SKUSKA
Virych Hlieb
2024-12-18
library(datasets)
library(moments)
data("ChickWeight")1.
#a
max_values <- sapply(airquality, max, na.rm = TRUE)
max_variable <- names(which.max(max_values))
max_variable## [1] "Solar.R" #b
missing_vars <- names(airquality)[sapply(airquality, function(x) any(is.na(x)))]
airquality_clean <- na.omit(airquality)
#c
sk_values <- sapply(airquality_clean,skewness)
max_sk_var <- names(which.max(sk_values))
max_sk_var## [1] "Ozone" #d
hist(airquality_clean[[max_sk_var]],main = paste("Hist: ",max_sk_var))
boxplot(airquality_clean[[max_sk_var]],main = paste("Boxplot: ",max_sk_var)) 
e
Histogram ukazuje posun doľava alebo doprava. Zosikmenie premennej (skewness) môžeme na histograme identifikovať podľa toho, ako je rozdelenie hodnôt “naklonené”. Ak je distribúcia šikmá na pravú stranu (prítomnosť dlhšieho chvosta na pravej strane), hovoríme o pravej šikmosti (positívna šikmosť). Naopak, ak je rozdelenie šikmé na ľavú stranu (dlhší chvost na ľavej strane), ide o ľavú šikmosť (negatívna šikmosť). Ak je histogram symetrický, znamená to, že distribúcia je blízka normálnemu rozdeleniu a sklon je nula.
Na boxplote si môžete všimnúť asymetriu fúzov alebo umiestnenie mediánu.Na boxplote môžeme tiež pozorovať šikmosť. Ak sú “us” (whiskers) na jednej strane boxu dlhšie než na druhej strane, môže to naznačovať šikmosť. Ďalším indikátorom je pozícia mediány v rámci boxu: ak je mediána bližšie k spodnej alebo hornej časti boxu, môže to naznačovať sklon distribúcie.
2.
#a
sp_result <- sapply(ToothGrowth, function(x) if (is.numeric(x)) shapiro.test(x)$p.value else NA)
normal_var <- names(sp_result)[which(sp_result > 0.1)]
normal_var## [1] "len"#b
t.test(ToothGrowth[[normal_var]],mu=20)##
## One Sample t-test
##
## data: ToothGrowth[[normal_var]]
## t = -1.2017, df = 59, p-value = 0.2343
## alternative hypothesis: true mean is not equal to 20
## 95 percent confidence interval:
## 16.83731 20.78936
## sample estimates:
## mean of x
## 18.81333#c
t.test(ToothGrowth[[normal_var]] ~ ToothGrowth$supp, var.equal = TRUE)##
## Two Sample t-test
##
## data: ToothGrowth[[normal_var]] by ToothGrowth$supp
## t = 1.9153, df = 58, p-value = 0.06039
## alternative hypothesis: true difference in means between group OJ and group VC is not equal to 0
## 95 percent confidence interval:
## -0.1670064 7.5670064
## sample estimates:
## mean in group OJ mean in group VC
## 20.66333 16.96333t.test(ToothGrowth[[normal_var]] ~ ToothGrowth$supp, var.equal = TRUE, conf.level = 0.9)##
## Two Sample t-test
##
## data: ToothGrowth[[normal_var]] by ToothGrowth$supp
## t = 1.9153, df = 58, p-value = 0.06039
## alternative hypothesis: true difference in means between group OJ and group VC is not equal to 0
## 90 percent confidence interval:
## 0.4708204 6.9291796
## sample estimates:
## mean in group OJ mean in group VC
## 20.66333 16.963333.
#a
anova_model <- aov(weight ~ Diet, data = ChickWeight)
summary(anova_model)## Df Sum Sq Mean Sq F value Pr(>F)
## Diet 3 155863 51954 10.81 6.43e-07 ***
## Residuals 574 2758693 4806
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#c
TukeyHSD(anova_model)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = weight ~ Diet, data = ChickWeight)
