library(MASS)
head (Boston)
##      crim zn indus chas   nox    rm  age    dis rad tax ptratio  black lstat
## 1 0.00632 18  2.31    0 0.538 6.575 65.2 4.0900   1 296    15.3 396.90  4.98
## 2 0.02731  0  7.07    0 0.469 6.421 78.9 4.9671   2 242    17.8 396.90  9.14
## 3 0.02729  0  7.07    0 0.469 7.185 61.1 4.9671   2 242    17.8 392.83  4.03
## 4 0.03237  0  2.18    0 0.458 6.998 45.8 6.0622   3 222    18.7 394.63  2.94
## 5 0.06905  0  2.18    0 0.458 7.147 54.2 6.0622   3 222    18.7 396.90  5.33
## 6 0.02985  0  2.18    0 0.458 6.430 58.7 6.0622   3 222    18.7 394.12  5.21
##   medv
## 1 24.0
## 2 21.6
## 3 34.7
## 4 33.4
## 5 36.2
## 6 28.7
dat <- Boston[, c("age", "medv", "crim", "tax", "dis")]
head (dat)
##    age medv    crim tax    dis
## 1 65.2 24.0 0.00632 296 4.0900
## 2 78.9 21.6 0.02731 242 4.9671
## 3 61.1 34.7 0.02729 242 4.9671
## 4 45.8 33.4 0.03237 222 6.0622
## 5 54.2 36.2 0.06905 222 6.0622
## 6 58.7 28.7 0.02985 222 6.0622
correlation_matrix <- cor(dat[, c("medv", "dis", "crim", "age")])

# Korelasyon matrisini görüntüleme
print(correlation_matrix)
##            medv        dis       crim        age
## medv  1.0000000  0.2499287 -0.3883046 -0.3769546
## dis   0.2499287  1.0000000 -0.3796701 -0.7478805
## crim -0.3883046 -0.3796701  1.0000000  0.3527343
## age  -0.3769546 -0.7478805  0.3527343  1.0000000

#en yüksek korelasyon crim değişkeni ile olduğu için ondan başlıyoruz.

library(knitr)
library(broom)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:MASS':
## 
##     select
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(magrittr)
model1  <- lm(medv ~ crim , data = dat)
glance(model1) %>%  kable(digit=3)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.151 0.149 8.484 89.486 0 1 -1798.89 3603.781 3616.46 36275.51 504 506
model2 <- lm(medv ~ crim + age, data = dat)
glance(model2) %>%  kable(digit=3)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.217 0.213 8.157 69.519 0 2 -1778.493 3564.987 3581.893 33465.74 503 506
model3  <- lm(medv ~ age + crim + dis, data=dat)
glance(model3) %>%  kable(digit=3)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.227 0.222 8.112 49.064 0 3 -1775.187 3560.374 3581.506 33031.21 502 506
tidy(anova(model1, model2, model3))
## # A tibble: 3 × 7
##   term                    df.residual    rss    df sumsq statistic   p.value
##   <chr>                         <dbl>  <dbl> <dbl> <dbl>     <dbl>     <dbl>
## 1 medv ~ crim                     504 36276.    NA   NA      NA    NA       
## 2 medv ~ crim + age               503 33466.     1 2810.     42.7   1.57e-10
## 3 medv ~ age + crim + dis         502 33031.     1  435.      6.60  1.05e- 2

#Değişken ekledikçe hem hatalar azaldı hemde F değerleri istatistiksel olarak anlamlı bulundu bu yüzden eklediğimiz değişkenlerle regresyon yapılabilir.

Etkili Gözlemlerin Belirlenmesi

Cook’s D

library(olsrr)
## 
## Attaching package: 'olsrr'
## The following object is masked from 'package:MASS':
## 
##     cement
## The following object is masked from 'package:datasets':
## 
##     rivers
ols_plot_cooksd_bar(model3)

#çizginin üzerindeki gözlemler etkili gözlemdir. Çok fazla veri olduğu için grafiği büyüterek bakmak gerekebilir. ## DFBETA

ols_plot_dfbetas(model3)

#kesişim ve bağımsız değişkenler için Threshold değerlerini geçen gözlemler etkili gözlemlerdir.

