23.9 0.0 1.2 21.6 23.8 26.2 5757 1
## a[4] 25.9 0.0 1.2 23.7 25.9 28.2 5563 1
## a[5] 14.4 0.0 1.7 11.3 14.3 18.3 3341 1
## a[6] 15.8 0.0 1.7 13.0 15.6 19.5 3519 1
## a[7] 14.9 0.0 1.4 12.3 14.8 17.9 4351 1
## a[8] 13.4 0.0 1.2 11.2 13.3 15.8 4591 1
## a[9] 31.8 0.0 1.1 29.7 31.8 34.1 4271 1
## a[10] 17.9 0.0 1.1 15.8 17.8 19.9 5847 1
## a[11] 19.6 0.0 1.1 17.5 19.6 22.0 5398 1
## a[12] 16.3 0.0 1.0 14.5 16.3 18.3 4894 1
## a[13] 11.6 0.0 1.4 9.1 11.5 14.7 3719 1
## a[14] 24.9 0.0 1.3 22.3 24.8 27.6 5407 1
## a[15] 16.7 0.0 1.1 14.5 16.6 19.0 5550 1
## a[16] 31.9 0.0 1.0 29.9 31.9 33.9 4874 1
## b[1] 0.3 0.0 0.1 0.2 0.3 0.4 5126 1
## b[2] 0.3 0.0 0.1 0.1 0.3 0.5 4559 1
## b[3] 0.3 0.0 0.0 0.2 0.3 0.4 5370 1
## b[4] 0.3 0.0 0.0 0.2 0.3 0.4 4901 1
## b[5] 0.2 0.0 0.1 0.1 0.2 0.3 3548 1
## b[6] 0.2 0.0 0.1 0.1 0.2 0.4 3885 1
## b[7] 0.2 0.0 0.1 0.1 0.2 0.4 5023 1
## b[8] 0.4 0.0 0.1 0.2 0.4 0.6 4128 1
## b[9] 0.4 0.0 0.1 0.3 0.4 0.5 4639 1
## b[10] 0.4 0.0 0.1 0.3 0.4 0.6 4383 1
## b[11] 0.4 0.0 0.1 0.3 0.4 0.6 5570 1
## b[12] 0.5 0.0 0.1 0.3 0.5 0.8 3984 1
## b[13] 0.2 0.0 0.1 0.1 0.2 0.4 3792 1
## b[14] 0.3 0.0 0.0 0.2 0.2 0.3 4833 1
## b[15] 0.3 0.0 0.1 0.2 0.3 0.5 4774 1
## b[16] 0.5 0.0 0.1 0.4 0.5 0.6 4418 1
## s_a 78.7 1.2 54.6 28.2 64.8 210.1 1926 1
## s_b 0.0 0.0 0.0 0.0 0.0 0.1 1620 1
## s_Y 1.7 0.0 0.2 1.4 1.7 2.0 3676 1
## y_new[1,1] 0.0 0.0 1.7 -3.3 0.0 3.4 3991 1
## y_new[1,2] 1.3 0.0 1.7 -2.1 1.3 4.8 3801 1
## y_new[1,3] 2.5 0.0 1.8 -0.9 2.5 5.9 4143 1
## y_new[1,4] 3.5 0.0 1.9 0.0 3.5 7.2 4321 1
## y_new[1,5] 4.5 0.0 1.9 0.9 4.5 8.3 4106 1
## y_new[1,6] 5.3 0.0 1.9 1.5 5.3 9.2 3973 1
## y_new[1,7] 6.1 0.0 1.9 2.3 6.1 9.8 4066 1
## y_new[1,8] 6.7 0.0 2.0 2.8 6.7 10.5 4177 1
## y_new[1,9] 7.3 0.0 2.0 3.4 7.3 11.3 3877 1
## y_new[1,10] 7.9 0.0 2.0 4.0 7.9 11.7 4289 1
## y_new[1,11] 8.3 0.0 1.9 4.5 8.3 12.2 4119 1
## y_new[1,12] 8.8 0.0 2.0 4.9 8.8 12.6 4132 1
## y_new[1,13] 9.2 0.0 1.9 5.3 9.2 13.2 4230 1
## y_new[1,14] 9.5 0.0 1.9 5.8 9.5 13.3 3947 1
## y_new[1,15] 9.9 0.0 1.9 6.1 9.8 13.6 3902 1
## y_new[1,16] 10.1 0.0 1.9 6.3 10.1 13.9 4202 1
## y_new[1,17] 10.4 0.0 1.9 6.6 10.4 14.3 4114 1
## y_new[1,18] 10.6 0.0 1.9 6.9 10.6 14.3 4009 1
## y_new[1,19] 10.8 0.0 1.9 7.1 10.9 14.6 3973 1
## y_new[1,20] 11.0 0.0 1.9 7.1 11.0 14.8 4147 1
## y_new[1,21] 11.2 0.0 1.9 7.3 11.2 15.0 3974 1
## y_new[1,22] 11.3 0.0 1.9 7.6 11.3 15.2 4002 1
## y_new[1,23] 11.5 0.0 1.9 7.7 11.5 15.3 4068 1
## y_new[1,24] 11.6 0.0 1.9 8.0 11.6 15.5 4227 1
## y_new[1,25] 11.7 0.0 2.0 7.8 11.8 15.5 4037 1
## y_new[1,26] 11.8 0.0 1.9 8.1 11.9 15.6 4267 1
## y_new[1,27] 12.0 0.0 1.9 8.2 11.9 15.7 4180 1
## y_new[1,28] 12.1 0.0 2.0 8.3 12.1 15.9 4317 1
## y_new[1,29] 12.1 0.0 2.0 8.2 12.1 16.0 4313 1
## y_new[1,30] 12.2 0.0 2.0 8.5 12.2 16.0 3917 1
## y_new[1,31] 12.3 0.0 2.0 8.3 12.3 16.1 4278 1
## y_new[1,32] 12.3 0.0 2.0 8.3 12.3 16.1 4389 1
## y_new[1,33] 12.4 0.0 2.0 8.6 12.4 16.3 4328 1
## y_new[1,34] 12.5 0.0 2.0 8.6 12.4 16.4 4259 1
## y_new[1,35] 12.5 0.0 2.0 8.6 12.6 16.5 4014 1
## y_new[1,36] 12.5 0.0 2.0 8.7 12.4 16.3 4504 1
## y_new[1,37] 12.6 0.0 2.0 8.7 12.6 16.5 4123 1
## y_new[1,38] 12.6 0.0 2.0 8.7 12.6 16.4 4204 1
## y_new[1,39] 12.6 0.0 2.0 8.5 12.6 16.6 4343 1
## y_new[1,40] 12.7 0.0 2.0 8.6 12.7 16.7 4473 1
## y_new[1,41] 12.6 0.0 2.0 8.6 12.6 16.7 4518 1
## y_new[1,42] 12.7 0.0 2.0 8.8 12.7 16.7 4096 1
## y_new[1,43] 12.7 0.0 2.0 8.8 12.7 16.6 3775 1
## y_new[1,44] 12.8 0.0 2.1 8.7 12.7 16.8 4559 1
## y_new[1,45] 12.8 0.0 2.0 8.7 12.8 16.7 3990 1
## y_new[1,46] 12.7 0.0 2.0 8.8 12.8 16.7 4381 1
## y_new[1,47] 12.8 0.0 2.1 8.7 12.8 16.8 3588 1
## y_new[1,48] 12.8 0.0 2.1 8.8 12.8 16.9 4232 1
## y_new[1,49] 12.8 0.0 2.0 8.7 12.8 16.8 4392 1
## y_new[1,50] 12.8 0.0 2.0 8.8 12.9 16.8 4548 1
## y_new[1,51] 12.8 0.0 2.1 8.8 12.8 16.9 4473 1
## y_new[1,52] 12.9 0.0 2.1 8.8 12.9 17.0 4318 1
## y_new[1,53] 12.8 0.0 2.1 8.7 12.8 17.0 4491 1
## y_new[1,54] 12.9 0.0 2.1 8.7 12.9 17.0 4335 1
## y_new[1,55] 12.9 0.0 2.1 8.8 12.8 17.0 4217 1
## y_new[1,56] 12.9 0.0 2.1 8.8 12.9 17.1 4322 1
## y_new[1,57] 12.9 0.0 2.1 8.8 12.9 16.9 4265 1
## y_new[1,58] 12.9 0.0 2.1 8.9 12.9 17.1 4544 1
## y_new[1,59] 12.9 0.0 2.1 8.8 12.9 16.9 4186 1
## y_new[1,60] 12.9 0.0 2.1 8.8 12.9 17.0 4121 1
## y_new[2,1] 0.0 0.0 1.7 -3.4 0.0 3.4 3969 1
## y_new[2,2] 0.9 0.0 1.7 -2.6 0.9 4.4 4014 1
## y_new[2,3] 1.6 0.0 1.8 -2.0 1.6 5.0 3962 1
## y_new[2,4] 2.3 0.0 1.8 -1.3 2.2 5.9 4275 1
## y_new[2,5] 2.9 0.0 1.9 -0.7 2.9 6.6 3578 1
## y_new[2,6] 3.4 0.0 1.9 -0.2 3.4 7.1 4026 1
## y_new[2,7] 3.9 0.0 1.9 0.2 3.9 7.6 4019 1
## y_new[2,8] 4.3 0.0 1.9 0.5 4.3 7.9 4150 1
## y_new[2,9] 4.7 0.0 1.9 0.9 4.7 8.5 4079 1
## y_new[2,10] 5.0 0.0 1.9 1.3 5.0 8.6 3852 1
## y_new[2,11] 5.3 0.0 2.0 1.5 5.3 9.2 4255 1
## y_new[2,12] 5.6 0.0 1.9 1.7 5.6 9.4 4067 1
## y_new[2,13] 5.8 0.0 1.9 2.0 5.8 9.5 4139 1
## y_new[2,14] 6.0 0.0 1.9 2.3 6.0 9.7 4013 1
## y_new[2,15] 6.2 0.0 1.9 2.3 6.2 9.9 4040 1
## y_new[2,16] 6.4 0.0 1.9 2.5 6.4 10.2 3998 1
## y_new[2,17] 6.5 0.0 1.9 2.9 6.5 10.3 3877 1
## y_new[2,18] 6.7 0.0 1.9 3.0 6.6 10.4 4479 1
## y_new[2,19] 6.8 0.0 1.9 2.9 6.8 10.6 4042 1
## y_new[2,20] 6.8 0.0 1.9 3.2 6.9 10.6 4210 1
## y_new[2,21] 7.0 0.0 1.9 3.2 7.0 10.7 3999 1
## y_new[2,22] 7.1 0.0 1.9 3.3 7.1 10.9 4166 1
## y_new[2,23] 7.2 0.0 1.9 3.6 7.1 11.0 4149 1
## y_new[2,24] 7.3 0.0 1.9 3.6 7.3 10.9 4089 1
## y_new[2,25] 7.4 0.0 1.9 3.6 7.4 11.0 4252 1
## y_new[2,26] 7.4 0.0 1.9 3.7 7.4 11.3 4094 1
## y_new[2,27] 7.5 0.0 1.9 3.7 7.5 11.3 4368 1
## y_new[2,28] 7.5 0.0 1.9 3.8 7.5 11.4 3868 1
## y_new[2,29] 7.5 0.0 1.9 3.7 7.5 11.4 4020 1
## y_new[2,30] 7.6 0.0 2.0 3.8 7.6 11.4 4175 1
## y_new[2,31] 7.7 0.0 1.9 3.9 7.6 11.4 3955 1
## y_new[2,32] 7.7 0.0 1.9 3.8 7.6 11.5 4418 1
## y_new[2,33] 7.7 0.0 2.0 3.9 7.7 11.6 4238 1
## y_new[2,34] 7.8 0.0 1.9 4.0 7.7 11.6 3946 1
## y_new[2,35] 7.8 0.0 2.0 3.9 7.8 11.6 4250 1
## y_new[2,36] 7.8 0.0 2.0 4.1 7.8 11.6 4035 1
## y_new[2,37] 7.8 0.0 2.0 3.9 7.8 11.8 4307 1
## y_new[2,38] 7.9 0.0 2.0 4.1 7.8 11.8 4035 1
## y_new[2,39] 7.9 0.0 2.0 3.9 7.9 11.7 4244 1
## y_new[2,40] 7.9 0.0 2.0 4.0 7.9 11.7 4369 1
## y_new[2,41] 7.9 0.0 2.0 4.1 7.8 11.8 4191 1
## y_new[2,42] 7.9 0.0 2.0 4.0 7.9 12.0 4293 1