##
## $Diet
## diff lwr upr p adj
## 2-1 19.971212 -0.2998092 40.24223 0.0552271
## 3-1 40.304545 20.0335241 60.57557 0.0000025
## 4-1 32.617257 12.2353820 52.99913 0.0002501
## 3-2 20.333333 -2.7268370 43.39350 0.1058474
## 4-2 12.646045 -10.5116315 35.80372 0.4954239
## 4-3 -7.687288 -30.8449649 15.47039 0.82778104.
#a
cor_matrix <- cor(airquality_clean,use="complete.obs")
ozone_cor <- cor_matrix["Ozone",]
strngst_pos <- names(which.max(ozone_cor[ozone_cor<1]))
strngst_neg <- names(which.min(ozone_cor))
strngst_pos## [1] "Temp"strngst_neg## [1] "Wind"#b
spearman_cor <- cor(airquality_clean,method = "spearman",use = "complete.obs")
kendall_cor <- cor(airquality_clean,method = "kendall",use = "complete.obs")
spearman_cor["Ozone",]## Ozone Solar.R Wind Temp Month Day
## 1.00000000 0.34818647 -0.60513642 0.77293193 0.11669011 -0.03504654kendall_cor["Ozone",]## Ozone Solar.R Wind Temp Month Day
## 1.00000000 0.24031942 -0.44045944 0.58614712 0.08859401 -0.03041526#c
plot(airquality_clean$Ozone,airquality_clean[[strngst_pos]],main = "Ozone vs strongest Positive")
plot(airquality_clean$Ozone,airquality_clean[[strngst_neg]],main = "Ozone vs strongest Negative")
5.
#a
linear_model <- lm(weight ~ Time + Diet, data = ChickWeight)
summary(linear_model)$adj.r.squared## [1] 0.7435224summary(linear_model)##
## Call:
## lm(formula = weight ~ Time + Diet, data = ChickWeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -136.851 -17.151 -2.595 15.033 141.816
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.9244 3.3607 3.251 0.00122 **
## Time 8.7505 0.2218 39.451 < 2e-16 ***
## Diet2 16.1661 4.0858 3.957 8.56e-05 ***
## Diet3 36.4994 4.0858 8.933 < 2e-16 ***
## Diet4 30.2335 4.1075 7.361 6.39e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35.99 on 573 degrees of freedom
## Multiple R-squared: 0.7453, Adjusted R-squared: 0.7435
## F-statistic: 419.2 on 4 and 573 DF, p-value: < 2.2e-16#b
full_model <- lm(weight ~ . , data = ChickWeight)
summary(full_model)$adj.r.squared ## [1] 0.8416462summary(full_model)##
## Call:
## lm(formula = weight ~ ., data = ChickWeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -80.128 -15.976 -2.476 13.844 91.955
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.8983 2.2157 12.591 < 2e-16 ***