influence.measures(model3, infl = influence(model3))
## Influence measures of
##   lm(formula = medv ~ age + crim + dis, data = dat) :
## 
##        dfb.1_   dfb.age  dfb.crim   dfb.dis     dffit cov.r   cook.d     hat
## 1    4.05e-05  4.87e-06 -8.89e-05  1.75e-07  0.000244 1.010 1.49e-08 0.00233
## 2    2.80e-04 -3.17e-04  9.31e-05 -3.04e-04 -0.000439 1.014 4.83e-08 0.00560
## 3   -1.14e-02  1.51e-02 -1.49e-02  2.88e-02  0.071077 0.997 1.26e-03 0.00281
## 4   -6.85e-03 -2.27e-04 -3.48e-04  3.21e-02  0.067631 1.004 1.14e-03 0.00427
## 5   -3.81e-02  3.01e-02 -3.61e-03  6.87e-02  0.103526 0.994 2.67e-03 0.00467
## 6   -2.29e-02  2.00e-02 -2.49e-03  3.45e-02  0.047118 1.010 5.56e-04 0.00521
## 7   -6.40e-04  6.43e-04 -1.46e-04  8.47e-04  0.001175 1.013 3.46e-07 0.00484
## 8   -1.19e-01  1.23e-01 -1.45e-02  1.18e-01  0.139504 1.018 4.86e-03 0.01790
## 9    2.71e-02 -2.77e-02  2.94e-03 -2.64e-02 -0.031080 1.029 2.42e-04 0.02122
## 10   1.01e-02 -9.84e-03  6.49e-04 -1.06e-02 -0.011935 1.026 3.57e-05 0.01715
## 11   5.71e-02 -5.73e-02  4.94e-03 -5.75e-02 -0.066011 1.027 1.09e-03 0.01988
## 12   1.59e-02 -1.58e-02  1.50e-03 -1.70e-02 -0.019565 1.021 9.59e-05 0.01316
## 13  -1.48e-02  1.74e-02  1.06e-03  1.75e-04 -0.036611 1.010 3.36e-04 0.00417
## 14   1.15e-03 -2.74e-03  3.92e-03 -6.19e-03 -0.020609 1.009 1.06e-04 0.00247
## 15   1.63e-02 -1.98e-02  6.07e-03 -1.63e-02 -0.026151 1.012 1.71e-04 0.00536
## 16  -8.63e-03  6.27e-03  5.36e-03  4.96e-04 -0.028378 1.008 2.02e-04 0.00243
## 17  -4.38e-02  4.48e-02 -2.29e-04  2.73e-02 -0.052742 1.013 6.96e-04 0.00809
## 18   1.68e-02 -2.18e-02  8.29e-03 -1.71e-02 -0.032012 1.010 2.57e-04 0.00414
## 19  -7.15e-02  6.75e-02  6.52e-03  5.17e-02 -0.079829 1.009 1.59e-03 0.00782
## 20  -4.29e-03 -2.60e-03  1.05e-02  9.03e-04 -0.030362 1.007 2.31e-04 0.00225
## 21   4.24e-02 -5.41e-02  1.59e-02 -3.58e-02 -0.064290 1.011 1.03e-03 0.00738
## 22   6.03e-03 -7.86e-03  2.76e-03 -5.48e-03 -0.010218 1.013 2.62e-05 0.00534
## 23   3.03e-02 -3.87e-02  1.17e-02 -2.71e-02 -0.048527 1.011 5.89e-04 0.00586
## 24   4.12e-02 -4.98e-02  1.27e-02 -3.59e-02 -0.056976 1.015 8.13e-04 0.00920
## 25   3.47e-02 -4.10e-02  1.03e-02 -3.20e-02 -0.048142 1.014 5.80e-04 0.00816
## 26   4.17e-02 -5.01e-02  1.40e-02 -4.11e-02 -0.064808 1.008 1.05e-03 0.00562
## 27   2.90e-02 -3.32e-02  7.61e-03 -2.80e-02 -0.039793 1.014 3.97e-04 0.00793
## 28   3.86e-02 -4.57e-02  1.15e-02 -3.71e-02 -0.056530 1.011 8.00e-04 0.00651
## 29   1.18e-02 -1.38e-02  3.31e-03 -1.09e-02 -0.016108 1.016 6.50e-05 0.00849
## 30  -1.33e-03  1.66e-03 -4.98e-04  1.27e-03  0.002148 1.013 1.16e-06 0.00540
## 31   5.39e-02 -6.49e-02  1.62e-02 -4.90e-02 -0.076977 1.009 1.48e-03 0.00746
## 32   4.12e-02 -4.89e-02  1.08e-02 -3.63e-02 -0.055590 1.015 7.74e-04 0.00943
## 33   2.74e-02 -3.89e-02  1.53e-02 -2.74e-02 -0.060996 1.003 9.30e-04 0.00356
## 34   4.27e-02 -5.58e-02  1.81e-02 -3.63e-02 -0.068782 1.008 1.18e-03 0.00635
## 35   4.08e-02 -5.24e-02  1.46e-02 -3.45e-02 -0.063168 1.010 9.98e-04 0.00678
## 36  -1.44e-02  5.51e-03  1.43e-02  1.18e-02 -0.033068 1.007 2.74e-04 0.00269
## 37  -2.24e-02  1.48e-02  1.23e-02  1.78e-02 -0.034148 1.008 2.92e-04 0.00320
## 38  -4.82e-02  4.42e-02  8.76e-03  3.36e-02 -0.056970 1.010 8.12e-04 0.00586
## 39  -4.29e-02  4.12e-02  4.07e-03  3.13e-02 -0.046974 1.017 5.53e-04 0.01018
## 40   1.88e-02 -2.09e-02  5.98e-04 -8.96e-03  0.026422 1.016 1.75e-04 0.00848
## 41   5.56e-02 -6.16e-02  2.63e-03 -2.92e-02  0.073245 1.015 1.34e-03 0.01079
## 42  -4.91e-02  5.56e-02 -4.84e-03  2.65e-02 -0.063289 1.022 1.00e-03 0.01595
## 43  -5.42e-02  6.17e-02 -5.28e-03  2.81e-02 -0.071659 1.019 1.29e-03 0.01406
## 44  -6.12e-02  6.96e-02 -6.03e-03  3.18e-02 -0.080803 1.019 1.63e-03 0.01411
## 45  -9.48e-03  1.30e-02  1.97e-04 -6.00e-03 -0.037888 1.009 3.59e-04 0.00413
## 46  -4.65e-02  4.98e-02  2.09e-03  1.99e-02 -0.071583 1.006 1.28e-03 0.00542
## 47  -4.36e-02  4.68e-02  1.71e-03  1.90e-02 -0.066459 1.007 1.10e-03 0.00554
## 48   3.81e-02 -3.94e-02  5.54e-03 -3.96e-02 -0.047951 1.018 5.76e-04 0.01102
## 49   6.24e-02 -6.44e-02  7.66e-03 -6.17e-02 -0.073420 1.023 1.35e-03 0.01686
## 50   1.89e-02 -1.71e-02  1.52e-03 -2.61e-02 -0.033537 1.012 2.82e-04 0.00585
## 51   1.70e-02 -1.01e-02 -2.73e-03 -3.31e-02 -0.047791 1.012 5.72e-04 0.00637
## 52   1.55e-02 -1.36e-02  8.03e-05 -1.98e-02 -0.022782 1.017 1.30e-04 0.00948
## 53  -8.42e-03  1.37e-02 -3.56e-03 -4.36e-03 -0.028784 1.015 2.07e-04 0.00786
## 54  -1.31e-02  