library(psych)
library(tidyverse)
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library(tidymodels)
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library(vip)
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## Attaching package: 'vip'
##
## The following object is masked from 'package:utils':
##
## vi
library(ISLR2)
data(mtcars)
describe(mtcars)
## vars n mean sd median trimmed mad min max range skew
## mpg 1 32 20.09 6.03 19.20 19.70 5.41 10.40 33.90 23.50 0.61
## cyl 2 32 6.19 1.79 6.00 6.23 2.97 4.00 8.00 4.00 -0.17
## disp 3 32 230.72 123.94 196.30 222.52 140.48 71.10 472.00 400.90 0.38
## hp 4 32 146.69 68.56 123.00 141.19 77.10 52.00 335.00 283.00 0.73
## drat 5 32 3.60 0.53 3.70 3.58 0.70 2.76 4.93 2.17 0.27
## wt 6 32 3.22 0.98 3.33 3.15 0.77 1.51 5.42 3.91 0.42
## qsec 7 32 17.85 1.79 17.71 17.83 1.42 14.50 22.90 8.40 0.37
## vs 8 32 0.44 0.50 0.00 0.42 0.00 0.00 1.00 1.00 0.24
## am 9 32 0.41 0.50 0.00 0.38 0.00 0.00 1.00 1.00 0.36
## gear 10 32 3.69 0.74 4.00 3.62 1.48 3.00 5.00 2.00 0.53
## carb 11 32 2.81 1.62 2.00 2.65 1.48 1.00 8.00 7.00 1.05
## kurtosis se
## mpg -0.37 1.07
## cyl -1.76 0.32
## disp -1.21 21.91
## hp -0.14 12.12
## drat -0.71 0.09
## wt -0.02 0.17
## qsec 0.34 0.32
## vs -2.00 0.09
## am -1.92 0.09
## gear -1.07 0.13
## carb 1.26 0.29
model <- lm(mpg ~ ., data = mtcars)
summary(model)
##
## Call:
## lm(formula = mpg ~ ., data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4506 -1.6044 -0.1196 1.2193 4.6271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.30337 18.71788 0.657 0.5181
## cyl -0.11144 1.04502 -0.107 0.9161
## disp 0.01334 0.01786 0.747 0.4635
## hp -0.02148 0.02177 -0.987 0.3350
## drat 0.78711 1.63537 0.481 0.6353
## wt -3.71530 1.89441 -1.961 0.0633 .
## qsec 0.82104 0.73084 1.123 0.2739
## vs 0.31776 2.10451 0.151 0.8814
## am 2.52023 2.05665 1.225 0.2340
## gear 0.65541 1.49326 0.439 0.6652
## carb -0.19942 0.82875 -0.241 0.8122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.65 on 21 degrees of freedom
## Multiple R-squared: 0.869, Adjusted R-squared: 0.8066
## F-statistic: 13.93 on 10 and 21 DF, p-value: 3.793e-07
pairs(mtcars, main = "Scatterplot Matrix of mtcars Variables")
model_all <- lm(mpg ~ ., data = mtcars)
summary(model_all)
##
## Call:
## lm(formula = mpg ~ ., data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4506 -1.6044 -0.1196 1.2193 4.6271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.30337 18.71788 0.657 0.5181
## cyl -0.11144 1.04502 -0.107 0.9161
## disp 0.01334 0.01786 0.747 0.4635
## hp -0.02148 0.02177 -0.987 0.3350
## drat 0.78711 1.63537 0.481 0.6353
## wt -3.71530 1.89441 -1.961 0.0633 .
## qsec 0.82104 0.73084 1.123 0.2739
## vs 0.31776 2.10451 0.151 0.8814
## am 2.52023 2.05665 1.225 0.2340
## gear 0.65541 1.49326 0.439 0.6652
## carb -0.19942 0.82875 -0.241 0.8122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.65 on 21 degrees of freedom
## Multiple R-squared: 0.869, Adjusted R-squared: 0.8066
## F-statistic: 13.93 on 10 and 21 DF, p-value: 3.793e-07
model_excl_disp <- lm(mpg ~ . - disp, data = mtcars)
summary(model_excl_disp)
##
## Call:
## lm(formula = mpg ~ . - disp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7863 -1.4055 -0.2635 1.2029 4.4753
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.55052 18.52585 0.677 0.5052
## cyl 0.09627 0.99715 0.097 0.9240
## hp -0.01295 0.01834 -0.706 0.4876
## drat 0.92864 1.60794 0.578 0.5694
## wt -2.62694 1.19800 -2.193 0.0392 *
## qsec 0.66523 0.69335 0.959 0.3478
## vs 0.16035 2.07277 0.077 0.9390
## am 2.47882 2.03513 1.218 0.2361
## gear 0.74300 1.47360 0.504 0.6191
## carb -0.61686 0.60566 -1.018 0.3195
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.623 on 22 degrees of freedom
## Multiple R-squared: 0.8655, Adjusted R-squared: 0.8105
## F-statistic: 15.73 on 9 and 22 DF, p-value: 1.183e-07
model_excl_disp_cyl <- lm(mpg ~ . - disp - cyl, data = mtcars)
summary(model_excl_disp_cyl)
##
## Call:
## lm(formula = mpg ~ . - disp - cyl, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8187 -1.3903 -0.3045 1.2269 4.5183
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.80810 12.88582 1.072 0.2950
## hp -0.01225 0.01649 -0.743 0.4650
## drat 0.88894 1.52061 0.585 0.5645
## wt -2.60968 1.15878 -2.252 0.0342 *
## qsec 0.63983 0.62752 1.020 0.3185
## vs 0.08786 1.88992 0.046 0.9633
## am 2.42418 1.91227 1.268 0.2176
## gear 0.69390 1.35294 0.513 0.6129
## carb -0.61286 0.59109 -1.037 0.3106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.566 on 23 degrees of freedom
## Multiple R-squared: 0.8655, Adjusted R-squared: 0.8187
## F-statistic: 18.5 on 8 and 23 DF, p-value: 2.627e-08
library(ISLR2)
sales_model <- lm(Sales ~ Price + Urban + US, data = Carseats)
summary(sales_model)
##
## Call:
## lm(formula = Sales ~ Price + Urban + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9206 -1.6220 -0.0564 1.5786 7.0581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.043469 0.651012 20.036 < 2e-16 ***
## Price -0.054459 0.005242 -10.389 < 2e-16 ***
## UrbanYes -0.021916 0.271650 -0.081 0.936
## USYes 1.200573 0.259042 4.635 4.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.472 on 396 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335
## F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16
smaller_model <- lm(Sales ~ Price + US, data = Carseats)
confint(smaller_model)
## 2.5 % 97.5 %
## (Intercept) 11.79032020 14.27126531
## Price -0.06475984 -0.04419543
## USYes 0.69151957 1.70776632
par(mfrow=c(2,2))
plot(smaller_model)
leverage <- hatvalues(smaller_model)
high_leverage <- which(leverage > 2 * mean(leverage))
high_leverage
## 43 126 156 157 160 166 172 175 192 204 209 270 273 314 316 357 366 368 384 387
## 43 126 156 157 160 166 172 175 192 204 209 270 273 314 316 357 366 368 384 387