Data605 HW 11 Linear Regression

Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.)

Building Linear Model

Step 1: using lm function to build the model

cars_lm <- lm(dist~speed,data=cars)

(cars_lm)
## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Coefficients:
## (Intercept)        speed  
##     -17.579        3.932

The linear model (y = a0 + a1x1) is:

y = -17.579 + 3.932x

Step 2: plot lm model

plot(cars$dist, cars$speed)
abline(cars_lm, col="red")

Step 3: check summary

summary(cars_lm)
## 
## 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
plot(cars_lm$residuals)

Residual Aanlysis

Scatter plot: The residual values are concentraded between 20 to 60, but it is hard to determine the distribution of residual values

plot(fitted(cars_lm), resid(cars_lm))

Now, let’s try QQ plot.

qqnorm(resid(cars_lm)) 
qqline(resid(cars_lm))

From the QQ plot, the residual values are normal distributed.