2.15e-02 -5.63e-03 -7.22e-03 -0.045826 1.014 5.26e-04 0.00780
## 55   2.98e-02 -2.08e-02 -4.21e-03 -4.72e-02 -0.058909 1.014 8.69e-04 0.00872
## 56  -3.49e-02  3.49e-03  2.50e-02  8.65e-02  0.131348 1.011 4.31e-03 0.01322
## 57  -4.74e-03  2.98e-03  1.33e-03  7.24e-03  0.008425 1.026 1.78e-05 0.01792
## 58  -5.63e-02  3.62e-02  1.36e-02  8.83e-02  0.105753 1.014 2.80e-03 0.01303
## 59   6.80e-03 -6.41e-05 -4.97e-03 -1.92e-02 -0.031317 1.017 2.46e-04 0.00943
## 60   2.03e-02 -1.33e-02 -2.86e-03 -3.56e-02 -0.048202 1.012 5.82e-04 0.00696
## 61   3.17e-02 -2.79e-02 -6.95e-04 -3.83e-02 -0.042262 1.020 4.47e-04 0.01301
## 62   4.28e-02 -4.19e-02  2.48e-03 -4.37e-02 -0.048831 1.031 5.97e-04 0.02331
## 63  -7.99e-03  7.10e-03  1.10e-04  9.52e-03  0.010463 1.022 2.74e-05 0.01361
## 64  -7.02e-03  4.67e-03  1.53e-03  1.09e-02  0.013172 1.020 4.35e-05 0.01153
## 65  -1.93e-01  1.58e-01  2.25e-02  2.35e-01  0.245665 1.018 1.51e-02 0.02694
## 66  -2.27e-02  3.17e-02 -6.10e-03 -6.99e-04 -0.053599 1.014 7.19e-04 0.00853
## 67  -8.64e-03  2.01e-02 -6.16e-03 -2.10e-02 -0.068589 1.008 1.18e-03 0.00606
## 68  -2.48e-02  3.50e-02 -6.46e-03 -2.64e-03 -0.062765 1.012 9.86e-04 0.00762
## 69  -5.18e-04  1.24e-02 -5.54e-03 -3.13e-02 -0.076837 1.005 1.48e-03 0.00540
## 70  -5.96e-03  1.41e-02 -4.21e-03 -1.57e-02 -0.050643 1.010 6.42e-04 0.00569
## 71  -8.00e-02  8.76e-02 -4.55e-03  4.75e-02 -0.097552 1.019 2.38e-03 0.01556
## 72  -7.18e-02  7.88e-02 -3.01e-03  3.86e-02 -0.093481 1.012 2.19e-03 0.01040
## 73  -9.35e-02  1.02e-01 -5.17e-03  5.50e-02 -0.114595 1.016 3.28e-03 0.01493
## 74  -9.12e-02  1.00e-01 -5.77e-03  5.42e-02 -0.111099 1.018 3.09e-03 0.01579
## 75  -1.20e-01  1.23e-01  3.01e-04  8.55e-02 -0.130485 1.023 4.26e-03 0.02115
## 76  -2.39e-02  2.25e-02  5.43e-03  1.23e-02 -0.036543 1.009 3.34e-04 0.00383
## 77   3.94e-03 -7.69e-03  6.82e-03 -5.07e-03 -0.018262 1.010 8.35e-05 0.00281
## 78  -3.49e-02  3.13e-02  8.21e-03  2.26e-02 -0.045541 1.009 5.19e-04 0.00439
## 79  -2.84e-03  2.37e-03  3.80e-03 -4.60e-03 -0.023055 1.009 1.33e-04 0.00276
## 80  -5.07e-02  4.99e-02  6.02e-03  3.02e-02 -0.065219 1.008 1.06e-03 0.00577
## 81   4.80e-03 -5.42e-03 -1.19e-04 -1.37e-03  0.008696 1.013 1.89e-05 0.00518
## 82  -7.67e-03  8.02e-03 -2.00e-03  9.47e-03  0.013108 1.013 4.30e-05 0.00506
## 83  -1.26e-02  1.42e-02  1.95e-04  4.01e-03 -0.021875 1.013 1.20e-04 0.00547
## 84  -3.26e-03  4.06e-03  1.40e-03 -3.39e-03 -0.017687 1.011 7.84e-05 0.00334
## 85  -5.52e-03  5.22e-03  1.83e-03  1.46e-03 -0.011958 1.011 3.58e-05 0.00314
## 86   3.89e-03 -2.79e-03 -2.77e-03 -8.91e-04  0.010906 1.010 2.98e-05 0.00253
## 87  -1.96e-02  1.82e-02  4.57e-03  1.07e-02 -0.028875 1.010 2.09e-04 0.00392
## 88  -1.36e-02  1.01e-02  6.36e-03  9.42e-03 -0.020830 1.010 1.09e-04 0.00312
## 89  -4.35e-03  8.24e-03 -6.16e-03  3.26e-03  0.014197 1.012 5.05e-05 0.00388
## 90   1.61e-02 -9.79e-03 -1.04e-02 -1.27e-02  0.027164 1.009 1.85e-04 0.00296
## 91  -8.26e-03  4.67e-03  5.57e-03  7.24e-03 -0.013471 1.011 4.55e-05 0.00327
## 92  -3.39e-03  2.16e-04  4.89e-03  3.31e-03 -0.010171 1.011 2.59e-05 0.00288
## 93  -1.58e-02  1.26e-02  5.80e-03  1.15e-02 -0.021126 1.011 1.12e-04 0.00377
## 94  -4.72e-02  4.51e-02  4.85e-03  3.55e-02 -0.050688 1.018 6.43e-04 0.01161
## 95   1.29e-03 -5.06e-03  6.26e-03 -1.40e-03 -0.014128 1.010 5.00e-05 0.00282
## 96   1.62e-02 -1.19e-02 -7.24e-03 -1.24e-02  0.022846 1.010 1.31e-04 0.00344
## 97  -4.57e-03  6.54e-04  6.38e-03  3.41e-03 -0.014698 1.010 5.41e-05 0.00251
## 98   2.83e-03  2.55e-02 -4.57e-02 -1.49e-03  0.100882 0.981 2.53e-03 0.00268
## 99   1.74e-01 -1.60e-01 -2.62e-02 -1.34e-01  0.188596 0.986 8.84e-03 0.00901
## 100  3.29e-02 -2.02e-02 -2.12e-02 -2.50e-02  0.056636 1.002 8.02e-04 0.00289
## 101  7.70e-03  3.34e-03 -1.61e-02 -9.73e-03  0.032078 1.009 2.58e-04 0.00327
## 102  9.42e-03 -3.98e-03 -8.08e-03 -9.12e-03  0.017797 1.011 7.93e-05 0.00330
## 103 -1.54e-03 -8.04e-03  1.37e-02  4.54e-03 -0.027399 1.010 1.88e-04 0.00361
## 104  3.46e-04 -7.61e-03  1.04e-02  2.23e-03 -0.020940 1.011 1.10e-04 0.00381
## 105 -4.18e-04 -5.00e-03  7.66e-03  2.68e-03 -0.014916 1.012 5.57e-05 0.00428
## 106  8.55e-04 -6.94e-03  8.41e-03  2.38e-03 -0.016496 1.013 6.82e-05 0.00536
## 107 -1.08e-03 -6.26e-03  1.02e-02  4.42e-03 -0.019722 1.012 9.74e-05 0.00465
## 108 -6.13e-03 -1.04e-03  9.92e-03  8.59e-03 -0.019243 1.012 9.27e-05 0.00439
## 109  2.19e-03 -6.08e-03  5.50e-03 -1.06e-04 -0.011302 1.013 3.20e-05 0.00533
## 110  1.26e-03 -7.74e-03  9.11e-03  1.56e-03 -0.018413 1.012 8.49e-05 0.00431
## 111 -3.87e-02  3.05e-02  1.22e-02  3.36e-02 -0.043853 1.012 4.81e-04 0.00629
## 112 -5.09e-05 -3.05e-05  1.18e-04  7.00e-05 -0.000232 1.012 1.35e-08 0.00345
## 113  9.06e-04 -9.59e-03  1.22e-02  3.16e-03 -0.023963 1.012 1.44e-04 0.00468
## 114  4.20e-03 -1.15e-02  1.03e-02 -4.94e-04 -0.021446 1.012 1.15e-04 0.00498
## 115 -1.03e-02 -2.26e-03  1.75e-02  1.43e-02 -0.033982 1.010 2.89e-04 0.00412
## 116 -2.16e-03 -8.80e-03  1.55e-02  6.35e-03 -0.030182 1.010 2.28e-04 0.00406
## 117 -1.06e-02  4.33e-03  9.12e-03  1.06e-02 -0.019837 1.011 9.85e-05 0.00347
## 118 -3.68e-03 -4.99e-03  1.26e-02  5.85e-03 -0.024861 1.010 1.55e-04 0.00341
## 119 -1.68e-02  7.72e-03  1.29e-02  1.73e-02 -0.028324 1.010 2.01e-04 0.00400
## 120 -3.18e-02  2.03e-02  1.70e-02  2.93e-02 -0.043897 1.008 4.82e-04 0.00414
## 121 -1.66e-02  9.84e-03  9.56e-03  1.67e-02 -0.023002 1.012 1.33e-04 0.00506
## 122 -6.76e-03 -8.60e-04  1.07e-02  9.19e-03 -0.020607 1.012 1.06e-04 0.00426
## 123 -8.48e-04 -3.48e-03  6.00e-03  2.89e-03 -0.011471 1.013 3.30e-05 0.00492
## 124 -1.33e-04 -1.41e-02  1.94e-02  7.74e-03 -0.037642 1.012 3.55e-04 0.00553
## 125 -3.81e-04 -8.85e-03  1.27e-02  5.16e-03 -0.024526 1.013 1.51e-04 0.00534
## 126 -2.25e-03 -1.04e-03  4.50e-03  3.58e-03 -0.008679 1.013 1.89e-05 0.00471
## 127 -6.35e-03 -1.46e-02  2.76e-02  1.72e-02 -0.054315 1.009 7.38e-04 0.00551
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## 158  1.97e-03  6.70e-02 -8.28e-02 -3.96e-02  0.182543 0.964 8.24e-03 0.00522
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## 178  1.78e-03  4.06e-04 -3.47e-03 -1.58e-03  0.007394 1.011 1.37e-05 0.00266
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## 180  8.56e-02 -6.36e-02 -3.31e-02 -7.50e-02  0.102958 0.997 2.64e-03 0.00516
## 181  1.57e-02  2.84e-02 -6.47e-02 -2.75e-02  0.126220 0.976 3.95e-03 0.00349
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## 190  5.17e-02 -5.07e-02 -7.17e-03 -2.89e-02  0.070309 1.005 1.24e-03 0.00503
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## 199 -3.10e-02  1.23e-02  1.09e-02  6.90e-02  0.103274 1.005 2.66e-03 0.00771
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## 201  1.07e-02 -2.47e-02  1.09e-02  1.74e-02  0.062751 1.016 9.86e-04 0.01041
## 202 -7.81e-04  2.82e-03 -6.23e-04 -5.38e-03 -0.014941 1.013 5.59e-05 0.00489
## 203  9.13e-02 -1.15e-01  1.52e-02 -2.28e-02  0.163706 0.995 6.68e-03 0.00928
## 204  1.29e-01 -1.38e-01 -7.01e-03 -5.57e-02  0.197319 0.959 9.62e-03 0.00555
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## 206 -9.04e-02  8.91e-02  5.28e-03  6.55e-02 -0.097944 1.016 2.40e-03 0.01339
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## 233 -6.57e-03  3.32e-02 -4.22e-02  1.46e-02  0.115477 0.968 3.30e-03 0.00246
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## 254 -1.35e-02 -4.68e-02  5.46e-02  1.14e-01  0.231823 0.995 1.34e-02 0.01494
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## 257  2.42e-02 -4.78e-02  9.54e-03  4.43e-02  0.160720 0.975 6.41e-03 0.00534
## 258  9.08e-02 -6.16e-05 -1.16e-01 -1.26e-01  0.240551 0.924 1.42e-02 0.00491
## 259 -9.72e-03  6.30e-02 -6.87e-02 -2.12e-02  0.143190 0.986 5.10e-03 0.00580
## 260 -9.86e-03  4.17e-02 -4.14e-02 -8.66e-03  0.087348 1.003 1.91e-03 0.00573
## 261  3.83e-02 -6.73e-03 -4.13e-02 -4.70e-02  0.087169 0.998 1.90e-03 0.00428
## 262  2.92e-02  3.62e-02 -8.62e-02 -5.62e-02  0.173437 0.959 7.43e-03 0.00439
## 263  7.40e-03  7.54e-02 -1.11e-01 -4.44e-02  0.224942 0.925 1.24e-02 0.00441
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## 268  1.66e-01 -1.06e-01 -7.90e-02 -1.59e-01  0.218634 0.936 1.17e-02 0.00477
## 269  1.53e-01 -1.24e-01 -4.01e-02 -1.30e-01  0.171242 0.978 7.28e-03 0.00630
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## 271 -3.28e-02  3.14e-02  5.17e-03  1.87e-02 -0.045071 1.009 5.08e-04 0.00451
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## 273 -1.52e-03  1.04e-03  9.10e-04  9.20e-04 -0.002885 1.011 2.08e-06 0.00267
## 274  3.57e-02 -3.03e-02 -1.35e-02 -1.65e-02  0.065897 0.999 1.08e-03 0.00294
## 275  4.36e-02 -4.21e-02 -4.79e-03 -3.03e-02  0.049653 1.014 6.17e-04 0.00821
## 276  3.48e-02 -3.25e-02 -6.69e-03 -2.15e-02  0.045703 1.009 5.23e-04 0.00469
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## 278  4.23e-02 -4.42e-02 -1.57e-03 -2.40e-02  0.054271 1.013 7.37e-04 0.00770
