Check the first 6 rows of the cars dataset.

head(cars)
##   speed dist
## 1     4    2
## 2     4   10
## 3     7    4
## 4     7   22
## 5     8   16
## 6     9   10
#summary(cars$dist)

Summary of linear regression model. The y-intercept is -17.579 and the slope is 3.932. “The residuals are the differences between the actual measured values and the corresponding values on the fitted regression line. A good model’s residual should be roughly balanced around from the mean of zero.”

The standard error should also be five to ten times smaller thand the corresponding coefficient for a good model.

lmcar <-lm(cars$dist ~ cars$speed)
lmcar
## 
## Call:
## lm(formula = cars$dist ~ cars$speed)
## 
## Coefficients:
## (Intercept)   cars$speed  
##     -17.579        3.932
summary(lmcar)
## 
## Call:
## lm(formula = cars$dist ~ cars$speed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## cars$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
{plot(cars$speed,cars$dist,main = "1920 Cars speed and number of Feet Taken to Stop",
      col = 'navyblue', pch = 16, xlab = "Speed (mph)", ylab = "Stopping Distance (feet)")
abline(lmcar, col = "red")}

Plotting the residuals from above model to analyze

plot(fitted(lmcar),resid(lmcar),col = 'navyblue', pch = 16, main = "The residual values vs. input values: \n well fitted model will have uniformly distribution around zero")

Plotting Q-Q plot: quantile-versus-quantile. Q-Q plot is used for visually examining whether the residuals are normally distributed. Notes: points forming along the qqline indicates normally distributed residuals.

qqnorm(resid(lmcar))
qqline(resid(lmcar), col = "red")