#1. Libraries
install.packages("MASS")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.3'
## (as 'lib' is unspecified)
install.packages("ISLR2")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.3'
## (as 'lib' is unspecified)
library(MASS)
library(ISLR2)
##
## Attaching package: 'ISLR2'
## The following object is masked from 'package:MASS':
##
## Boston
#2. simple Linear Regression
head(Boston)
## crim zn indus chas nox rm age dis rad tax ptratio lstat medv
## 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 4.98 24.0
## 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 9.14 21.6
## 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 4.03 34.7
## 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 2.94 33.4
## 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 5.33 36.2
## 6 0.02985 0 2.18 0 0.458 6.430 58.7 6.0622 3 222 18.7 5.21 28.7
lm.fit <- lm(medv ~ lstat, data = Boston)
attach(Boston)
lm.fit <- lm(medv ~ lstat)
lm.fit
##
## Call:
## lm(formula = medv ~ lstat)
##
## Coefficients:
## (Intercept) lstat
## 34.55 -0.95
summary(lm.fit)
##
## Call:
## lm(formula = medv ~ lstat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.168 -3.990 -1.318 2.034 24.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
## lstat -0.95005 0.03873 -24.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
## F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16
names(lm.fit)
## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"
coef(lm.fit)
## (Intercept) lstat
## 34.5538409 -0.9500494
confint(lm.fit)
## 2.5 % 97.5 %
## (Intercept) 33.448457 35.6592247
## lstat -1.026148 -0.8739505
predict(lm.fit, data.frame(lstat = (c(5, 10, 15))),
interval = "confidence")
## fit lwr upr
## 1 29.80359 29.00741 30.59978
## 2 25.05335 24.47413 25.63256
## 3 20.30310 19.73159 20.87461
predict(lm.fit, data.frame(lstat = (c(5, 10, 15))),
interval = "prediction")
## fit lwr upr
## 1 29.80359 17.565675 42.04151
## 2 25.05335 12.827626 37.27907
## 3 20.30310 8.077742 32.52846
plot(lstat, medv)
abline(lm.fit)
abline(lm.fit, lwd=3)
abline(lm.fit, lwd=3, col = "red")
plot(lstat, medv, col = "red")
plot(lstat, medv, pch = 20)
plot(lstat, medv,pch = "+")
plot(1:20, 1:20, pch = 1:20)
par(mfrow = c(2,2))
plot(lm.fit)
plot(predict(lm.fit), residuals(lm.fit))
plot(predict(lm.fit),rstudent(lm.fit))
plot(predict(lm.fit), residuals(lm.fit))
plot(predict(lm.fit), rstudent(lm.fit))
plot(hatvalues(lm.fit))
which.max(hatvalues(lm.fit))
## 375
## 375
#3. Multiple Linear Regression
lm.fit <- lm(medv~lstat + age, data = Boston)
summary(lm.fit)
##
## Call:
## lm(formula = medv ~ lstat + age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.981 -3.978 -1.283 1.968 23.158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.22276 0.73085 45.458 < 2e-16 ***
## lstat -1.03207 0.04819 -21.416 < 2e-16 ***
## age 0.03454 0.01223 2.826 0.00491 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.173 on 503 degrees of freedom
## Multiple R-squared: 0.5513, Adjusted R-squared: 0.5495
## F-statistic: 309 on 2 and 503 DF, p-value: < 2.2e-16
lm.fit <- lm(medv~., data = Boston)
summary(lm.fit)
##
## Call:
## lm(formula = medv ~ ., data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.1304 -2.7673 -0.5814 1.9414 26.2526
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.617270 4.936039 8.431 3.79e-16 ***
## crim -0.121389 0.033000 -3.678 0.000261 ***
## zn 0.046963 0.013879 3.384 0.000772 ***
## indus 0.013468 0.062145 0.217 0.828520
## chas 2.839993 0.870007 3.264 0.001173 **
## nox -18.758022 3.851355 -4.870 1.50e-06 ***
## rm 3.658119 0.420246 8.705 < 2e-16 ***
## age 0.003611 0.013329 0.271 0.786595
## dis -1.490754 0.201623 -7.394 6.17e-13 ***
## rad 0.289405 0.066908 4.325 1.84e-05 ***
## tax -0.012682 0.003801 -3.337 0.000912 ***
## ptratio -0.937533 0.132206 -7.091 4.63e-12 ***
## lstat -0.552019 0.050659 -10.897 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.798 on 493 degrees of freedom
## Multiple R-squared: 0.7343, Adjusted R-squared: 0.7278
## F-statistic: 113.5 on 12 and 493 DF, p-value: < 2.2e-16
install.packages("car")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.3'
## (as 'lib' is unspecified)
library(car)
## Loading required package: carData
vif(lm.fit)
## crim zn indus chas nox rm age dis
## 1.767486 2.298459 3.987181 1.071168 4.369093 1.912532 3.088232 3.954037
## rad tax ptratio lstat
## 7.445301 9.002158 1.797060 2.870777
lm.fit <- lm(medv~ . - age, data = Boston)
summary(cars)
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