## y_new[2,43] 7.9 0.0 2.0 4.0 7.9 11.7 4143 1
## y_new[2,44] 7.9 0.0 2.0 4.0 7.9 11.9 4198 1
## y_new[2,45] 8.0 0.0 2.0 4.0 8.0 11.9 4066 1
## y_new[2,46] 8.0 0.0 2.0 4.2 8.0 12.0 4196 1
## y_new[2,47] 8.0 0.0 2.0 4.0 8.0 12.1 4310 1
## y_new[2,48] 8.0 0.0 2.0 4.1 8.0 12.1 4204 1
## y_new[2,49] 8.0 0.0 2.0 4.1 8.0 12.0 4429 1
## y_new[2,50] 8.0 0.0 2.0 4.0 8.0 12.0 4090 1
## y_new[2,51] 8.0 0.0 2.1 3.9 8.0 12.0 4191 1
## y_new[2,52] 8.0 0.0 2.0 4.1 8.0 12.1 4158 1
## y_new[2,53] 8.0 0.0 2.0 4.1 8.0 12.1 3917 1
## y_new[2,54] 8.0 0.0 2.0 4.1 8.0 12.0 4212 1
## y_new[2,55] 8.1 0.0 2.0 4.1 8.1 12.0 4304 1
## y_new[2,56] 8.1 0.0 2.0 4.1 8.0 12.0 4098 1
## y_new[2,57] 8.1 0.0 2.1 4.1 8.0 12.2 4094 1
## y_new[2,58] 8.1 0.0 2.1 4.2 8.1 12.3 4275 1
## y_new[2,59] 8.1 0.0 2.1 4.0 8.1 12.2 4255 1
## y_new[2,60] 8.1 0.0 2.1 4.1 8.1 12.2 3776 1
## y_new[3,1] 0.0 0.0 1.7 -3.5 0.0 3.3 4037 1
## y_new[3,2] 2.8 0.0 1.8 -0.8 2.8 6.2 3708 1
## y_new[3,3] 5.2 0.0 1.8 1.6 5.3 8.8 3801 1
## y_new[3,4] 7.4 0.0 1.9 3.8 7.4 11.1 4178 1
## y_new[3,5] 9.3 0.0 1.9 5.7 9.3 13.2 3927 1
## y_new[3,6] 11.0 0.0 2.0 7.1 11.0 14.8 4264 1
## y_new[3,7] 12.4 0.0 2.0 8.6 12.4 16.3 4222 1
## y_new[3,8] 13.8 0.0 2.0 9.8 13.7 17.8 4569 1
## y_new[3,9] 14.8 0.0 2.0 10.8 14.8 18.8 3493 1
## y_new[3,10] 16.0 0.0 2.0 12.0 16.0 19.9 4319 1
## y_new[3,11] 16.8 0.0 2.0 12.9 16.8 20.9 4145 1
## y_new[3,12] 17.5 0.0 1.9 13.8 17.6 21.3 4444 1
## y_new[3,13] 18.3 0.0 2.0 14.4 18.3 22.2 4012 1
## y_new[3,14] 18.9 0.0 2.0 15.0 18.9 22.8 3891 1
## y_new[3,15] 19.5 0.0 1.9 15.9 19.5 23.2 4039 1
## y_new[3,16] 19.9 0.0 1.9 16.0 19.9 23.7 3954 1
## y_new[3,17] 20.4 0.0 1.9 16.7 20.4 24.0 3699 1
## y_new[3,18] 20.8 0.0 1.9 16.9 20.8 24.5 4272 1
## y_new[3,19] 21.1 0.0 1.9 17.4 21.1 24.9 4186 1
## y_new[3,20] 21.5 0.0 1.9 17.7 21.5 25.0 4261 1
## y_new[3,21] 21.7 0.0 2.0 17.8 21.7 25.6 4084 1
## y_new[3,22] 22.0 0.0 1.9 18.2 22.0 25.6 3990 1
## y_new[3,23] 22.2 0.0 1.9 18.5 22.2 26.0 4337 1
## y_new[3,24] 22.3 0.0 1.9 18.6 22.3 26.1 4175 1
## y_new[3,25] 22.5 0.0 1.9 18.7 22.5 26.3 3777 1
## y_new[3,26] 22.7 0.0 1.9 18.9 22.7 26.5 3831 1
## y_new[3,27] 22.8 0.0 2.0 18.9 22.8 26.6 4254 1
## y_new[3,28] 22.9 0.0 2.0 19.1 22.8 26.9 4279 1
## y_new[3,29] 23.0 0.0 2.0 19.3 23.1 26.9 4477 1
## y_new[3,30] 23.1 0.0 2.0 19.1 23.1 27.0 4287 1
## y_new[3,31] 23.2 0.0 2.0 19.3 23.2 27.1 4336 1
## y_new[3,32] 23.3 0.0 2.0 19.3 23.3 27.3 4496 1
## y_new[3,33] 23.3 0.0 2.0 19.4 23.4 27.2 4192 1
## y_new[3,34] 23.4 0.0 1.9 19.6 23.4 27.3 4525 1
## y_new[3,35] 23.5 0.0 2.0 19.5 23.5 27.4 4173 1
## y_new[3,36] 23.5 0.0 2.0 19.6 23.5 27.6 4542 1
## y_new[3,37] 23.5 0.0 2.0 19.6 23.6 27.5 4221 1
## y_new[3,38] 23.6 0.0 2.0 19.6 23.6 27.5 4312 1
## y_new[3,39] 23.6 0.0 2.0 19.6 23.6 27.5 4318 1
## y_new[3,40] 23.6 0.0 2.1 19.4 23.6 27.7 4521 1
## y_new[3,41] 23.7 0.0 2.0 19.7 23.7 27.6 4442 1
## y_new[3,42] 23.7 0.0 2.1 19.7 23.7 27.9 4236 1
## y_new[3,43] 23.7 0.0 2.0 19.7 23.7 27.6 4420 1
## y_new[3,44] 23.7 0.0 2.1 19.6 23.7 27.7 4222 1
## y_new[3,45] 23.8 0.0 2.1 19.7 23.8 27.8 4608 1
## y_new[3,46] 23.8 0.0 2.1 19.7 23.8 27.9 4392 1
## y_new[3,47] 23.8 0.0 2.1 19.8 23.8 27.9 4443 1
## y_new[3,48] 23.8 0.0 2.1 19.6 23.8 28.0 4641 1
## y_new[3,49] 23.8 0.0 2.1 19.7 23.8 27.9 4521 1
## y_new[3,50] 23.8 0.0 2.1 19.8 23.8 27.8 4179 1
## y_new[3,51] 23.8 0.0 2.1 19.7 23.8 28.0 4379 1
## y_new[3,52] 23.8 0.0 2.0 19.9 23.8 27.8 4345 1
## y_new[3,53] 23.8 0.0 2.1 19.6 23.8 27.8 3944 1
## y_new[3,54] 23.8 0.0 2.1 19.7 23.8 28.0 4314 1
## y_new[3,55] 23.8 0.0 2.1 19.8 23.8 27.8 4311 1
## y_new[3,56] 23.8 0.0 2.0 19.7 23.9 27.8 4224 1
## y_new[3,57] 23.8 0.0 2.1 19.7 23.8 28.0 4432 1
## y_new[3,58] 23.8 0.0 2.1 19.7 23.8 28.0 4342 1
## y_new[3,59] 23.9 0.0 2.1 19.7 23.9 28.0 4555 1
## y_new[3,60] 23.8 0.0 2.1 19.9 23.8 28.0 4479 1
## y_new[4,1] 0.0 0.0 1.7 -3.4 0.0 3.4 4056 1
## y_new[4,2] 3.2 0.0 1.8 -0.2 3.2 6.7 4072 1
## y_new[4,3] 6.0 0.0 1.8 2.5 6.0 9.7 4190 1
## y_new[4,4] 8.5 0.0 1.9 4.8 8.5 12.0 4298 1
## y_new[4,5] 10.6 0.0 2.0 6.9 10.6 14.7 4228 1
## y_new[4,6] 12.5 0.0 2.0 8.6 12.5 16.3 4242 1
## y_new[4,7] 14.2 0.0 2.0 10.3 14.2 18.3 3925 1
## y_new[4,8] 15.7 0.0 2.0 11.6 15.7 19.6 4224 1
## y_new[4,9] 16.8 0.0 2.0 12.9 16.9 21.0 4323 1
## y_new[4,10] 18.0 0.0 2.0 14.1 18.0 21.9 4043 1
## y_new[4,11] 19.0 0.0 2.0 15.0 19.0 22.9 4145 1
## y_new[4,12] 19.8 0.0 2.0 15.9 19.8 23.6 4297 1
## y_new[4,13] 20.5 0.0 1.9 16.6 20.5 24.2 4171 1
## y_new[4,14] 21.2 0.0 1.9 17.3 21.2 24.9 4220 1
## y_new[4,15] 21.7 0.0 1.9 18.1 21.7 25.5 4167 1
## y_new[4,16] 22.3 0.0 1.9 18.5 22.3 26.1 3958 1
## y_new[4,17] 22.6 0.0 1.9 18.8 22.6 26.5 3835 1
## y_new[4,18] 23.1 0.0 1.9 19.3 23.1 26.8 4056 1
## y_new[4,19] 23.4 0.0 1.9 19.6 23.5 27.2 4152 1
## y_new[4,20] 23.7 0.0 1.9 20.1 23.7 27.4 4300 1
## y_new[4,21] 23.9 0.0 1.9 20.2 24.0 27.6 4126 1
## y_new[4,22] 24.2 0.0 1.9 20.6 24.2 27.9 4088 1
## y_new[4,23] 24.4 0.0 1.9 20.7 24.4 28.1 4445 1
## y_new[4,24] 24.5 0.0 1.9 20.8 24.5 28.3 4439 1
## y_new[4,25] 24.7 0.0 1.9 20.9 24.7 28.4 3999 1
## y_new[4,26] 24.9 0.0 2.0 21.2 24.9 28.8 4163 1
## y_new[4,27] 25.0 0.0 2.0 21.1 25.0 28.7 4287 1
## y_new[4,28] 25.1 0.0 2.0 21.2 25.2 29.0 4253 1
## y_new[4,29] 25.2 0.0 2.0 21.3 25.2 29.1 4048 1
## y_new[4,30] 25.3 0.0 2.0 21.4 25.3 29.1 4141 1
## y_new[4,31] 25.4 0.0 2.0 21.6 25.3 29.3 4445 1
## y_new[4,32] 25.4 0.0 2.0 21.5 25.4 29.2 4203 1
## y_new[4,33] 25.5 0.0 2.0 21.6 25.5 29.4 4501 1
## y_new[4,34] 25.5 0.0 2.0 21.6 25.5 29.4 4572 1
## y_new[4,35] 25.6 0.0 2.0 21.7 25.6 29.5 4335 1
## y_new[4,36] 25.6 0.0 2.0 21.7 25.6 29.5 4031 1
## y_new[4,37] 25.6 0.0 2.0 21.7 25.6 29.4 4392 1
## y_new[4,38] 25.7 0.0 2.0 21.7 25.7 29.8 4251 1
## y_new[4,39] 25.7 0.0 2.0 21.7 25.7 29.7 4209 1
## y_new[4,40] 25.7 0.0 2.0 21.7 25.7 29.6 4598 1
## y_new[4,41] 25.7 0.0 2.0 21.8 25.7 29.8 4114 1
## y_new[4,42] 25.7 0.0 2.0 21.7 25.7 29.7 4156 1
## y_new[4,43] 25.8 0.0 2.0 21.9 25.8 29.8 4096 1
## y_new[4,44] 25.8 0.0 2.0 21.8 25.8 29.8 4350 1
## y_new[4,45] 25.7 0.0 2.0 21.8 25.7 29.8 4210 1
## y_new[4,46] 25.7 0.0 2.1 21.6 25.7 29.7 4021 1
## y_new[4,47] 25.8 0.0 2.1 21.9 25.8 29.9 3971 1
## y_new[4,48] 25.8 0.0 2.1 21.8 25.8 29.9 4358 1
## y_new[4,49] 