## 279  1.05e-02 -1.02e-02 -1.06e-03 -7.19e-03  0.012004 1.016 3.61e-05 0.00828
## 280  7.09e-02 -6.88e-02 -6.65e-03 -4.89e-02  0.080645 1.010 1.63e-03 0.00837
## 281 -2.18e-02  3.57e-02 -3.68e-02  5.00e-02  0.139668 0.954 4.82e-03 0.00266
## 282  3.91e-02 -4.28e-02 -3.18e-03 -1.09e-02  0.072869 1.003 1.33e-03 0.00454
## 283  2.47e-02 -2.71e-02 -1.65e-02  2.62e-02  0.143142 0.959 5.06e-03 0.00304
## 284  1.24e-01 -1.52e-01  1.15e-02 -2.90e-02  0.230716 0.955 1.31e-02 0.00691
## 285  7.43e-03 -1.90e-02  8.32e-03  1.74e-02  0.056021 1.014 7.86e-04 0.00858
## 286  5.97e-03  2.40e-03 -5.29e-03 -2.34e-02 -0.042750 1.014 4.58e-04 0.00762
## 287  3.71e-02 -2.06e-02 -1.28e-02 -6.15e-02 -0.075204 1.022 1.42e-03 0.01639
## 288  3.89e-03  2.13e-03 -3.89e-03 -1.64e-02 -0.030487 1.015 2.33e-04 0.00767
## 289  1.02e-02 -6.69e-03 -1.76e-03 -1.70e-02 -0.021835 1.016 1.19e-04 0.00842
## 290 -2.06e-03  7.35e-03 -3.77e-03 -9.17e-03 -0.025531 1.016 1.63e-04 0.00832
## 291  4.36e-03 -4.68e-03 -8.89e-05 -2.17e-03  0.006055 1.015 9.18e-06 0.00703
## 292  7.08e-02 -7.61e-02 -1.08e-03 -3.53e-02  0.098056 1.004 2.40e-03 0.00710
## 293 -5.07e-03  5.45e-03  1.26e-06  2.72e-03 -0.006661 1.017 1.11e-05 0.00855
## 294 -4.30e-02  4.83e-02 -2.40e-03  2.06e-02 -0.059778 1.015 8.94e-04 0.00951
## 295 -8.89e-03  1.10e-02  1.28e-03 -3.57e-03 -0.031425 1.010 2.47e-04 0.00377
## 296  5.99e-03 -7.89e-03  7.38e-04  5.86e-04  0.015465 1.013 5.99e-05 0.00550
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## 298  1.53e-02 -1.30e-02  5.37e-04 -2.24e-02 -0.028982 1.013 2.10e-04 0.00605
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## 300  1.78e-03 -3.87e-03  1.71e-03  2.33e-03  0.009138 1.020 2.09e-05 0.01153
## 301 -8.84e-03  6.35e-03  1.43e-03  1.31e-02  0.015355 1.019 5.91e-05 0.01142
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## 304  3.74e-02 -4.20e-02  2.15e-03 -1.83e-02  0.051510 1.016 6.64e-04 0.00980
## 305  7.12e-02 -6.59e-02 -1.27e-02 -4.86e-02  0.085420 1.004 1.82e-03 0.00573
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## 309 -6.29e-04  1.94e-03 -1.92e-03  3.91e-04  0.004455 1.011 4.97e-06 0.00314
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## 311 -1.62e-01  1.47e-01  7.11e-03  1.36e-01 -0.166498 1.005 6.92e-03 0.01347
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## 321 -4.06e-03  3.44e-03  1.84e-03  1.24e-03 -0.009198 1.011 2.12e-05 0.00278
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## 325 -8.64e-03  8.65e-03  9.98e-04  4.21e-03 -0.012903 1.012 4.17e-05 0.00448
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## 331 -2.53e-02  3.25e-02 -1.97e-03 -1.56e-03 -0.063676 1.007 1.01e-03 0.00529
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## 333 -2.62e-02  4.09e-02 -9.22e-03 -1.15e-02 -0.085456 1.007 1.83e-03 0.00728
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## 335  1.27e-03  5.32e-03 -2.50e-03 -1.94e-02 -0.044650 1.010 4.99e-04 0.00523
## 336 -1.37e-02  1.95e-02 -1.52e-03 -6.23e-03 -0.047157 1.009 5.57e-04 0.00496
## 337 -1.23e-02  1.35e-02  4.10e-03 -3.67e-03 -0.042793 1.007 4.58e-04 0.00328
## 338  1.52e-02 -1.43e-02  4.28e-03 -2.53e-02 -0.039979 1.009 4.00e-04 0.00398
## 339 -3.82e-02  3.88e-02  4.41e-03  1.88e-02 -0.055583 1.008 7.73e-04 0.00500
## 340 -2.63e-02  2.56e-02  6.56e-03  8.71e-03 -0.050384 1.006 6.35e-04 0.00346
## 341 -1.20e-03 -1.02e-03  7.69e-03 -8.36e-03 -0.034957 1.007 3.06e-04 0.00256
## 342 -4.64e-02  3.33e-02  4.90e-03  7.45e-02  0.095204 1.006 2.27e-03 0.00767
## 343  3.58e-02 -3.13e-02  2.38e-03 -5.07e-02 -0.064785 1.009 1.05e-03 0.00614
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## 345  1.08e-02 -1.74e-02  3.58e-03  7.30e-03  0.041437 1.012 4.30e-04 0.00628
## 346  5.10e-02 -3.76e-02 -7.88e-03 -7.26e-02 -0.083176 1.017 1.73e-03 0.01281
## 347  5.54e-02 -4.29e-02 -7.04e-03 -7.50e-02 -0.083782 1.018 1.76e-03 0.01383
## 348  1.23e-02 -4.20e-03 -6.14e-03 -2.55e-02 -0.035596 1.020 3.17e-04 0.01263
## 349  4.77e-03 -1.73e-03 -2.25e-03 -9.86e-03 -0.013792 1.020 4.76e-05 0.01178
## 350 -1.52e-02  8.81e-03  4.77e-03  2.49e-02  0.030360 1.023 2.31e-04 0.01493
## 351  4.83e-03 -3.44e-03 -9.72e-04 -6.81e-03 -0.007622 1.026 1.46e-05 0.01718
## 352 -1.49e-02  1.03e-02  3.81e-03  2.04e-02  0.022121 1.041 1.23e-04 0.03181
## 353  6.93e-02 -3.49e-02 -3.00e-02 -1.15e-01 -0.138504 1.030 4.80e-03 0.02664
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## 358 -6.90e-04  3.49e-03 -1.82e-03 -4.99e-04  0.008473 1.011 1.80e-05 0.00339
