Homework 11

Load data and build a model

# Load the dataset
data(cars)

# Fit linear regression model
model <- lm(dist ~ speed, data = cars)

# Summary of the model
summary(model)

## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## speed         3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12

The model indicates that speed significantly predicts stopping distance (p < 0.001), with an increase of approximately 3.9324 units in stopping distance for every one-unit increase in speed. The model explains about 65.11% of the variance in stopping distance, and the overall model is highly significant.

Residual

par(mfrow=c(2,2))
plot(model)

The QQ plot diverge at the end. This suggests that the residuals are approximately normally distributed for most of the data, but there might be some outliers or extreme values causing the deviation at the end.

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