25.8 0.0 2.0 21.8 25.8 29.8 3711 1
## y_new[4,50] 25.9 0.0 2.0 21.8 25.9 29.9 4667 1
## y_new[4,51] 25.8 0.0 2.0 21.9 25.8 29.9 4027 1
## y_new[4,52] 25.8 0.0 2.1 21.8 25.8 29.9 4324 1
## y_new[4,53] 25.8 0.0 2.0 21.9 25.8 29.9 4466 1
## y_new[4,54] 25.9 0.0 2.0 21.8 25.8 29.9 4351 1
## y_new[4,55] 25.9 0.0 2.1 22.0 25.8 30.1 3922 1
## y_new[4,56] 25.9 0.0 2.1 21.8 25.9 29.9 4539 1
## y_new[4,57] 25.9 0.0 2.1 21.8 25.9 29.9 4310 1
## y_new[4,58] 25.9 0.0 2.1 21.8 25.8 30.1 3965 1
## y_new[4,59] 25.8 0.0 2.1 21.8 25.8 30.0 4021 1
## y_new[4,60] 25.8 0.0 2.0 21.8 25.8 29.9 3860 1
## y_new[5,1] 0.0 0.0 1.7 -3.5 0.1 3.3 3926 1
## y_new[5,2] 1.1 0.0 1.7 -2.3 1.1 4.4 3548 1
## y_new[5,3] 2.0 0.0 1.8 -1.4 2.0 5.6 4304 1
## y_new[5,4] 3.0 0.0 1.8 -0.5 2.9 6.7 3916 1
## y_new[5,5] 3.8 0.0 1.8 0.1 3.7 7.3 4023 1
## y_new[5,6] 4.5 0.0 1.9 0.8 4.5 8.2 3903 1
## y_new[5,7] 5.2 0.0 1.9 1.5 5.2 9.1 3822 1
## y_new[5,8] 5.8 0.0 1.9 2.1 5.8 9.7 4055 1
## y_new[5,9] 6.4 0.0 2.0 2.5 6.4 10.4 3861 1
## y_new[5,10] 7.0 0.0 2.0 3.1 7.0 10.9 4049 1
## y_new[5,11] 7.5 0.0 2.0 3.7 7.5 11.5 3901 1
## y_new[5,12] 7.9 0.0 2.0 4.2 7.9 11.9 3921 1
## y_new[5,13] 8.4 0.0 2.0 4.6 8.4 12.4 4219 1
## y_new[5,14] 8.8 0.0 2.0 4.8 8.8 12.8 3757 1
## y_new[5,15] 9.2 0.0 2.0 5.3 9.2 13.2 3845 1
## y_new[5,16] 9.5 0.0 2.0 5.7 9.5 13.5 3926 1
## y_new[5,17] 9.9 0.0 1.9 6.0 9.9 13.7 3744 1
## y_new[5,18] 10.2 0.0 2.0 6.3 10.2 14.0 3897 1
## y_new[5,19] 10.4 0.0 1.9 6.6 10.5 14.2 3524 1
## y_new[5,20] 10.7 0.0 2.0 6.7 10.7 14.5 3824 1
## y_new[5,21] 10.9 0.0 2.0 7.0 11.0 14.8 3919 1
## y_new[5,22] 11.2 0.0 1.9 7.3 11.1 15.0 3778 1
## y_new[5,23] 11.4 0.0 1.9 7.6 11.4 15.1 4277 1
## y_new[5,24] 11.6 0.0 2.0 7.7 11.6 15.4 3477 1
## y_new[5,25] 11.7 0.0 1.9 7.8 11.8 15.6 4123 1
## y_new[5,26] 11.9 0.0 1.9 8.1 11.9 15.5 3892 1
## y_new[5,27] 12.0 0.0 2.0 8.1 12.0 15.8 4100 1
## y_new[5,28] 12.2 0.0 1.9 8.4 12.2 16.0 3906 1
## y_new[5,29] 12.3 0.0 2.0 8.4 12.3 16.2 3995 1
## y_new[5,30] 12.5 0.0 1.9 8.8 12.5 16.2 4126 1
## y_new[5,31] 12.6 0.0 1.9 8.8 12.6 16.3 4262 1
## y_new[5,32] 12.7 0.0 2.0 8.7 12.7 16.6 3747 1
## y_new[5,33] 12.8 0.0 2.0 9.0 12.8 16.9 3937 1
## y_new[5,34] 12.9 0.0 2.0 8.9 13.0 16.8 3999 1
## y_new[5,35] 13.0 0.0 2.0 9.1 13.0 16.8 3973 1
## y_new[5,36] 13.1 0.0 2.0 9.2 13.1 17.1 4375 1
## y_new[5,37] 13.2 0.0 2.0 9.3 13.2 17.2 4170 1
## y_new[5,38] 13.2 0.0 2.0 9.2 13.2 17.2 4080 1
## y_new[5,39] 13.4 0.0 2.1 9.4 13.4 17.4 4114 1
## y_new[5,40] 13.3 0.0 2.0 9.4 13.4 17.3 4153 1
## y_new[5,41] 13.4 0.0 2.0 9.4 13.4 17.4 4202 1
## y_new[5,42] 13.4 0.0 2.0 9.4 13.4 17.4 3889 1
## y_new[5,43] 13.5 0.0 2.1 9.4 13.5 17.5 3994 1
## y_new[5,44] 13.6 0.0 2.1 9.4 13.5 17.8 4100 1
## y_new[5,45] 13.7 0.0 2.1 9.5 13.6 17.6 4304 1
## y_new[5,46] 13.6 0.0 2.1 9.4 13.7 17.8 3802 1
## y_new[5,47] 13.7 0.0 2.1 9.6 13.7 17.8 3781 1
## y_new[5,48] 13.8 0.0 2.1 9.6 13.8 17.9 4145 1
## y_new[5,49] 13.8 0.0 2.2 9.5 13.8 17.9 3585 1
## y_new[5,50] 13.9 0.0 2.1 9.6 13.9 18.2 3807 1
## y_new[5,51] 13.9 0.0 2.1 9.7 13.9 17.9 4134 1
## y_new[5,52] 13.9 0.0 2.2 9.8 13.9 18.3 3879 1
## y_new[5,53] 13.9 0.0 2.2 9.8 13.9 18.0 4011 1
## y_new[5,54] 14.0 0.0 2.2 9.6 14.0 18.2 4396 1
## y_new[5,55] 14.0 0.0 2.2 9.6 14.0 18.3 4050 1
## y_new[5,56] 14.0 0.0 2.2 9.6 14.0 18.2 3702 1
## y_new[5,57] 14.0 0.0 2.2 9.8 14.0 18.2 3940 1
## y_new[5,58] 14.0 0.0 2.2 9.6 14.0 18.3 3947 1
## y_new[5,59] 14.0 0.0 2.2 9.7 14.0 18.5 3870 1
## y_new[5,60] 14.1 0.0 2.2 9.8 14.1 18.5 4282 1
## y_new[6,1] 0.0 0.0 1.7 -3.4 0.0 3.6 4177 1
## y_new[6,2] 1.4 0.0 1.7 -2.0 1.4 4.8 4166 1
## y_new[6,3] 2.7 0.0 1.8 -0.7 2.7 6.4 3879 1
## y_new[6,4] 3.9 0.0 1.9 0.2 3.9 7.6 3788 1
## y_new[6,5] 4.9 0.0 2.0 1.1 4.9 8.9 4310 1
## y_new[6,6] 5.9 0.0 2.0 2.1 5.9 9.9 3971 1
## y_new[6,7] 6.8 0.0 2.1 2.9 6.7 11.0 4210 1
## y_new[6,8] 7.5 0.0 2.0 3.5 7.5 11.4 4223 1
## y_new[6,9] 8.3 0.0 2.1 4.2 8.3 12.5 4103 1
## y_new[6,10] 8.9 0.0 2.1 4.8 8.8 12.9 4329 1
## y_new[6,11] 9.5 0.0 2.0 5.5 9.5 13.6 4069 1
## y_new[6,12] 10.0 0.0 2.1 5.9 10.0 14.1 4355 1
## y_new[6,13] 10.5 0.0 2.1 6.5 10.5 14.7 3921 1
## y_new[6,14] 10.9 0.0 2.0 6.8 10.8 14.8 3851 1
## y_new[6,15] 11.3 0.0 2.0 7.5 11.3 15.2 3847 1
## y_new[6,16] 11.6 0.0 2.0 7.8 11.7 15.5 4151 1
## y_new[6,17] 12.1 0.0 2.0 8.0 12.1 15.8 4049 1
## y_new[6,18] 12.3 0.0 2.0 8.6 12.3 16.3 4052 1
## y_new[6,19] 12.6 0.0 1.9 8.7 12.6 16.4 4075 1
## y_new[6,20] 12.8 0.0 2.0 9.0 12.9 16.6 4033 1
## y_new[6,21] 13.1 0.0 2.0 9.2 13.0 17.1 3953 1
## y_new[6,22] 13.3 0.0 1.9 9.5 13.3 17.0 4080 1
## y_new[6,23] 13.5 0.0 1.9 9.7 13.5 17.3 4155 1
## y_new[6,24] 13.6 0.0 1.9 9.7 13.6 17.4 4143 1
## y_new[6,25] 13.8 0.0 1.9 10.0 13.8 17.6 3808 1
## y_new[6,26] 14.0 0.0 1.9 10.2 14.0 17.9 3906 1
## y_new[6,27] 14.1 0.0 1.9 10.3 14.1 17.8 4023 1
## y_new[6,28] 14.2 0.0 1.9 10.3 14.2 18.0 4243 1
## y_new[6,29] 14.4 0.0 1.9 10.6 14.4 18.1 3869 1
## y_new[6,30] 14.4 0.0 2.0 10.5 14.5 18.2 3632 1
## y_new[6,31] 14.6 0.0 2.0 10.8 14.6 18.5 3727 1
## y_new[6,32] 14.6 0.0 2.0 10.7 14.6 18.4 3875 1
## y_new[6,33] 14.7 0.0 2.0 10.7 14.7 18.7 3991 1
## y_new[6,34] 14.8 0.0 2.0 10.7 14.8 18.8 4333 1
## y_new[6,35] 14.9 0.0 2.0 10.8 14.9 18.8 4049 1
## y_new[6,36] 14.9 0.0 2.0 10.9 14.9 18.9 4132 1
## y_new[6,37] 14.9 0.0 2.0 11.0 14.9 18.8 4004 1
## y_new[6,38] 15.0 0.0 2.0 11.0 15.0 19.0 4469 1
## y_new[6,39] 15.0 0.0 2.0 11.0 15.1 19.1 4313 1
## y_new[6,40] 15.2 0.0 2.1 11.2 15.2 19.3 4215 1
## y_new[6,41] 15.1 0.0 2.1 11.0 15.2 19.1 4271 1
## y_new[6,42] 15.2 0.0 2.1 11.2 15.2 19.2 3963 1
## y_new[6,43] 15.2 0.0 2.1 11.1 15.2 19.5 3827 1
## y_new[6,44] 15.3 0.0 2.1 11.1 15.3 19.5 4293 1
## y_new[6,45] 15.3 0.0 2.1 11.2 15.3 19.4 3987 1
## y_new[6,46] 15.3 0.0 2.1 11.2 15.3 19.6 3393 1
## y_new[6,47] 15.4 0.0 2.1 11.2 15.4 19.6 3607 1
## y_new[6,48] 15.4 0.0 2.2 11.1 15.4 19.5 3959 1
## y_new[6,49] 15.4 0.0 2.2 11.2 15.4 19.8 4404 1
## y_new[6,50] 15.4 0.0 2.2 11.1 15.4 19.8 3983 1
## y_new[6,51] 15.5 0.0 2.2 11.1 15.5 19.7 4273 1
## y_new[6,52] 15.5 0.0 2.2 11.3 15.4 19.9 3979 1
## y_new[6,53] 15.5 0.0 2.2 11.1 15.5 19.9 3521 1
## y_new[6,54] 15.5 0.0 2.2 11.4 15.5 20.0 3721 1
## y_new[6,55] 15.5 0.0 2.2 11.1 15.5 19.9 4012 1
## y_new[6,56] 15.5 0.0 2.2 