## 359  1.13e-03  2.23e-03 -3.43e-04 -1.78e-03  0.011468 1.010 3.29e-05 0.00259
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## 362 -1.07e-04 -1.81e-03  1.29e-03  9.41e-04 -0.005522 1.011 7.64e-06 0.00349
## 363 -3.28e-04  2.02e-03 -1.28e-03 -5.77e-04  0.004803 1.012 5.78e-06 0.00420
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## 366  2.13e-02 -3.41e-03 -1.01e-02 -2.84e-02  0.050554 1.008 6.39e-04 0.00431
## 367  1.76e-03  8.27e-04 -1.93e-03 -2.93e-03  0.006955 1.012 1.21e-05 0.00420
## 368 -4.93e-04  1.28e-02  2.60e-02 -7.92e-03  0.059325 1.009 8.81e-04 0.00585
## 369  3.41e-02  6.78e-02 -6.09e-02 -9.48e-02  0.273216 0.906 1.82e-02 0.00521
## 370  5.64e-02  3.89e-02 -4.05e-02 -1.09e-01  0.261956 0.906 1.67e-02 0.00483
## 371  6.64e-02  3.00e-02 -2.65e-02 -1.21e-01  0.271155 0.905 1.79e-02 0.00508
## 372  4.56e-02  4.52e-02  2.90e-02 -1.02e-01  0.287207 0.896 2.00e-02 0.00526
## 373  1.35e-01 -5.17e-02  1.66e-02 -1.71e-01  0.274008 0.908 1.83e-02 0.00535
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## 377 -7.39e-03  1.81e-03 -1.81e-02  1.03e-02 -0.033301 1.013 2.78e-04 0.00662
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## 379 -7.06e-04  2.05e-04 -1.04e-02  1.16e-03 -0.013050 1.021 4.27e-05 0.01288
## 380 -4.88e-04 -7.19e-03 -3.75e-02  6.35e-03 -0.059157 1.013 8.76e-04 0.00815
## 381 -5.31e-02 -1.47e-01  1.28e+00  1.46e-01  1.296630 1.225 4.16e-01 0.21587
## 382  7.57e-05 -8.57e-03 -3.07e-02  5.87e-03 -0.054026 1.012 7.31e-04 0.00685
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## 384 -1.24e-03 -1.62e-02 -2.00e-03  1.21e-02 -0.054131 1.008 7.33e-04 0.00471
## 385 -1.52e-02  8.97e-03 -6.31e-02  1.79e-02 -0.085791 1.012 1.84e-03 0.00970
## 386 -4.74e-03 -8.78e-03 -5.71e-02  1.40e-02 -0.094340 1.006 2.22e-03 0.00738
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## 388 -1.70e-02  1.36e-02 -8.42e-02  1.76e-02 -0.105332 1.013 2.77e-03 0.01196
## 389  2.63e-03 -1.40e-02 -3.02e-02  5.33e-03 -0.061352 1.009 9.42e-04 0.00613
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## 391  1.36e-03 -1.15e-02  3.94e-05  4.34e-03 -0.031776 1.010 2.53e-04 0.00407
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## 394 -6.71e-03 -5.58e-03 -6.52e-03  1.26e-02 -0.042045 1.008 4.42e-04 0.00396
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## 406 -2.30e-02 -1.72e-02  2.97e-01  3.86e-02  0.303107 1.139 2.30e-02 0.11984
## 407 -1.83e-03 -1.51e-03 -2.48e-02  4.62e-03 -0.035061 1.018 3.08e-04 0.01037
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## 410  2.77e-04  2.03e-02  5.21e-02 -1.45e-02  0.107317 1.000 2.87e-03 0.00625
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## 412 -9.47e-05  1.12e-03  2.48e-03 -6.16e-04  0.005261 1.014 6.93e-06 0.00605
## 413 -1.64e-03  5.04e-03  2.25e-02 -1.15e-03  0.033094 1.016 2.74e-04 0.00872
## 414 -6.16e-03  5.06e-03  6.83e-02  4.71e-03  0.078630 1.025 1.55e-03 0.01885
## 415 -2.83e-03 -4.66e-05  2.83e-02  3.73e-03  0.029675 1.062 2.21e-04 0.05114
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## 417 -1.67e-02 -4.59e-03 -3.15e-02  2.58e-02 -0.090536 0.997 2.05e-03 0.00427
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## 419 -7.05e-02 -2.56e-02  6.55e-01  1.09e-01  0.665670 1.153 1.10e-01 0.14363
## 420 -6.40e-02  4.69e-02 -4.66e-02  6.24e-02 -0.109311 0.997 2.98e-03 0.00561
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## 428 -9.36e-04  1.65e-03 -7.03e-03  3.83e-04 -0.007474 1.045 1.40e-05 0.03553
## 429 -4.93e-02  2.85e-02 -9.39e-03  5.14e-02 -0.081448 0.999 1.66e-03 0.00404
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## 440 -4.46e-03 -8.57e-03 -1.02e-02  1.11e-02 -0.047270 1.008 5.59e-04 0.00409
## 441 -7.17e-04 -6.01e-04 -4.49e-02  1.39e-03 -0.055193 1.017 7.63e-04 0.01110
## 442  1.05e-03 -3.04e-03 -1.98e-03  1.20e-04 -0.007990 1.012 1.60e-05 0.00430
## 443  9.89e-04 -2.97e-03  6.95e-04  2.20e-04 -0.006056 1.013 9.19e-06 0.00450
## 444  3.55e-03 -8.46e-03 -4.67e-03 -3.48e-04 -0.019647 1.012 9.67e-05 0.00471
## 445  3.17e-03 -1.41e-02 -2.61e-02  3.41e-03 -0.057142 1.008 8.17e-04 0.00512
## 446  1.24e-03 -1.32e-02 -1.70e-02  5.14e-03 -0.051208 1.007 6.56e-04 0.00429
## 447  2.90e-03 -1.39e-02  1.55e-03  3.14e-03 -0.034396 1.010 2.96e-04 0.00395
## 448  7.55e-03 -1.77e-02 -1.23e-02 -1.68e-03 -0.043719 1.009 4.78e-04 0.00428
## 449  8.20e-03 -1.57e-02 -6.96e-03 -3.53e-03 -0.031465 1.011 2.48e-04 0.00449
## 450  9.30e-03 -2.20e-02 -2.98e-03 -1.70e-03 -0.044934 1.008 5.05e-04 0.00421
## 451  3.36e-03 -1.64e-02 -1.60e-03  2.70e-03 -0.044151 1.007 4.88e-04 