## Time 8.7152 0.1759 49.538 < 2e-16 ***
## Chick.L 130.2672 9.5424 13.651 < 2e-16 ***
## Chick.Q -24.9790 10.1028 -2.472 0.013732 *
## Chick.C -16.2937 10.4180 -1.564 0.118422
## Chick^4 16.8300 10.5032 1.602 0.109674
## Chick^5 -11.8874 10.4181 -1.141 0.254373
## Chick^6 62.0273 10.2441 6.055 2.67e-09 ***
## Chick^7 -5.7763 10.0555 -0.574 0.565913
## Chick^8 -2.1871 9.8366 -0.222 0.824137
## Chick^9 -2.5741 9.5743 -0.269 0.788145
## Chick^10 -15.8198 9.3250 -1.696 0.090382 .
## Chick^11 -29.2864 9.0988 -3.219 0.001367 **
## Chick^12 12.6115 8.8899 1.419 0.156599
## Chick^13 45.5732 8.7345 5.218 2.61e-07 ***
## Chick^14 8.4847 8.6499 0.981 0.327089
## Chick^15 -36.7921 8.5910 -4.283 2.19e-05 ***
## Chick^16 -18.5430 8.5389 -2.172 0.030332 *
## Chick^17 13.8154 8.5068 1.624 0.104966
## Chick^18 19.2098 8.4673 2.269 0.023690 *
## Chick^19 -15.1139 8.3971 -1.800 0.072450 .
## Chick^20 19.1073 8.3290 2.294 0.022178 *
## Chick^21 10.3924 8.3016 1.252 0.211177
## Chick^22 -13.8848 8.2768 -1.678 0.094028 .
## Chick^23 -2.6091 8.2224 -0.317 0.751133
## Chick^24 3.7279 8.1876 0.455 0.649070
## Chick^25 -30.7405 8.2072 -3.746 0.000200 ***
## Chick^26 22.9762 8.2255 2.793 0.005407 **
## Chick^27 37.2504 8.1981 4.544 6.86e-06 ***
## Chick^28 11.6756 8.1679 1.429 0.153467
## Chick^29 -15.8480 8.1893 -1.935 0.053501 .
## Chick^30 -9.6065 8.2243 -1.168 0.243313
## Chick^31 2.6487 8.2253 0.322 0.747567
## Chick^32 15.8318 8.1691 1.938 0.053157 .
## Chick^33 -4.2143 8.1816 -0.515 0.606701
## Chick^34 -8.3473 8.1762 -1.021 0.307759
## Chick^35 0.6771 8.1644 0.083 0.933933
## Chick^36 -17.3659 8.1675 -2.126 0.033948 *
## Chick^37 -2.6001 8.1705 -0.318 0.750436
## Chick^38 -15.5406 8.1727 -1.902 0.057778 .
## Chick^39 -2.8088 8.2396 -0.341 0.733324
## Chick^40 39.4063 8.2667 4.767 2.42e-06 ***
## Chick^41 -15.4934 8.2493 -1.878 0.060914 .
## Chick^42 -27.7127 8.1962 -3.381 0.000775 ***
## Chick^43 -32.3320 8.1715 -3.957 8.64e-05 ***
## Chick^44 -9.6068 8.1724 -1.176 0.240318
## Chick^45 -12.8100 8.1665 -1.569 0.117338
## Chick^46 21.7381 8.1646 2.662 0.007994 **
## Chick^47 6.3382 8.1950 0.773 0.439623
## Chick^48 16.3989 8.1667 2.008 0.045152 *
## Chick^49 -25.3853 8.1647 -3.109 0.001978 **
## Diet2 NA NA NA NA
## Diet3 NA NA NA NA
## Diet4 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28.28 on 527 degrees of freedom
## Multiple R-squared: 0.8554, Adjusted R-squared: 0.8416
## F-statistic: 62.33 on 50 and 527 DF, p-value: < 2.2e-16#c
AIC(linear_model,full_model)## df AIC
## linear_model 6 5789.607
## full_model 52 5554.520BIC(linear_model,full_model)## df BIC
## linear_model 6 5815.765
## full_model 52 5781.218#d
linear_model##
## Call:
## lm(formula = weight ~ Time + Diet, data = ChickWeight)
##
## Coefficients:
## (Intercept) Time Diet2 Diet3 Diet4
## 10.92 8.75 16.17 36.50 30.23full_model##
## Call:
## lm(formula = weight ~ ., data = ChickWeight)
##
## Coefficients:
## (Intercept) Time Chick.L Chick.Q Chick.C Chick^4
## 27.8983 8.7152 130.2672 -24.9790 -16.2937 16.8300
## Chick^5 Chick^6 Chick^7 Chick^8 Chick^9 Chick^10
## -11.8874 62.0273 -5.7763 -2.1871 -2.5741 -15.8198
## Chick^11 Chick^12 Chick^13 Chick^14 Chick^15 Chick^16
## -29.2864 12.6115 45.5732 8.4847 -36.7921 -18.5430
## Chick^17 Chick^18 Chick^19 Chick^20 Chick^21 Chick^22
## 13.8154 19.2098 -15.1139 19.1073 10.3924 -13.8848
## Chick^23 Chick^24 Chick^25 Chick^26 Chick^27 Chick^28
## -2.6091 3.7279 -30.7405 22.9762 37.2504 11.6756
## Chick^29 Chick^30 Chick^31 Chick^32 Chick^33 Chick^34
## -15.8480 -9.6065 2.6487 15.8318 -4.2143 -8.3473
## Chick^35 Chick^36 Chick^37 Chick^38 Chick^39 Chick^40
## 0.6771 -17.3659 -2.6001 -15.5406 -2.8088 39.4063
## Chick^41 Chick^42 Chick^43 Chick^44 Chick^45 Chick^46
## -15.4934 -27.7127 -32.3320 -9.6068 -12.8100 21.7381
## Chick^47 Chick^48 Chick^49 Diet2 Diet3 Diet4
## 6.3382 16.3989 -25.3853 NA NA NA#best_model <- ifelse(AIC(linear_model) < AIC(full_model), linear_model, full_model)
#best_model