11.1 15.6 19.9 3590 1
## y_new[6,57] 15.5 0.0 2.2 11.4 15.5 19.9 4077 1
## y_new[6,58] 15.6 0.0 2.2 11.2 15.6 19.9 3730 1
## y_new[6,59] 15.6 0.0 2.2 11.2 15.6 20.0 4143 1
## y_new[6,60] 15.6 0.0 2.2 11.4 15.5 20.0 3835 1
## y_new[7,1] 0.0 0.0 1.8 -3.6 0.0 3.4 3764 1
## y_new[7,2] 1.4 0.0 1.7 -1.9 1.4 4.9 4214 1
## y_new[7,3] 2.7 0.0 1.8 -0.7 2.6 6.2 3994 1
## y_new[7,4] 3.7 0.0 1.9 0.1 3.8 7.5 3948 1
## y_new[7,5] 4.8 0.0 1.9 1.1 4.9 8.5 4099 1
## y_new[7,6] 5.8 0.0 1.9 2.0 5.8 9.6 3937 1
## y_new[7,7] 6.6 0.0 2.0 2.7 6.7 10.7 4142 1
## y_new[7,8] 7.3 0.0 2.0 3.6 7.3 11.2 4097 1
## y_new[7,9] 8.0 0.0 2.0 4.1 8.0 11.9 3828 1
## y_new[7,10] 8.6 0.0 2.0 4.6 8.6 12.6 4233 1
## y_new[7,11] 9.1 0.0 2.0 5.1 9.2 13.0 3951 1
## y_new[7,12] 9.7 0.0 2.0 5.8 9.7 13.6 3924 1
## y_new[7,13] 10.2 0.0 2.0 6.5 10.2 14.2 3675 1
## y_new[7,14] 10.5 0.0 2.0 6.6 10.5 14.6 3740 1
## y_new[7,15] 11.0 0.0 2.0 7.3 10.9 14.8 3937 1
## y_new[7,16] 11.3 0.0 2.0 7.4 11.3 15.1 4105 1
## y_new[7,17] 11.6 0.0 2.0 7.7 11.6 15.4 3945 1
## y_new[7,18] 11.9 0.0 1.9 8.0 11.9 15.6 3943 1
## y_new[7,19] 12.2 0.0 1.9 8.3 12.2 16.0 3792 1
## y_new[7,20] 12.4 0.0 1.9 8.7 12.4 16.2 3876 1
## y_new[7,21] 12.7 0.0 1.9 8.9 12.7 16.5 3915 1
## y_new[7,22] 12.8 0.0 1.9 9.1 12.8 16.6 4017 1
## y_new[7,23] 12.9 0.0 1.9 9.1 12.9 16.7 3912 1
## y_new[7,24] 13.1 0.0 2.0 9.1 13.1 16.9 3768 1
## y_new[7,25] 13.2 0.0 1.9 9.5 13.2 17.0 3621 1
## y_new[7,26] 13.3 0.0 2.0 9.5 13.3 17.2 4063 1
## y_new[7,27] 13.5 0.0 1.9 9.8 13.5 17.3 4195 1
## y_new[7,28] 13.6 0.0 2.0 9.8 13.7 17.4 3625 1
## y_new[7,29] 13.7 0.0 2.0 9.9 13.7 17.6 4014 1
## y_new[7,30] 13.9 0.0 1.9 10.1 13.8 17.7 4201 1
## y_new[7,31] 13.9 0.0 2.0 10.1 13.9 17.8 4244 1
## y_new[7,32] 14.0 0.0 2.0 10.0 13.9 17.8 3991 1
## y_new[7,33] 14.1 0.0 2.0 10.1 14.1 17.9 3841 1
## y_new[7,34] 14.1 0.0 2.0 10.2 14.1 18.1 3985 1
## y_new[7,35] 14.2 0.0 2.0 10.2 14.2 18.2 4089 1
## y_new[7,36] 14.2 0.0 2.0 10.3 14.2 18.2 3636 1
## y_new[7,37] 14.3 0.0 2.0 10.2 14.4 18.2 3679 1
## y_new[7,38] 14.4 0.0 2.0 10.4 14.4 18.4 4214 1
## y_new[7,39] 14.4 0.0 2.0 10.4 14.4 18.2 3715 1
## y_new[7,40] 14.4 0.0 2.1 10.1 14.4 18.5 3785 1
## y_new[7,41] 14.5 0.0 2.0 10.5 14.5 18.4 4127 1
## y_new[7,42] 14.5 0.0 2.1 10.5 14.6 18.6 4166 1
## y_new[7,43] 14.5 0.0 2.1 10.4 14.5 18.7 4267 1
## y_new[7,44] 14.5 0.0 2.1 10.3 14.5 18.7 4134 1
## y_new[7,45] 14.6 0.0 2.1 10.4 14.6 18.7 4083 1
## y_new[7,46] 14.6 0.0 2.1 10.4 14.6 18.8 4370 1
## y_new[7,47] 14.7 0.0 2.1 10.6 14.6 18.9 4346 1
## y_new[7,48] 14.6 0.0 2.1 10.4 14.6 18.8 3942 1
## y_new[7,49] 14.7 0.0 2.1 10.6 14.7 18.8 4262 1
## y_new[7,50] 14.7 0.0 2.1 10.5 14.6 18.7 4010 1
## y_new[7,51] 14.7 0.0 2.2 10.5 14.6 19.0 4455 1
## y_new[7,52] 14.7 0.0 2.1 10.6 14.7 19.0 4450 1
## y_new[7,53] 14.7 0.0 2.1 10.6 14.7 18.9 4006 1
## y_new[7,54] 14.7 0.0 2.2 10.5 14.8 18.9 4346 1
## y_new[7,55] 14.7 0.0 2.1 10.4 14.7 18.9 4274 1
## y_new[7,56] 14.7 0.0 2.2 10.6 14.8 19.1 4139 1
## y_new[7,57] 14.7 0.0 2.1 10.5 14.7 19.0 4156 1
## y_new[7,58] 14.8 0.0 2.2 10.6 14.8 19.0 4299 1
## y_new[7,59] 14.8 0.0 2.2 10.7 14.7 19.1 4343 1
## y_new[7,60] 14.8 0.0 2.2 10.5 14.8 19.0 4431 1
## y_new[8,1] 0.0 0.0 1.7 -3.4 -0.1 3.4 3974 1
## y_new[8,2] 1.8 0.0 1.8 -1.6 1.8 5.3 3857 1
## y_new[8,3] 3.3 0.0 1.9 -0.4 3.3 7.1 4047 1
## y_new[8,4] 4.7 0.0 1.9 0.8 4.7 8.5 4088 1
## y_new[8,5] 5.8 0.0 2.0 2.0 5.8 9.9 4425 1
## y_new[8,6] 6.8 0.0 2.0 3.0 6.8 10.9 3713 1
## y_new[8,7] 7.6 0.0 2.0 3.7 7.6 11.7 4241 1
## y_new[8,8] 8.4 0.0 2.0 4.4 8.4 12.5 4400 1
## y_new[8,9] 9.1 0.0 2.0 5.1 9.1 13.0 3623 1
## y_new[8,10] 9.5 0.0 2.0 5.5 9.5 13.4 4344 1
## y_new[8,11] 10.0 0.0 2.0 6.2 10.0 13.8 4008 1
## y_new[8,12] 10.5 0.0 2.0 6.6 10.4 14.5 4434 1
## y_new[8,13] 10.8 0.0 2.0 7.0 10.8 14.6 3760 1
## y_new[8,14] 11.1 0.0 1.9 7.3 11.2 14.9 3627 1
## y_new[8,15] 11.4 0.0 1.9 7.6 11.4 15.1 4028 1
## y_new[8,16] 11.7 0.0 1.9 7.8 11.7 15.4 4171 1
## y_new[8,17] 11.8 0.0 1.9 8.2 11.8 15.7 4274 1
## y_new[8,18] 12.0 0.0 1.9 8.3 12.0 15.7 4286 1
## y_new[8,19] 12.2 0.0 1.9 8.5 12.2 15.9 4013 1
## y_new[8,20] 12.3 0.0 1.9 8.4 12.3 16.1 4211 1
## y_new[8,21] 12.4 0.0 1.9 8.6 12.4 16.3 4049 1
## y_new[8,22] 12.5 0.0 1.9 8.7 12.5 16.3 3921 1
## y_new[8,23] 12.6 0.0 1.9 8.9 12.6 16.4 4270 1
## y_new[8,24] 12.7 0.0 1.9 8.9 12.7 16.5 4255 1
## y_new[8,25] 12.8 0.0 2.0 8.8 12.8 16.7 4227 1
## y_new[8,26] 12.9 0.0 1.9 9.1 12.9 16.7 4020 1
## y_new[8,27] 12.9 0.0 1.9 9.0 12.9 16.7 4217 1
## y_new[8,28] 13.0 0.0 1.9 9.1 13.0 16.7 3954 1
## y_new[8,29] 13.0 0.0 1.9 9.2 13.0 16.8 4179 1
## y_new[8,30] 13.0 0.0 2.0 9.2 13.0 16.8 4056 1
## y_new[8,31] 13.1 0.0 1.9 9.2 13.1 17.0 4226 1
## y_new[8,32] 13.1 0.0 1.9 9.3 13.1 16.9 4271 1
## y_new[8,33] 13.1 0.0 2.0 9.2 13.1 17.2 4142 1
## y_new[8,34] 13.2 0.0 2.0 9.4 13.2 17.2 4271 1
## y_new[8,35] 13.2 0.0 2.0 9.4 13.2 17.3 4398 1
## y_new[8,36] 13.2 0.0 2.0 9.2 13.2 17.0 3824 1
## y_new[8,37] 13.2 0.0 2.0 9.3 13.2 17.3 4326 1
## y_new[8,38] 13.2 0.0 2.0 9.3 13.3 17.2 3543 1
## y_new[8,39] 13.2 0.0 2.0 9.3 13.2 17.3 3962 1
## y_new[8,40] 13.2 0.0 2.0 9.3 13.2 17.3 4502 1
## y_new[8,41] 13.3 0.0 2.0 9.3 13.3 17.2 4034 1
## y_new[8,42] 13.3 0.0 2.0 9.4 13.3 17.1 4415 1
## y_new[8,43] 13.3 0.0 2.0 9.3 13.3 17.3 4112 1
## y_new[8,44] 13.3 0.0 2.0 9.3 13.3 17.3 3955 1
## y_new[8,45] 13.3 0.0 2.1 9.4 13.3 17.4 4057 1
## y_new[8,46] 13.3 0.0 2.0 9.3 13.3 17.4 4058 1
## y_new[8,47] 13.4 0.0 2.1 9.3 13.3 17.4 3859 1
## y_new[8,48] 13.3 0.0 2.1 9.2 13.4 17.5 4026 1
## y_new[8,49] 13.3 0.0 2.1 9.3 13.3 17.5 3917 1
## y_new[8,50] 13.3 0.0 2.1 9.3 13.3 17.4 4350 1
## y_new[8,51] 13.4 0.0 2.1 9.4 13.3 17.6 4178 1
## y_new[8,52] 13.4 0.0 2.0 9.4 13.3 17.3 4306 1
## y_new[8,53] 13.4 0.0 2.1 9.1 13.4 17.4 4283 1
## y_new[8,54] 13.4 0.0 2.1 9.5 13.4 17.5 4544 1
## y_new[8,55] 13.4 0.0 2.0 9.3 13.3 17.5 3867 1
## y_new[8,56] 13.4 0.0 2.0 9.4 13.4 17.4 4042 1
## y_new[8,57] 13.3 0.0 2.1 9.2 13.4 17.4 4131 1
## y_new[8,58] 13.3 0.0 2.1 9.3 13.3 17.5 4159 1
## y_new[8,59] 13.4 0.0 2.1 9.4 13.3 17.5 3752 1
## y_new[8,60] 13.4 0.0 2.1 9.2 13.4 17.5 3928 1
## y_new[9,1] 0.0 0.0 1.7 -3.5 0.0 3.3 4123 1
## y_new[9,2] 4.8 0.0 1.8 1.1 4.7 8.3 4139 1
## y_new[9,3] 8.8 0.0 1.9 5.1 8.8 12.5 3808 1