0.00344
## 452  8.43e-03 -1.82e-02  3.15e-03 -2.77e-03 -0.032233 1.010 2.60e-04 0.00426
## 453  1.56e-03 -1.08e-02  3.24e-03  2.58e-03 -0.028768 1.009 2.07e-04 0.00338
## 454  7.44e-04 -1.25e-03 -3.04e-04 -4.25e-04 -0.002115 1.013 1.12e-06 0.00457
## 455  5.90e-03 -1.14e-02 -7.67e-03 -3.10e-03 -0.026091 1.011 1.70e-04 0.00396
## 456 -5.61e-03 -9.15e-03  5.51e-03  1.03e-02 -0.045199 1.005 5.11e-04 0.00295
## 457  5.07e-04 -1.73e-02  6.42e-03  5.26e-03 -0.053143 1.003 7.06e-04 0.00297
## 458 -7.17e-03 -1.55e-03 -1.37e-02  6.79e-03 -0.043362 1.005 4.70e-04 0.00272
## 459 -7.82e-04 -6.47e-03 -8.17e-03  1.71e-03 -0.032671 1.008 2.67e-04 0.00275
## 460 -5.71e-05 -3.02e-04 -1.94e-04  1.26e-04 -0.001403 1.011 4.93e-07 0.00269
## 461  2.73e-03 -1.10e-02  2.98e-03  5.40e-04 -0.026852 1.009 1.81e-04 0.00316
## 462  2.83e-04 -7.51e-03  4.80e-03  2.34e-03 -0.021809 1.010 1.19e-04 0.00312
## 463 -5.50e-04 -9.52e-04 -7.86e-04  7.66e-04 -0.005874 1.011 8.64e-06 0.00261
## 464 -5.88e-04  1.32e-03  3.42e-05  3.13e-04  0.002762 1.011 1.91e-06 0.00315
## 465 -3.06e-03  2.47e-03 -1.65e-03  2.35e-03 -0.004922 1.011 6.07e-06 0.00342
## 466 -5.32e-02  4.71e-02  1.06e-03  4.24e-02 -0.058455 1.010 8.55e-04 0.00655
## 467  3.79e-04 -4.46e-03  2.32e-03  6.05e-04 -0.013414 1.010 4.51e-05 0.00271
## 468  1.31e-03 -3.12e-03  9.51e-04 -4.05e-04 -0.005866 1.012 8.62e-06 0.00379
## 469  7.04e-04 -7.21e-04  2.00e-03 -3.93e-04  0.002593 1.014 1.68e-06 0.00632
## 470 -9.99e-03  9.97e-03 -8.88e-03  7.33e-03 -0.015314 1.015 5.87e-05 0.00760
## 471  5.93e-04 -2.29e-03  5.54e-04 -2.78e-04 -0.006136 1.011 9.43e-06 0.00260
## 472  1.32e-03 -2.25e-03  4.75e-04 -9.50e-04 -0.003654 1.012 3.34e-06 0.00356
## 473  2.02e-03 -5.47e-04 -7.76e-04 -1.91e-03  0.005162 1.010 6.67e-06 0.00243
## 474  3.75e-02 -2.63e-02 -1.27e-03 -3.41e-02  0.050201 1.006 6.30e-04 0.00374
## 475  8.60e-03 -1.79e-02 -5.69e-03 -3.59e-03 -0.037153 1.009 3.46e-04 0.00388
## 476  8.19e-03 -2.20e-02  1.21e-03 -3.01e-04 -0.045512 1.008 5.18e-04 0.00406
## 477  2.11e-03 -1.01e-02  3.52e-03  1.80e-03 -0.024497 1.010 1.50e-04 0.00362
## 478  6.70e-03 -1.20e-02 -2.45e-02 -3.13e-03 -0.041724 1.012 4.36e-04 0.00619
## 479  4.44e-03 -1.06e-02 -8.13e-03 -8.64e-04 -0.026979 1.011 1.82e-04 0.00435
## 480  5.65e-03 -1.16e-03  1.98e-02 -6.95e-03  0.033112 1.012 2.75e-04 0.00543
## 481  1.48e-03 -1.11e-03  6.52e-04 -9.45e-04  0.002896 1.010 2.10e-06 0.00249
## 482  1.66e-03  9.23e-04  2.11e-03 -5.97e-04  0.013387 1.009 4.49e-05 0.00214
## 483 -5.82e-04  4.91e-03  3.59e-03  2.00e-03  0.023052 1.008 1.33e-04 0.00222
## 484 -3.28e-02  3.23e-02 -2.65e-03  2.09e-02 -0.040317 1.011 4.07e-04 0.00566
## 485 -4.89e-02  4.60e-02  1.56e-04  3.47e-02 -0.056053 1.010 7.86e-04 0.00623
## 486 -1.55e-02  1.43e-02 -2.42e-03  8.84e-03 -0.023018 1.010 1.33e-04 0.00326
## 487  2.10e-03 -3.69e-03 -1.33e-03 -2.45e-03 -0.009267 1.010 2.15e-05 0.00249
## 488 -2.85e-02  2.52e-02 -3.42e-03  2.19e-02 -0.033652 1.011 2.84e-04 0.00491
## 489 -1.12e-02 -1.23e-02  3.20e-02  2.24e-02 -0.061172 1.008 9.36e-04 0.00526
## 490 -5.13e-03 -4.73e-02  7.06e-02  3.42e-02 -0.136855 0.989 4.66e-03 0.00590
## 491 -2.58e-03 -4.49e-02  6.40e-02  2.87e-02 -0.124740 0.992 3.88e-03 0.00577
## 492  1.38e-03 -2.87e-02  3.74e-02  1.39e-02 -0.072496 1.007 1.31e-03 0.00588
## 493 -8.98e-03  2.67e-04  1.21e-02  1.17e-02 -0.023627 1.011 1.40e-04 0.00441
## 494 -4.76e-02  3.77e-02  1.39e-02  4.29e-02 -0.052113 1.014 6.80e-04 0.00812
## 495 -4.48e-02  3.87e-02  8.49e-03  3.90e-02 -0.046484 1.019 5.41e-04 0.01240
## 496 -9.81e-02  9.05e-02  1.14e-02  8.07e-02 -0.100673 1.020 2.54e-03 0.01666
## 497 -1.43e-02  5.26e-03  1.30e-02  1.43e-02 -0.028797 1.009 2.08e-04 0.00327
## 498 -2.17e-02  9.72e-03  1.75e-02  2.07e-02 -0.040106 1.007 4.03e-04 0.00323
## 499 -2.67e-02  1.77e-02  1.25e-02  2.54e-02 -0.033970 1.011 2.89e-04 0.00520
## 500 -3.13e-02  1.46e-02  2.34e-02  3.26e-02 -0.051888 1.007 6.74e-04 0.00415
## 501 -1.75e-02  7.90e-04  2.35e-02  2.09e-02 -0.047381 1.007 5.62e-04 0.00364
## 502 -1.23e-02  7.09e-03  7.44e-03  1.21e-02 -0.017660 1.012 7.81e-05 0.00444
## 503 -1.36e-02  5.00e-03  1.21e-02  1.50e-02 -0.025209 1.011 1.59e-04 0.00425
## 504  1.64e-03  4.33e-03 -8.36e-03 -4.28e-03  0.015922 1.012 6.35e-05 0.00466
## 505 -3.29e-05 -1.49e-04  2.57e-04  1.07e-04 -0.000496 1.012 6.17e-08 0.00425
## 506 -2.73e-02 -2.62e-03  4.31e-02  3.42e-02 -0.084031 0.996 1.76e-03 0.00369
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Leverage (hi)