#residuals(best_model)
#shapiro.test(residuals(best_model))
#acf(residuals(best_model))
best_model <- linear_model
best_model##
## Call:
## lm(formula = weight ~ Time + Diet, data = ChickWeight)
##
## Coefficients:
## (Intercept) Time Diet2 Diet3 Diet4
## 10.92 8.75 16.17 36.50 30.23residuals(best_model)## 1 2 3 4 5
## 31.07560890 22.57462541 13.07364193 0.57265844 -4.92832504
## 6 7 8 9 10
## -5.42930852 -9.93029201 -8.43127549 -1.93225898 2.56675754
## 11 12 13 14 15
## 13.06577405 10.31528231 29.07560890 20.57462541 12.07364193
## 16 17 18 19 20
## 8.57265844 3.07167496 4.57069148 6.06970799 4.56872451
## 21 22 23 24 25
## 11.06774102 18.56675754 23.06577405 20.31528231 32.07560890
## 26 27 28 29 30
## 10.57462541 9.07364193 3.57265844 3.07167496 0.57069148
## 31 32 33 34 35
## -0.93029201 4.56872451 12.06774102 18.56675754 12.06577405
## 36 37 38 39 40
## 7.31528231 31.07560890 20.57462541 10.07364193 3.57265844
## 41 42 43 44 45
## -6.92832504 -11.42930852 -13.93029201 -25.43127549 -14.93225898
## 46 47 48 49 50
## -14.43324246 -25.93422595 -37.68471769 30.07560890 13.57462541
## 51 52 53 54 55
## 2.07364193 -3.42734156 -1.92832504 7.57069148 25.06970799
## 56 57 58 59 60
## 30.56872451 46.06774102 30.56675754 34.06577405 28.31528231
## 61 62 63 64 65
## 30.07560890 20.57462541 13.07364193 10.57265844 16.07167496
## 66 67 68 69 70
## 25.57069148 25.06970799 14.56872451 4.06774102 -8.43324246
## 71 72 73 74 75
## -25.93422595 -37.68471769 30.07560890 20.57462541 11.07364193
## 76 77 78 79 80
## 7.57265844 8.07167496 13.57069148 30.06970799 40.56872451
## 81 82 83 84 85
## 67.06774102 81.56675754 102.06577405 110.31528231 31.07560890
## 86 87 88 89 90
## 21.57462541 15.07364193 7.57265844 3.07167496 -5.42930852
## 91 92 93 94 95
## -5.93029201 -17.43127549 -24.93225898 -34.43324246 -60.93422595
## 96 97 98 99 100
## 31.07560890 22.57462541 13.07364193 4.57265844 4.07167496
## 101 102 103 104 105
## -2.42930852 -25.93029201 -41.43127549 -57.93225898 -68.43324246
## 106 107 108 109 110
## -85.93422595 -96.68471769 30.07560890 15.57462541 6.07364193
## 111 112 113 114 115
## -0.42734156 -6.92832504 -17.42930852 -26.93029201 -37.43127549
## 116 117 118 119 120
## -49.93225898 -56.43324246 -65.93422595 -70.68471769 32.07560890
## 121 122 123 124 125
## 22.57462541 17.07364193 20.57265844 31.07167496 40.57069148
## 126 127 128 129 130
## 52.06970799 43.56872451 31.06774102 15.56675754 -4.93422595
## 131 132 133 134 135
## -19.68471769 30.07560890 20.57462541 10.07364193 -1.42734156
## 136 137 138 139 140
## -8.92832504 -10.42930852 3.06970799 1.56872451 11.06774102
## 141 142 143 144 145
## 16.56675754 9.06577405 10.31528231 30.07560890 19.57462541
## 146 147 148 149 150
## 7.07364193 -3.42734156 -15.92832504 -31.42930852 -44.93029201
## 151 152 153 154 155
## -63.43127549 -79.93225898 -87.43324246 -94.93422595 -98.68471769
## 156 157 158 159 160
## 30.07560890 20.57462541 16.07364193 15.57265844 20.07167496
## 161 162 163 164 165
## 29.57069148 48.06970799 58.56872451 76.06774102 79.56675754
## 166 167 168 169 170
## 73.06577405 71.31528231 30.07560890 20.57462541 10.07364193
## 171 172 173 174 175
## 0.57265844 -12.92832504 -30.42930852 -48.93029201 -65.43127549
## 176 177 178 179 180
## 