## y_new[9,4] 12.2 0.0 2.0 8.4 12.2 16.0 4379 1
## y_new[9,5] 15.1 0.0 2.0 11.2 15.0 19.1 4084 1
## y_new[9,6] 17.5 0.0 2.1 13.5 17.5 21.6 4314 1
## y_new[9,7] 19.7 0.0 2.1 15.6 19.7 23.8 4233 1
## y_new[9,8] 21.4 0.0 2.0 17.3 21.4 25.4 4256 1
## y_new[9,9] 23.0 0.0 2.1 19.0 23.0 26.9 4239 1
## y_new[9,10] 24.3 0.0 2.0 20.2 24.3 28.2 4141 1
## y_new[9,11] 25.3 0.0 2.0 21.4 25.4 29.2 3988 1
## y_new[9,12] 26.3 0.0 2.0 22.4 26.3 30.2 4220 1
## y_new[9,13] 27.1 0.0 2.0 23.2 27.1 31.0 4273 1
## y_new[9,14] 27.8 0.0 1.9 24.0 27.8 31.5 3369 1
## y_new[9,15] 28.4 0.0 2.0 24.7 28.4 32.2 4547 1
## y_new[9,16] 28.8 0.0 1.9 25.2 28.8 32.7 4183 1
## y_new[9,17] 29.3 0.0 1.9 25.6 29.4 33.1 4174 1
## y_new[9,18] 29.7 0.0 2.0 25.8 29.6 33.5 3779 1
## y_new[9,19] 30.0 0.0 1.9 26.2 30.0 33.8 4176 1
## y_new[9,20] 30.2 0.0 1.9 26.4 30.2 34.0 4236 1
## y_new[9,21] 30.5 0.0 1.9 26.7 30.5 34.2 3870 1
## y_new[9,22] 30.7 0.0 1.9 27.0 30.7 34.5 3897 1
## y_new[9,23] 30.8 0.0 1.9 27.0 30.8 34.5 4243 1
## y_new[9,24] 30.9 0.0 2.0 27.0 31.0 34.8 3703 1
## y_new[9,25] 31.1 0.0 1.9 27.3 31.1 35.0 3934 1
## y_new[9,26] 31.2 0.0 2.0 27.3 31.2 35.1 4285 1
## y_new[9,27] 31.3 0.0 2.0 27.5 31.3 35.1 4088 1
## y_new[9,28] 31.3 0.0 2.0 27.3 31.3 35.3 3938 1
## y_new[9,29] 31.4 0.0 2.0 27.6 31.4 35.3 4193 1
## y_new[9,30] 31.4 0.0 2.0 27.7 31.4 35.3 4193 1
## y_new[9,31] 31.6 0.0 2.0 27.7 31.6 35.4 3766 1
## y_new[9,32] 31.5 0.0 2.0 27.7 31.6 35.5 4197 1
## y_new[9,33] 31.6 0.0 2.0 27.8 31.6 35.5 3648 1
## y_new[9,34] 31.6 0.0 2.0 27.6 31.6 35.5 4005 1
## y_new[9,35] 31.6 0.0 2.0 27.7 31.6 35.6 4093 1
## y_new[9,36] 31.7 0.0 2.0 27.8 31.7 35.5 4328 1
## y_new[9,37] 31.7 0.0 2.0 27.9 31.6 35.7 4099 1
## y_new[9,38] 31.7 0.0 2.0 27.8 31.7 35.6 4166 1
## y_new[9,39] 31.7 0.0 2.0 27.7 31.7 35.6 3978 1
## y_new[9,40] 31.7 0.0 2.1 27.6 31.7 35.9 4279 1
## y_new[9,41] 31.7 0.0 2.0 27.7 31.7 35.8 3880 1
## y_new[9,42] 31.7 0.0 2.0 27.8 31.7 35.7 4363 1
## y_new[9,43] 31.7 0.0 2.0 27.7 31.7 35.8 4167 1
## y_new[9,44] 31.8 0.0 2.1 27.7 31.8 35.8 3880 1
## y_new[9,45] 31.8 0.0 2.1 27.5 31.8 35.8 3848 1
## y_new[9,46] 31.7 0.0 2.0 27.7 31.7 35.6 4227 1
## y_new[9,47] 31.7 0.0 2.0 27.8 31.7 35.7 3976 1
## y_new[9,48] 31.8 0.0 2.0 27.7 31.8 35.9 4196 1
## y_new[9,49] 31.8 0.0 2.0 27.9 31.8 35.7 4078 1
## y_new[9,50] 31.8 0.0 2.1 27.7 31.8 35.8 4419 1
## y_new[9,51] 31.8 0.0 2.1 27.6 31.8 35.9 3444 1
## y_new[9,52] 31.8 0.0 2.0 27.7 31.8 35.7 3965 1
## y_new[9,53] 31.8 0.0 2.1 27.7 31.8 35.8 4523 1
## y_new[9,54] 31.8 0.0 2.0 27.9 31.8 35.8 4380 1
## y_new[9,55] 31.8 0.0 2.0 27.8 31.8 35.8 4095 1
## y_new[9,56] 31.7 0.0 2.0 27.8 31.8 35.8 3642 1
## y_new[9,57] 31.7 0.0 2.0 27.8 31.7 35.6 4052 1
## y_new[9,58] 31.8 0.0 2.1 27.8 31.7 35.8 3806 1
## y_new[9,59] 31.8 0.0 2.0 27.9 31.8 35.7 4212 1
## y_new[9,60] 31.8 0.0 2.1 27.7 31.8 35.8 4340 1
## y_new[10,1] 0.0 0.0 1.7 -3.4 0.0 3.4 4013 1
## y_new[10,2] 2.8 0.0 1.8 -0.7 2.8 6.3 3433 1
## y_new[10,3] 5.2 0.0 1.8 1.5 5.1 8.8 3939 1
## y_new[10,4] 7.2 0.0 2.0 3.2 7.2 10.9 3309 1
## y_new[10,5] 8.8 0.0 2.0 5.0 8.8 12.7 4445 1
## y_new[10,6] 10.2 0.0 2.0 6.2 10.2 14.1 4026 1
## y_new[10,7] 11.4 0.0 2.0 7.5 11.3 15.3 4184 1
## y_new[10,8] 12.3 0.0 2.0 8.3 12.3 16.3 4414 1
## y_new[10,9] 13.2 0.0 2.0 9.2 13.2 17.2 4013 1
## y_new[10,10] 13.9 0.0 1.9 10.2 13.9 17.7 3936 1
## y_new[10,11] 14.5 0.0 2.0 10.6 14.5 18.3 4281 1
## y_new[10,12] 14.9 0.0 1.9 11.0 15.0 18.7 4016 1
## y_new[10,13] 15.4 0.0 1.9 11.7 15.4 19.2 4177 1
## y_new[10,14] 15.7 0.0 1.9 11.9 15.7 19.3 4302 1
## y_new[10,15] 16.1 0.0 2.0 12.1 16.1 20.0 3438 1
## y_new[10,16] 16.3 0.0 1.9 12.6 16.3 20.0 3865 1
## y_new[10,17] 16.6 0.0 1.9 12.8 16.6 20.2 4173 1
## y_new[10,18] 16.7 0.0 1.9 12.9 16.7 20.4 3688 1
## y_new[10,19] 16.9 0.0 1.9 13.2 16.9 20.5 4077 1
## y_new[10,20] 17.0 0.0 1.9 13.3 17.0 20.7 3852 1
## y_new[10,21] 17.1 0.0 2.0 13.3 17.1 21.0 4180 1
## y_new[10,22] 17.2 0.0 1.9 13.5 17.2 21.0 3662 1
## y_new[10,23] 17.3 0.0 1.9 13.6 17.4 21.1 3999 1
## y_new[10,24] 17.4 0.0 1.9 13.5 17.4 21.2 3807 1
## y_new[10,25] 17.5 0.0 1.9 13.7 17.5 21.2 4281 1
## y_new[10,26] 17.5 0.0 2.0 13.7 17.5 21.4 4008 1
## y_new[10,27] 17.5 0.0 1.9 13.6 17.5 21.2 4339 1
## y_new[10,28] 17.6 0.0 2.0 13.8 17.6 21.5 3990 1
## y_new[10,29] 17.6 0.0 2.0 13.5 17.6 21.4 3943 1
## y_new[10,30] 17.7 0.0 2.0 13.8 17.7 21.6 3918 1
## y_new[10,31] 17.7 0.0 2.0 13.8 17.6 21.6 4312 1
## y_new[10,32] 17.7 0.0 2.0 14.0 17.7 21.6 4492 1
## y_new[10,33] 17.7 0.0 2.0 13.8 17.7 21.6 4393 1
## y_new[10,34] 17.7 0.0 2.0 13.8 17.7 21.6 4379 1
## y_new[10,35] 17.8 0.0 2.0 13.9 17.8 21.8 4387 1
## y_new[10,36] 17.7 0.0 2.0 14.0 17.7 21.7 4588 1
## y_new[10,37] 17.8 0.0 2.0 13.9 17.8 21.8 4367 1
## y_new[10,38] 17.8 0.0 2.0 14.0 17.7 21.7 4334 1
## y_new[10,39] 17.8 0.0 2.0 13.9 17.8 21.6 4261 1
## y_new[10,40] 17.8 0.0 2.0 13.9 17.8 21.7 3991 1
## y_new[10,41] 17.8 0.0 2.0 13.9 17.9 21.8 4243 1
## y_new[10,42] 17.9 0.0 2.0 13.9 17.9 21.9 4192 1
## y_new[10,43] 17.8 0.0 2.0 14.0 17.9 21.7 4397 1
## y_new[10,44] 17.8 0.0 2.0 13.9 17.8 21.6 4192 1
## y_new[10,45] 17.9 0.0 2.0 14.0 17.8 21.9 4632 1
## y_new[10,46] 17.9 0.0 2.0 13.8 17.9 21.8 4541 1
## y_new[10,47] 17.8 0.0 2.0 13.9 17.8 21.9 4432 1
## y_new[10,48] 17.9 0.0 2.0 13.9 17.9 21.9 4654 1
## y_new[10,49] 17.8 0.0 2.0 13.9 17.8 21.8 4732 1
## y_new[10,50] 17.8 0.0 2.0 14.0 17.8 21.8 4058 1
## y_new[10,51] 17.9 0.0 2.0 13.9 17.9 21.8 4412 1
## y_new[10,52] 17.9 0.0 2.0 13.9 17.9 21.9 4355 1
## y_new[10,53] 17.8 0.0 2.0 13.9 17.8 21.8 4239 1
## y_new[10,54] 17.8 0.0 2.0 13.9 17.8 21.7 4116 1
## y_new[10,55] 17.9 0.0 2.0 14.1 17.9 21.9 3850 1
## y_new[10,56] 17.9 0.0 2.0 13.9 17.9 21.7 4525 1
## y_new[10,57] 17.9 0.0 2.0 14.0 17.9 21.8 4283 1
## y_new[10,58] 17.8 0.0 2.1 13.8 17.8 21.9 4352 1
## y_new[10,59] 17.9 0.0 2.0 13.9 17.9 21.9 4092 1
## y_new[10,60] 17.9 0.0 2.0 13.9 17.9 21.9 4029 1
## y_new[11,1] 0.0 0.0 1.7 -3.4 0.0 3.4 4137 1
## y_new[11,2] 2.9 0.0 1.8 -0.5 2.9 6.5 4177 1
## y_new[11,3] 5.4 0.0 1.9 1.7 5.3 9.1 4279 1
## y_new[11,4] 7.4 0.0 2.0 3.6 7.4 11.4 4447 1
## y_new[11,5] 9.2 0.0 2.0 5.2 9.2 13.3 4242 1
## y_new[11,6] 10.7 0.0 2.0 6.5 10.7 14.8 4447 1
## y_new[11,7] 12.0 0.0 2.0 8.2 12.0 16.0 4321 