library(olsrr)
ols_plot_resid_lev(model3)

#hem leverage hemde uzaklık değerleri beraber incelenerek veri setinden çıkarılmalı

Influence (Etki)

ols_plot_dffits(model3)

#en üstteki ve en alttaki çizginin dışındaki değerler veri setinde çıkarılabilir. #Veri seti çok büyük olduğu için tek tek seçemiyorum o yüzddn aşağıdaki kodu kullandım

#DFFITS ile elde edilen etkili gözlemler

# Etkili gözlem ölçülerini al
influence_measures <- influence.measures(model3)

# DFFITS değerlerini çıkarın
dffits_values <- influence_measures$infmat[, "dffit"]

# Gözlem sayısı ve parametre sayısını hesaplayın
n <- nrow(dat)  # Gözlem sayısı
p <- length(coef(model3))  # Parametre sayısı

# Etkili gözlemler için eşik değeri hesaplayın
threshold <- 2 * sqrt(p / n)  # Eşik değeri

# Eşik değeri aşan gözlemleri seçin
influential_observations <- which(abs(dffits_values) > threshold)

# Etkili gözlemleri listeleyin
influential_observations
##  65  99 158 162 163 164 167 187 196 204 205 226 229 254 258 263 268 284 354 369 
##  65  99 158 162 163 164 167 187 196 204 205 226 229 254 258 263 268 284 354 369 
## 370 371 372 373 381 406 411 419 
## 370 371 372 373 381 406 411 419