30.07560890 16.57462541 3.07364193 -12.42734156 -23.92832504
## 181 182 183 184 185
## -47.42930852 -61.93029201 31.07560890 22.57462541 15.07364193
## 186 187 188 189 190
## 8.57265844 2.07167496 -9.42930852 -17.93029201 -30.43127549
## 191 192 193 194 195
## -37.93225898 -45.43324246 -52.93422595 -52.68471769 28.07560890
## 196 197 198 199 200
## 6.57462541 32.07560890 19.57462541 9.07364193 -1.42734156
## 201 202 203 204 205
## -15.92832504 -27.42930852 -33.93029201 -45.43127549 -44.93225898
## 206 207 208 209 210
## -48.43324246 -41.93422595 -37.68471769 30.07560890 18.57462541
## 211 212 213 214 215
## 8.07364193 -5.42734156 -15.92832504 -25.42930852 -38.93029201
## 216 217 218 219 220
## -44.43127549 -52.93225898 -61.43324246 -70.93422595 -77.68471769
## 221 222 223 224 225
## 12.90953485 5.40855137 -0.09243212 6.40658440 27.90560091
## 226 227 228 229 230
## 48.40461743 84.90363395 90.40265046 107.90166698 122.40068349
## 231 232 233 234 235
## 115.89970001 120.14920827 13.90953485 10.40855137 1.90756788
## 236 237 238 239 240
## -2.59341560 -7.09439909 -19.59538257 -24.09636605 -38.59734954
## 241 242 243 244 245
## -36.09833302 -36.59931651 -38.10029999 -43.85079173 15.90953485
## 246 247 248 249 250
## 7.40855137 -1.09243212 -6.59341560 -7.09439909 -11.59538257
## 251 252 253 254 255
## -5.09636605 -14.59734954 -22.09833302 -21.59931651 -32.10029999
## 256 257 258 259 260
## -35.85079173 14.90953485 7.40855137 -4.09243212 -5.59341560
## 261 262 263 264 265
## -31.09439909 -46.59538257 -62.09636605 -78.59734954 -95.09833302
## 266 267 268 269 270
## -112.59931651 -126.10029999 -136.85079173 12.90953485 4.40855137
## 271 272 273 274 275
## -0.09243212 -1.59341560 4.90560091 9.40461743 13.90363395
## 276 277 278 279 280
## 14.40265046 29.90166698 46.40068349 56.89970001 54.14920827
## 281 282 283 284 285
## 14.90953485 3.40855137 -5.09243212 -5.59341560 -4.09439909
## 286 287 288 289 290
## -0.59538257 3.90363395 -2.59734954 1.90166698 20.40068349
## 291 292 293 294 295
## 33.89970001 40.14920827 11.90953485 1.40855137 -4.09243212
## 296 297 298 299 300
## -6.59341560 -10.09439909 -14.59538257 -17.09636605 -26.59734954
## 301 302 303 304 305
## -23.09833302 -21.59931651 -17.10029999 -18.85079173 11.90953485
## 306 307 308 309 310
## 1.40855137 -4.09243212 -6.59341560 -5.09439909 -0.59538257
## 311 312 313 314 315
## 12.90363395 6.40265046 16.90166698 22.40068349 9.89970001
## 316 317 318 319 320
## 22.14920827 11.90953485 3.40855137 -3.09243212 -5.59341560
## 321 322 323 324 325
## -10.09439909 -8.59538257 1.90363395 0.40265046 19.90166698
## 326 327 328 329 330
## 45.40068349 76.89970001 98.14920827 14.90953485 3.40855137
## 331 332 333 334 335
## -3.09243212 -7.59341560 -12.09439909 -16.59538257 -17.09636605
## 336 337 338 339 340
## -27.59734954 -24.09833302 -33.59931651 -45.10029999 -60.85079173
## 341 342 343 344 345
## -5.42379848 -11.92478197 -20.42576545 -26.92674893 -32.42773242
## 346 347 348 349 350
## -32.92871590 -29.42969939 -31.93068287 -17.43166636 -0.93264984
## 351 352 353 354 355
## 12.56636667 24.81587493 -6.42379848 -15.92478197 -17.42576545
## 356 357 358 359 360
## -17.92674893 -10.42773242 -5.92871590 6.57030061 9.06931713
## 361 362 363 364 365
## 33.56833364 58.06735016 68.56636667 73.81587493 -8.42379848
## 366 367 368 369 370
## -14.92478197 -19.42576545 -22.92674893 -21.42773242 -23.92871590
## 371 372 373 374 375
## -15.42969939 -25.93068287 -36.43166636 -58.93264984 -66.43363333
## 376 377 378 379 380
## -84.18412507 -6.42379848 -15.92478197 -19.42576545 -14.92674893
## 381 382 383 384 385
## -10.42773242 -0.92871590 11.57030061 16.06931713 47.56833364
## 386 387 388 389 390
## 89.06735016 104.56636667 109.81587493 -6.42379848 -11.92478197
## 391 392 393 394 395
## -18.42576545 -12.92674893 5.57226758 23.07128410 48.57030061
## 396 397 398 399 400
## 68.06931713 99.56833364 127.06735016 138.56636667 141.81587493
## 401 402 403 404 405
## -8.42379848 -16.92478197 -21.42576545 -23.92674893 -19.42773242
## 406 407 408 409 410
## -18.92871590 -7.42969939 -3.93068287 10.56833364 22.06735016
## 411 412 413 414 415
## 2.56636667 -11.18412507 -6.42379848 -16.92478197 -26.42576545
## 416 417 418 419 420
## -31.92674893 -37.42773242 -51.92871590 -49.42969939 -57.93068287
## 421 422 423 424 425
## -52.43166636 -47.93264984 -53.43363333 -53.18412507 -6.42379848
## 426 427 428 429 430
## -15.92478197 -21.42576545 -25.92674893 -19.42773242 -25.92871590
## 431 432 433 434 435
## -24.42969939 -15.93068287 4.56833364 27.06735016 57.56636667
## 436 437 438 439 440
## 58.81587493 -5.42379848 -14.92478197 -21.42576545 -21.92674893
## 441 442 443 444 445
## -28.42773242 -25.92871590 -22.42969939 -23.93068287 -17.43166636
## 446 447 448 449 450
## 9.06735016 27.56636667 40.81587493 -6.42379848 -9.92478197
## 451 452 453 454 455
## -16.42576545 -20.92674893 -16.42773242 -14.92871590 1.57030061
## 456 457 458 459 460
## 12.06931713 27.56833364 57.06735016 72.56636667 89.81587493
## 461 462 463 464 465
## 0.84215272 -7.65883076 -10.15981425 -8.66079773 -8.16178122
## 466 467 468 469 470
## -4.66276470 8.83625181 -10.66473167 -6.16571516 -14.66669864
## 471 472 473 474 475
## -17.16768213 -20.91817387 0.84215272 -9.65883076 -13.15981425
## 476 477 478 479 480
## -9.66079773 -8.16178122 -2.66276470 13.83625181 10.33526833
## 481 482 483 484 485
## 22.83428484 35.33330136 52.83231787 56.08182613 0.84215272
## 486 487 488 489 490
## -3.65883076 -7.15981425 2.33920227 19.83821878 28.33723530
## 491 492 493 494 495
## 37.83625181 24.33526833 15.83428484 -0.66669864 -17.16768213
## 496 497 498 499 500
## -24.91817387 0.84215272 -7.65883076 -11.15981425 -7.66079773
## 501 502 503 504 505
## -8.16178122 -10.66276470 -19.16374819 -25.66473167 -36.16571516
## 506 507 508 509 510
## -52.66669864 -0.15784728 -8.65883076 -15.15981425 -15.66079773
## 511 512 513 514 515
## -13.16178122 -11.66276470 -11.16374819 -22.66473167 -34.16571516
## 516 517 518 519 520
## -24.66669864 -19.16768213 -28.91817387 -1.15784728 -6.65883076
## 521 522 523 524 525
## -14.15981425 -11.66079773 -10.16178122 -8.66276470 -2.16374819
## 526 527 528 529 530
## -7.66473167 -8.16571516 11.33330136 14.83231787 13.08182613
## 531 532 533 534 535
## -0.15784728 -5.65883076 -10.15981425 -14.66079773 -11.16178122
## 536 537 538 539 540
## -5.66276470 1.83625181 -6.66473167 -13.16571516 -13.66669864
## 541 542 543 544 545
## -6.16768213 -19.91817387 -2.15784728 -8.65883076 -14.15981425
## 546 547 548 549 550
## -13.66079773 -7.16178122 -3.66276470 7.83625181 6.33526833
## 551 552 553 554 555
## 40.83428484 62.33330136 86.83231787 97.08182613 -1.15784728
## 556 557 558 559 560
## -5.65883076 -12.15981425 -8.66079773 -3.16178122 -0.66276470
## 561 562 563 564 565
## 5.83625181 2.33526833 2.83428484 4.33330136 16.83231787
## 566 567 568 569 570
## 12.08182613 -0.15784728 -4.65883076 -9.15981425 -9.66079773
## 571 572 573 574 575
## -6.16178122 -6.66276470 8.83625181 11.33526833 23.83428484
## 576 577 578
## 35.33330136 47.83231787 39.08182613shapiro.test(residuals(best_model)) ##
## Shapiro-Wilk normality test
##
## data: residuals(best_model)
## W = 0.94571, p-value = 1.032e-13acf(residuals(best_model))