1
## y_new[11,8] 13.1 0.0 2.1 9.1 13.1 17.0 4292 1
## y_new[11,9] 14.0 0.0 2.0 10.1 14.0 17.9 4026 1
## y_new[11,10] 14.8 0.0 2.0 10.8 14.8 18.6 3809 1
## y_new[11,11] 15.5 0.0 2.0 11.6 15.5 19.4 4354 1
## y_new[11,12] 16.1 0.0 2.0 12.2 16.1 19.9 3745 1
## y_new[11,13] 16.6 0.0 2.0 12.7 16.6 20.4 4030 1
## y_new[11,14] 16.9 0.0 1.9 13.1 17.0 20.7 4036 1
## y_new[11,15] 17.4 0.0 1.9 13.6 17.4 21.1 4146 1
## y_new[11,16] 17.7 0.0 1.9 13.9 17.7 21.5 4233 1
## y_new[11,17] 17.9 0.0 1.9 14.2 17.9 21.6 3918 1
## y_new[11,18] 18.2 0.0 1.9 14.5 18.1 21.8 4028 1
## y_new[11,19] 18.4 0.0 1.9 14.7 18.3 22.0 4407 1
## y_new[11,20] 18.5 0.0 1.9 14.7 18.5 22.3 4084 1
## y_new[11,21] 18.6 0.0 1.9 14.8 18.7 22.4 4082 1
## y_new[11,22] 18.8 0.0 1.9 15.1 18.8 22.7 4212 1
## y_new[11,23] 18.9 0.0 1.9 15.1 18.9 22.7 4497 1
## y_new[11,24] 19.0 0.0 1.9 15.3 19.0 22.8 4029 1
## y_new[11,25] 19.1 0.0 2.0 15.3 19.1 22.9 4005 1
## y_new[11,26] 19.1 0.0 2.0 15.2 19.1 23.0 3989 1
## y_new[11,27] 19.2 0.0 2.0 15.3 19.2 23.1 4009 1
## y_new[11,28] 19.3 0.0 2.0 15.5 19.3 23.3 4239 1
## y_new[11,29] 19.3 0.0 2.0 15.5 19.3 23.2 4528 1
## y_new[11,30] 19.3 0.0 2.0 15.4 19.3 23.3 4340 1
## y_new[11,31] 19.4 0.0 2.0 15.6 19.4 23.4 4035 1
## y_new[11,32] 19.4 0.0 2.0 15.4 19.4 23.4 4368 1
## y_new[11,33] 19.5 0.0 2.0 15.6 19.5 23.4 3512 1
## y_new[11,34] 19.5 0.0 2.0 15.7 19.5 23.3 4218 1
## y_new[11,35] 19.5 0.0 2.0 15.5 19.5 23.5 4346 1
## y_new[11,36] 19.5 0.0 2.0 15.4 19.5 23.6 4161 1
## y_new[11,37] 19.5 0.0 2.0 15.5 19.5 23.5 4393 1
## y_new[11,38] 19.5 0.0 2.1 15.5 19.5 23.6 4572 1
## y_new[11,39] 19.6 0.0 2.0 15.5 19.6 23.6 4412 1
## y_new[11,40] 19.5 0.0 2.0 15.6 19.5 23.5 4193 1
## y_new[11,41] 19.6 0.0 2.1 15.6 19.6 23.7 4276 1
## y_new[11,42] 19.6 0.0 2.0 15.6 19.6 23.7 4615 1
## y_new[11,43] 19.6 0.0 2.1 15.5 19.6 23.6 4252 1
## y_new[11,44] 19.6 0.0 2.1 15.4 19.6 23.6 4534 1
## y_new[11,45] 19.6 0.0 2.0 15.4 19.6 23.7 4469 1
## y_new[11,46] 19.6 0.0 2.0 15.6 19.6 23.6 4187 1
## y_new[11,47] 19.6 0.0 2.1 15.6 19.6 23.7 4496 1
## y_new[11,48] 19.6 0.0 2.0 15.7 19.6 23.6 4248 1
## y_new[11,49] 19.6 0.0 2.1 15.4 19.6 23.8 3977 1
## y_new[11,50] 19.6 0.0 2.1 15.7 19.6 23.7 4518 1
## y_new[11,51] 19.6 0.0 2.0 15.7 19.6 23.7 4104 1
## y_new[11,52] 19.6 0.0 2.1 15.6 19.6 23.7 4187 1
## y_new[11,53] 19.6 0.0 2.1 15.3 19.6 23.7 4628 1
## y_new[11,54] 19.7 0.0 2.0 15.7 19.7 23.7 4360 1
## y_new[11,55] 19.7 0.0 2.1 15.7 19.7 23.7 4103 1
## y_new[11,56] 19.6 0.0 2.1 15.5 19.6 23.6 4381 1
## y_new[11,57] 19.6 0.0 2.1 15.7 19.7 23.6 4445 1
## y_new[11,58] 19.6 0.0 2.1 15.7 19.6 23.6 4445 1
## y_new[11,59] 19.6 0.0 2.1 15.5 19.6 23.7 3921 1
## y_new[11,60] 19.6 0.0 2.1 15.6 19.6 23.8 4127 1
## y_new[12,1] 0.0 0.0 1.7 -3.4 0.0 3.3 3924 1
## y_new[12,2] 3.1 0.0 1.8 -0.5 3.1 6.6 3881 1
## y_new[12,3] 5.5 0.0 2.0 1.7 5.5 9.4 4344 1
## y_new[12,4] 7.6 0.0 2.0 3.6 7.6 11.5 3507 1
## y_new[12,5] 9.2 0.0 2.0 5.2 9.1 13.2 3922 1
## y_new[12,6] 10.4 0.0 2.0 6.5 10.4 14.3 3841 1
## y_new[12,7] 11.5 0.0 2.0 7.7 11.5 15.4 3960 1
## y_new[12,8] 12.4 0.0 2.0 8.4 12.4 16.3 4357 1
## y_new[12,9] 13.0 0.0 2.0 9.1 13.1 16.8 4534 1
## y_new[12,10] 13.6 0.0 1.9 9.8 13.6 17.5 4235 1
## y_new[12,11] 14.2 0.0 1.9 10.4 14.2 18.0 4347 1
## y_new[12,12] 14.5 0.0 1.9 10.7 14.5 18.3 4251 1
## y_new[12,13] 14.8 0.0 1.9 11.0 14.8 18.5 4444 1
## y_new[12,14] 15.1 0.0 1.9 11.4 15.0 18.7 4161 1
## y_new[12,15] 15.3 0.0 1.9 11.4 15.3 18.9 4401 1
## y_new[12,16] 15.4 0.0 1.9 11.7 15.4 19.1 4057 1
## y_new[12,17] 15.6 0.0 1.9 11.9 15.6 19.3 4500 1
## y_new[12,18] 15.7 0.0 1.9 12.0 15.8 19.4 4024 1
## y_new[12,19] 15.8 0.0 1.9 12.0 15.9 19.5 4331 1
## y_new[12,20] 15.9 0.0 1.9 12.1 15.9 19.7 4638 1
## y_new[12,21] 16.0 0.0 1.9 12.2 16.0 19.7 4018 1
## y_new[12,22] 16.0 0.0 1.9 12.3 16.0 19.8 4412 1
## y_new[12,23] 16.0 0.0 2.0 12.1 16.0 19.9 4455 1
## y_new[12,24] 16.1 0.0 1.9 12.3 16.1 20.0 4048 1
## y_new[12,25] 16.1 0.0 1.9 12.4 16.1 20.0 4361 1
## y_new[12,26] 16.2 0.0 2.0 12.4 16.3 19.9 4425 1
## y_new[12,27] 16.2 0.0 1.9 12.3 16.3 20.1 4013 1
## y_new[12,28] 16.2 0.0 1.9 12.3 16.2 19.9 3954 1
## y_new[12,29] 16.3 0.0 2.0 12.4 16.2 20.1 4151 1
## y_new[12,30] 16.2 0.0 1.9 12.4 16.3 20.0 4071 1
## y_new[12,31] 16.3 0.0 1.9 12.6 16.2 20.1 4174 1
## y_new[12,32] 16.3 0.0 2.0 12.4 16.3 20.1 4396 1
## y_new[12,33] 16.3 0.0 2.0 12.4 16.3 20.1 4043 1
## y_new[12,34] 16.3 0.0 1.9 12.5 16.3 20.2 4169 1
## y_new[12,35] 16.3 0.0 2.0 12.4 16.3 20.2 3755 1
## y_new[12,36] 16.3 0.0 1.9 12.4 16.3 20.1 4167 1
## y_new[12,37] 16.3 0.0 2.0 12.4 16.4 20.2 4504 1
## y_new[12,38] 16.3 0.0 1.9 12.5 16.3 20.0 4301 1
## y_new[12,39] 16.3 0.0 2.0 12.4 16.3 20.2 4215 1
## y_new[12,40] 16.4 0.0 2.0 12.5 16.3 20.3 3815 1
## y_new[12,41] 16.3 0.0 2.0 12.4 16.3 20.3 4184 1
## y_new[12,42] 16.3 0.0 2.0 12.4 16.4 20.2 3901 1
## y_new[12,43] 16.3 0.0 2.0 12.5 16.3 20.2 4261 1
## y_new[12,44] 16.3 0.0 2.0 12.6 16.3 20.3 4071 1
## y_new[12,45] 16.3 0.0 2.0 12.5 16.3 20.0 4104 1
## y_new[12,46] 16.4 0.0 2.0 12.5 16.4 20.2 4413 1
## y_new[12,47] 16.4 0.0 1.9 12.6 16.4 20.2 4040 1
## y_new[12,48] 16.3 0.0 2.0 12.5 16.3 20.3 4206 1
## y_new[12,49] 16.3 0.0 2.0 12.4 16.4 20.0 4001 1
## y_new[12,50] 16.3 0.0 2.0 12.4 16.3 20.2 4031 1
## y_new[12,51] 16.3 0.0 2.0 12.5 16.3 20.4 4049 1
## y_new[12,52] 16.3 0.0 2.0 12.5 16.3 20.2 4326 1
## y_new[12,53] 16.3 0.0 2.0 12.3 16.3 20.3 4279 1
## y_new[12,54] 16.4 0.0 2.0 12.5 16.4 20.2 4617 1
## y_new[12,55] 16.4 0.0 2.0 12.6 16.4 20.2 4208 1
## y_new[12,56] 16.4 0.0 1.9 12.6 16.4 20.2 3915 1
## y_new[12,57] 16.3 0.0 2.0 12.4 16.3 20.2 4082 1
## y_new[12,58] 16.3 0.0 2.0 12.4 16.4 20.1 4095 1
## y_new[12,59] 16.3 0.0 2.0 12.5 16.3 20.3 4293 1
## y_new[12,60] 16.4 0.0 2.0 12.4 16.4 20.2 4097 1
## y_new[13,1] 0.0 0.0 1.7 -3.4 0.0 3.3 3789 1
## y_new[13,2] 1.0 0.0 1.7 -2.4 1.0 4.5 4061 1
## y_new[13,3] 1.9 0.0 1.8 -1.5 1.9 5.4 4284 1
## y_new[13,4] 2.8 0.0 1.8 -0.9 2.8 6.4 4006 1
## y_new[13,5] 3.5 0.0 1.9 0.0 3.5 7.2 4054 1
## y_new[13,6] 4.2 0.0 1.9 0.4 4.2 7.8 4027 1
## y_new[13,7] 4.8 0.0 1.9 1.2 4.8 8.5 4369 1
## y_new[13,8] 5.4 0.0 1.9 1.8 5.4 9.3 3920 1
## y_new[13,9] 5.9 0.0 1.9 2.2 5.9 9.8 4298 1
## y_new[13,10] 6.4 0.0 1.9 2.5 6.4 10.2 4068 1
