library(tidyverse)
library(ggplot2)
mtcarsLINEAR MODELS
Loading the mtcars file
Summary of data
summary(mtcars) mpg cyl disp hp
Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
Median :19.20 Median :6.000 Median :196.3 Median :123.0
Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
drat wt qsec vs
Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
Median :3.695 Median :3.325 Median :17.71 Median :0.0000
Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
am gear carb
Min. :0.0000 Min. :3.000 Min. :1.000
1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
Median :0.0000 Median :4.000 Median :2.000
Mean :0.4062 Mean :3.688 Mean :2.812
3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
Max. :1.0000 Max. :5.000 Max. :8.000 Linear regression
plot(mtcars$wt, mtcars$mpg,
xlab = "Weight (1000 lbs)",
ylab = "Miles Per Gallon (mpg)",
main = "Effect of Weight on MPG",
pch = 16, col = "blue") %>%
summary()Length Class Mode
0 NULL NULL # linear regression model
model <- lm(mpg ~ wt, data = mtcars)
abline(model, col = "red", lwd = 2) 
summary(model)
Call:
lm(formula = mpg ~ wt, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.5432 -2.3647 -0.1252 1.4096 6.8727
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.2851 1.8776 19.858 < 2e-16 ***
wt -5.3445 0.5591 -9.559 1.29e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.046 on 30 degrees of freedom
Multiple R-squared: 0.7528, Adjusted R-squared: 0.7446
F-statistic: 91.38 on 1 and 30 DF, p-value: 1.294e-10model$residuals Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
-2.2826106 -0.9197704 -2.0859521 1.2973499
Hornet Sportabout Valiant Duster 360 Merc 240D
-0.2001440 -0.6932545 -3.9053627 4.1637381
Merc 230 Merc 280 Merc 280C Merc 450SE
2.3499593 0.2998560 -1.1001440 0.8668731
Merc 450SL Merc 450SLC Cadillac Fleetwood Lincoln Continental
-0.0502472 -1.8830236 1.1733496 2.1032876
Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla
5.9810744 6.8727113 1.7461954 6.4219792
Toyota Corona Dodge Challenger AMC Javelin Camaro Z28
-2.6110037 -2.9725862 -3.7268663 -3.4623553
Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa
2.4643670 0.3564263 0.1520430 1.2010593
Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
-4.5431513 -2.7809399 -3.2053627 -1.0274952 # Calculate the density of residuals
residual_density <- density(model$residuals)
# Plot the density curve
plot(residual_density,
main = "Density Plot of Residuals",
xlab = "Residuals",
ylab = "Density",
lwd = 2)
# Fill the area under the curve with red color
polygon(residual_density, col = "red")
# Shapiro-Wilk test on residuals
shapiro.test(model$residuals)
Shapiro-Wilk normality test
data: model$residuals
W = 0.94508, p-value = 0.1044ANOVA
#Anova
anova(model)Analysis of Variance Table
Response: mpg
Df Sum Sq Mean Sq F value Pr(>F)
wt 1 847.73 847.73 91.375 1.294e-10 ***
Residuals 30 278.32 9.28
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1