## y_new[13,11] 6.8 0.0 1.9 3.1 6.8 10.6 3774 1
## y_new[13,12] 7.2 0.0 1.9 3.4 7.2 10.9 4045 1
## y_new[13,13] 7.5 0.0 1.9 3.7 7.6 11.2 4207 1
## y_new[13,14] 7.8 0.0 2.0 4.0 7.8 11.7 3993 1
## y_new[13,15] 8.1 0.0 1.9 4.4 8.1 12.0 3764 1
## y_new[13,16] 8.4 0.0 1.9 4.7 8.4 12.3 3894 1
## y_new[13,17] 8.7 0.0 1.9 4.9 8.7 12.5 4141 1
## y_new[13,18] 8.9 0.0 2.0 5.0 9.0 12.7 3889 1
## y_new[13,19] 9.2 0.0 1.9 5.5 9.1 13.0 3923 1
## y_new[13,20] 9.3 0.0 1.9 5.5 9.3 13.1 3765 1
## y_new[13,21] 9.5 0.0 1.9 5.6 9.5 13.1 4026 1
## y_new[13,22] 9.6 0.0 1.9 5.8 9.7 13.4 4001 1
## y_new[13,23] 9.8 0.0 1.9 6.1 9.8 13.5 4562 1
## y_new[13,24] 9.9 0.0 1.9 6.0 9.9 13.8 4089 1
## y_new[13,25] 10.1 0.0 1.9 6.2 10.1 13.7 4005 1
## y_new[13,26] 10.2 0.0 2.0 6.4 10.2 14.2 4393 1
## y_new[13,27] 10.3 0.0 2.0 6.4 10.3 14.2 3755 1
## y_new[13,28] 10.4 0.0 1.9 6.6 10.3 14.2 4042 1
## y_new[13,29] 10.4 0.0 1.9 6.5 10.4 14.2 4349 1
## y_new[13,30] 10.5 0.0 1.9 6.6 10.4 14.2 4064 1
## y_new[13,31] 10.6 0.0 1.9 6.9 10.6 14.3 4113 1
## y_new[13,32] 10.7 0.0 2.0 6.8 10.7 14.5 3950 1
## y_new[13,33] 10.8 0.0 2.0 6.9 10.7 14.8 4139 1
## y_new[13,34] 10.8 0.0 2.0 6.9 10.8 14.5 4031 1
## y_new[13,35] 10.8 0.0 2.0 7.0 10.9 14.7 4066 1
## y_new[13,36] 10.9 0.0 2.0 7.0 10.9 14.9 3794 1
## y_new[13,37] 10.9 0.0 2.0 7.1 10.9 14.9 4147 1
## y_new[13,38] 11.0 0.0 2.0 7.1 10.9 14.9 3851 1
## y_new[13,39] 11.1 0.0 2.0 7.3 11.0 15.1 4008 1
## y_new[13,40] 11.1 0.0 2.0 7.2 11.1 15.0 4325 1
## y_new[13,41] 11.1 0.0 2.0 7.1 11.1 15.1 4105 1
## y_new[13,42] 11.1 0.0 2.0 7.1 11.1 15.1 3976 1
## y_new[13,43] 11.2 0.0 2.0 7.3 11.2 15.1 3807 1
## y_new[13,44] 11.3 0.0 2.1 7.2 11.2 15.3 4237 1
## y_new[13,45] 11.2 0.0 2.0 7.3 11.2 15.2 3964 1
## y_new[13,46] 11.3 0.0 2.0 7.2 11.3 15.3 4382 1
## y_new[13,47] 11.3 0.0 2.1 7.0 11.3 15.5 4158 1
## y_new[13,48] 11.3 0.0 2.1 7.3 11.3 15.3 4501 1
## y_new[13,49] 11.3 0.0 2.1 7.1 11.3 15.4 3565 1
## y_new[13,50] 11.4 0.0 2.1 7.2 11.3 15.6 4116 1
## y_new[13,51] 11.3 0.0 2.1 7.2 11.3 15.4 4148 1
## y_new[13,52] 11.4 0.0 2.1 7.4 11.4 15.5 3772 1
## y_new[13,53] 11.4 0.0 2.1 7.3 11.3 15.4 4273 1
## y_new[13,54] 11.4 0.0 2.2 7.0 11.4 15.6 4048 1
## y_new[13,55] 11.4 0.0 2.1 7.2 11.4 15.5 4183 1
## y_new[13,56] 11.4 0.0 2.1 7.2 11.3 15.6 4294 1
## y_new[13,57] 11.4 0.0 2.2 7.2 11.4 15.8 3887 1
## y_new[13,58] 11.5 0.0 2.1 7.3 11.4 15.7 3907 1
## y_new[13,59] 11.5 0.0 2.1 7.4 11.5 15.6 4023 1
## y_new[13,60] 11.5 0.0 2.1 7.2 11.4 15.6 3888 1
## y_new[14,1] 0.0 0.0 1.7 -3.3 0.0 3.4 4085 1
## y_new[14,2] 2.4 0.0 1.7 -0.9 2.4 5.8 4048 1
## y_new[14,3] 4.6 0.0 1.8 1.0 4.6 8.1 3868 1
## y_new[14,4] 6.6 0.0 1.9 3.0 6.6 10.3 4087 1
## y_new[14,5] 8.3 0.0 1.9 4.6 8.3 12.0 3965 1
## y_new[14,6] 9.8 0.0 1.9 6.1 9.8 13.5 4164 1
## y_new[14,7] 11.3 0.0 2.0 7.6 11.3 15.2 4106 1
## y_new[14,8] 12.6 0.0 2.0 8.7 12.6 16.4 4094 1
## y_new[14,9] 13.8 0.0 2.0 9.9 13.8 17.7 4257 1
## y_new[14,10] 14.9 0.0 2.0 10.9 14.8 18.8 4269 1
## y_new[14,11] 15.8 0.0 2.0 11.9 15.8 19.9 4041 1
## y_new[14,12] 16.6 0.0 2.0 12.8 16.6 20.5 3795 1
## y_new[14,13] 17.5 0.0 2.0 13.6 17.5 21.5 3680 1
## y_new[14,14] 18.2 0.0 2.0 14.2 18.2 22.1 3907 1
## y_new[14,15] 18.8 0.0 2.0 14.9 18.8 22.6 4243 1
## y_new[14,16] 19.4 0.0 1.9 15.6 19.4 23.1 4167 1
## y_new[14,17] 19.8 0.0 1.9 16.1 19.8 23.6 4059 1
## y_new[14,18] 20.3 0.0 1.9 16.6 20.4 23.9 4008 1
## y_new[14,19] 20.7 0.0 1.9 16.9 20.7 24.6 4052 1
## y_new[14,20] 21.1 0.0 1.9 17.2 21.1 24.8 3923 1
## y_new[14,21] 21.5 0.0 1.9 17.8 21.5 25.4 4021 1
## y_new[14,22] 21.8 0.0 1.9 18.1 21.8 25.5 4069 1
## y_new[14,23] 22.1 0.0 1.9 18.4 22.1 25.8 4001 1
## y_new[14,24] 22.4 0.0 1.9 18.5 22.4 26.1 4054 1
## y_new[14,25] 22.6 0.0 1.9 18.8 22.6 26.4 3867 1
## y_new[14,26] 22.8 0.0 2.0 19.1 22.8 26.7 4208 1
## y_new[14,27] 22.9 0.0 1.9 19.1 22.9 26.7 4232 1
## y_new[14,28] 23.2 0.0 2.0 19.2 23.1 26.9 4354 1
## y_new[14,29] 23.3 0.0 1.9 19.4 23.3 27.0 4203 1
## y_new[14,30] 23.4 0.0 2.0 19.6 23.4 27.2 4041 1
## y_new[14,31] 23.6 0.0 2.0 19.7 23.6 27.4 3814 1
## y_new[14,32] 23.7 0.0 1.9 19.9 23.7 27.6 4278 1
## y_new[14,33] 23.8 0.0 2.0 19.9 23.8 27.7 4144 1
## y_new[14,34] 23.9 0.0 2.0 20.0 23.9 27.7 4278 1
## y_new[14,35] 24.0 0.0 2.0 20.2 24.0 27.9 4221 1
## y_new[14,36] 24.1 0.0 2.0 20.1 24.1 28.1 3885 1
## y_new[14,37] 24.1 0.0 2.0 20.0 24.1 28.0 4152 1
## y_new[14,38] 24.2 0.0 2.0 20.4 24.1 28.0 4426 1
## y_new[14,39] 24.3 0.0 2.0 20.3 24.3 28.2 4468 1
## y_new[14,40] 24.3 0.0 2.1 20.1 24.4 28.2 3966 1
## y_new[14,41] 24.4 0.0 2.1 20.4 24.4 28.6 4462 1
## y_new[14,42] 24.4 0.0 2.1 20.3 24.4 28.4 3732 1
## y_new[14,43] 24.5 0.0 2.1 20.4 24.4 28.5 4232 1
## y_new[14,44] 24.5 0.0 2.1 20.2 24.5 28.5 4137 1
## y_new[14,45] 24.5 0.0 2.1 20.4 24.5 28.6 4306 1
## y_new[14,46] 24.5 0.0 2.1 20.5 24.5 28.5 4205 1
## y_new[14,47] 24.6 0.0 2.1 20.4 24.6 28.5 4286 1
## y_new[14,48] 24.6 0.0 2.1 20.4 24.6 28.7 4149 1
## y_new[14,49] 24.7 0.0 2.1 20.5 24.6 28.7 4248 1
## y_new[14,50] 24.7 0.0 2.1 20.6 24.6 28.9 4425 1
## y_new[14,51] 24.7 0.0 2.1 20.5 24.7 29.0 4574 1
## y_new[14,52] 24.7 0.0 2.1 20.6 24.7 28.9 3982 1
## y_new[14,53] 24.6 0.0 2.1 20.4 24.7 28.7 3786 1
## y_new[14,54] 24.7 0.0 2.1 20.6 24.7 28.9 4666 1
## y_new[14,55] 24.7 0.0 2.1 20.7 24.8 29.0 4544 1
## y_new[14,56] 24.7 0.0 2.1 20.6 24.7 28.8 3975 1
## y_new[14,57] 24.8 0.0 2.1 20.5 24.8 28.9 3970 1
## y_new[14,58] 24.7 0.0 2.1 20.7 24.7 29.0 4451 1
## y_new[14,59] 24.8 0.0 2.1 20.6 24.7 29.1 4268 1
## y_new[14,60] 24.8 0.0 2.2 20.5 24.8 29.0 4145 1
## y_new[15,1] 0.0 0.0 1.7 -3.3 0.0 3.4 3936 1
## y_new[15,2] 2.1 0.0 1.7 -1.3 2.1 5.5 3959 1
## y_new[15,3] 3.8 0.0 1.7 0.4 3.8 7.2 4203 1
## y_new[15,4] 5.3 0.0 1.8 1.7 5.3 8.9 4327 1
## y_new[15,5] 6.7 0.0 1.9 3.0 6.7 10.5 3914 1
## y_new[15,6] 7.9 0.0 2.0 4.1 7.9 11.8 4299 1
## y_new[15,7] 9.0 0.0 1.9 5.2 8.9 12.8 3947 1
## y_new[15,8] 9.8 0.0 1.9 6.1 9.8 13.5 4248 1
## y_new[15,9] 10.6 0.0 2.0 6.7 10.6 14.6 4216 1
## y_new[15,10] 11.4 0.0 1.9 7.5 11.3 15.3 4307 1
## y_new[15,11] 12.0 0.0 1.9 8.1 12.0 15.9 4259 1
## y_new[15,12] 12.5 0.0 1.9 8.8 12.5 16.2 4262 1
## y_new[15,13] 13.0 0.0 1.9 9.0 13.0 16.8 4210 1
## y_new[15,14] 13.4 0.0 1.9 9.6 13.4 17.3 3490 1
## y_new[15,15] 13.8 0.0 1.9 10.0 13.8 17.6 4046 1
## y_new[15,16] 14.1 0.0 1.9 10.3 14.0 17.8 3982 1
## y_new[15,17] 14.4 0.0 1.9 10.7 14.5 18.2 3719 1
## y_new[15,18] 14.7 0.0 1.9 11.0 14.7 18.5 4049 1
## y_new[15,19] 14.9 0.0 1.9 11.1 14.9 18.8 3833 1
## y_new[15,20] 15.1 0.0 1.9 11.3 15.0 18.9 4028 1
## y_new[15,21] 15.3 0.0 1.9 11.4 15.3 19.0 4178 1
## y_new[15,22] 15.4 0.0 1.9 11.6 15.4 19.2 4366 1
## y_new[15,23] 15.6 0.0 1.9 11.8 15.6 19.3 4213 1
## y_new[15,24] 15.7 0.0 1.9 11.8 15.7 19.5 4175 1
## y_new[15,25] 15.8 0.0 1.9 12.0 15.8 19.7 4314 1
## y_new[15,26] 15.8 0.0 2.0 11.9 15.8 19.7 4235 1
## y_new[15,27] 15.9 0.0 1.9 12.1 15.9 19.7 4173 1
## y_new[15,28] 16.1 0.0 1.9 12.1 16.1 19.8 4287 1
## y_new[15,29] 16.1 0.0 2.0 12.3 16.1 20.1 3824 1
## y_new[15,30] 16.2 0.0 1.9 12.5 16.2 19.9 3955 1
## y_new[15,31] 16.2 0.0 2.0 12.4 16.2 20.0 4368 1
## y_new[15,32] 16.3 0.0 2.0 12.4 16.3 20.2 4432 1
## y_new[15,33] 16.3 0.0 2.0 12.5 16.3 20.2 4104 1
## y_new[15,34] 16.3 0.0 2.0 12.5 16.4 20.2 4452 1
## y_new[15,35] 16.4 0.0 2.0 12.7 16.4 20.3 4459 1
## y_new[15,36] 16.4 0.0 2.0 12.4 16.4 20.4 3999 1
## y_new[15,37] 16.5 0.0 2.0 12.7 16.5 20.4 3613 1
## y_new[15,38] 16.5 0.0 2.0 12.5 16.5 20.4 4611 1
## y_new[15,39] 16.5 0.0 2.0 12.6 16.5 20.4 4138 1
## y_new[15,40] 16.5 0.0 2.0 12.7 16.5 20.4 4444 1
## y_new[15,41] 16.5 0.0 2.0 12.6 16.6 20.5 3217 1
## y_new[15,42] 16.6 0.0 2.0 12.7 16.6 20.5 3971 1
## y_new[15,43] 16.6 0.0 2.0 12.6 16.6 20.5 4426 1
## y_new[15,44] 16.5 0.0 2.0 12.7 16.6 20.4 4020 1
## y_new[15,45] 16.6 0.0 2.1 12.6 16.6 20.7 4195 1
## y_new[15,46] 16.6 0.0 2.1 12.6 16.5 20.8 4125 1
## y_new[15,47] 16.6 0.0 2.0 12.7 16.6 20.6 4559 1
## y_new[15,48] 16.6 0.0 2.0 12.5 16.7 20.6 4245 1
## y_new[15,49] 16.6 0.0 2.0 12.6 16.6 20.6 4460 1
## y_new[15,50] 16.7 0.0 2.0 12.6 16.7 20.7 4526 1
## y_new[15,51] 16.7 0.0 2.0 12.7 16.7 20.7 4200 1
## y_new[15,52] 16.6 0.0 2.0 12.6 16.6 20.7 3982 1
## y_new[15,53] 16.6 0.0 2.1 12.6 16.6 20.7 4438 1
## y_new[15,54] 16.6 0.0 2.0 12.6 16.6 20.7 4491 1
## y_new[15,55] 16.6 0.0 2.0 12.7 16.6 20.7 4230 1
## y_new[15,56] 16.6 0.0 2.0 12.7 16.6 20.6 4604 1
## y_new[15,57] 16.6 0.0 2.1 12.5 16.6 20.8 4280 1
## y_new[15,58] 16.6 0.0 2.1 12.6 16.6 20.8 4424 1
## y_new[15,59] 16.7 0.0 2.1 12.6 16.7 20.8 4306 1
## y_new[15,60] 16.6 0.0 2.0 12.8 16.6 20.6 4458 1
## y_new[16,1] 0.0 0.0 1.7 -3.3 0.0 3.3 4214 1
## y_new[16,2] 6.0 0.0 1.8 2.5 6.0 9.6 3957 1
## y_new[16,3] 10.9 0.0 2.0 7.0 10.9 14.7 4278 1
## y_new[16,4] 14.8 0.0 2.1 10.8 14.8 18.9 4506 1
## y_new[16,5] 18.0 0.0 2.0 13.9 18.0 22.0 4423 1
## y_new[16,6] 20.5 0.0 2.1 16.4 20.6 24.6 4048 1
## y_new[16,7] 22.6 0.0 2.0 18.7 22.6 26.6 4446 1
## y_new[16,8] 24.4 0.0 2.0 20.4 24.4 28.4 3906 1
## y_new[16,9] 25.7 0.0 2.0 21.7 25.8 29.6 4326 1
## y_new[16,10] 26.9 0.0 2.0 22.9 26.9 30.8 4206 1
## y_new[16,11] 27.8 0.0 2.0 23.9 27.8 31.6 4180 1
## y_new[16,12] 28.5 0.0 1.9 24.8 28.5 32.3 3735 1
## y_new[16,13] 29.1 0.0 1.9 25.5 29.1 32.8 4273 1
## y_new[16,14] 29.6 0.0 1.9 25.8 29.7 33.4 4075 1
## y_new[16,15] 30.0 0.0 1.9 26.2 30.0 33.7 4118 1
## y_new[16,16] 30.3 0.0 1.9 26.6 30.3 34.0 4239 1
## y_new[16,17] 30.6 0.0 1.9 26.9 30.6 34.4 3783 1
## y_new[16,18] 30.8 0.0 1.9 27.0 30.9 34.7 4011 1
## y_new[16,19] 31.1 0.0 2.0 27.2 31.1 34.9 4058 1
## y_new[16,20] 31.2 0.0 1.9 27.3 31.2 35.0 4222 1
## y_new[16,21] 31.3 0.0 2.0 27.4 31.3 35.1 4366 1
## y_new[16,22] 31.5 0.0 2.0 27.5 31.5 35.3 4269 1
## y_new[16,23] 31.5 0.0 2.0 27.6 31.5 35.3 3958 1
## y_new[16,24] 31.6 0.0 2.0 27.7 31.6 35.6 3913 1
## y_new[16,25] 31.6 0.0 2.0 27.7 31.6 35.5 4060 1
## y_new[16,26] 31.6 0.0 2.0 27.8 31.6 35.5 4172 1
## y_new[16,27] 31.7 0.0 2.0 28.0 31.7 35.5 4065 1
## y_new[16,28] 31.7 0.0 2.0 28.0 31.7 35.6 4422 1
## y_new[16,29] 31.7 0.0 2.0 27.9 31.7 35.6 4085 1
## y_new[16,30] 31.8 0.0 2.0 27.8 31.7 35.8 3003 1
## y_new[16,31] 31.8 0.0 2.0 28.0 31.8 35.8 4136 1
## y_new[16,32] 31.8 0.0 2.0 27.8 31.8 35.7 4216 1
## y_new[16,33] 31.8 0.0 2.0 28.0 31.8 35.8 4206 1
## y_new[16,34] 31.8 0.0 2.0 28.0 31.8 35.6 4555 1
## y_new[16,35] 31.8 0.0 2.0 28.0 31.8 35.7 3828 1
## y_new[16,36] 31.9 0.0 2.0 28.0 31.9 35.9 4246 1
## y_new[16,37] 31.8 0.0 2.0 27.8 31.8 35.7 4286 1
## y_new[16,38] 31.9 0.0 2.0 27.8 31.8 35.9 3645 1
## y_new[16,39] 31.9 0.0 2.0 27.8 31.8 35.8 4141 1
## y_new[16,40] 31.8 0.0 2.0 27.9 31.8 35.8 4192 1
## y_new[16,41] 31.9 0.0 2.0 27.8 31.9 36.0 4268 1
## y_new[16,42] 31.8 0.0 2.0 27.9 31.8 35.9 3906 1
## y_new[16,43] 31.8 0.0 2.0 27.9 31.8 35.8 4214 1
## y_new[16,44] 31.8 0.0 2.0 27.9 31.9 35.8 4175 1
## y_new[16,45] 31.8 0.0 2.0 28.0 31.8 35.7 3970 1
## y_new[16,46] 31.9 0.0 2.0 27.9 31.9 35.9 4307 1
## y_new[16,47] 31.9 0.0 2.0 27.9 31.9 36.0 3909 1
## y_new[16,48] 31.8 0.0 2.0 27.9 31.8 35.8 4486 1
## y_new[16,49] 31.9 0.0 2.0 27.9 31.9 35.8 4483 1
## y_new[16,50] 31.9 0.0 2.0 28.1 31.9 35.9 4096 1
## y_new[16,51] 31.8 0.0 2.0 27.8 31.8 35.9 4591 1
## y_new[16,52] 31.8 0.0 2.0 27.9 31.8 35.7 4045 1
## y_new[16,53] 31.9 0.0 2.0 28.0 31.9 35.8 4316 1
## y_new[16,54] 31.9 0.0 2.0 27.8 31.9 35.8 4513 1
## y_new[16,55] 31.9 0.0 2.0 27.9 31.9 35.8 3886 1
## y_new[16,56] 31.9 0.0 2.0 27.9 31.9 35.9 4442 1
## y_new[16,57] 31.8 0.0 2.0 27.9 31.8 35.8 4257 1
## y_new[16,58] 31.8 0.0 2.0 27.8 31.8 35.8 4555 1
## y_new[16,59] 31.8 0.0 2.0 27.9 31.8 35.6 4135 1
## y_new[16,60] 31.9 0.0 2.0 27.9 31.9 36.0 3969 1
## lp__ -113.6 0.1 5.3 -125.1 -113.1 -104.5 1259 1
##
## Samples were drawn using NUTS(diag_e) at Tue Dec 26 23:07:53 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).MCMCで得られたデータを利用して予測分布を可視化する。
ms <- rstan::extract(fit_)
d_est <- data.frame()
for (n in 1:nrow(d)) {
qua <- apply(ms$y_new[,n,], 2, quantile, prob = c(0.025, 0.5, 0.975))
d_est <- rbind(d_est, data.frame(PersonID = n, Time = Time_new, t(qua), check.names = FALSE))
}
ggplot(data = d_est, aes(x = Time, y = `50%`)) +
theme_bw(base_size = 15) +
facet_wrap(~PersonID) +
geom_ribbon(aes(ymin = `2.5%`, ymax = `97.5%`), fill = 'black', alpha = 1/5) +
geom_line(linewidth = 0.5) +
geom_point(data = d2, aes(x = Time, y = Y), size = 3) +
labs(x = 'Time (hour)', y = 'Y') +
scale_x_continuous(breaks = Time, limit = c(0,24)) +
scale_y_continuous(breaks = seq(0,40,10), limit = c(-3,37))