data() # looking at base R datasets
#load libraries
library(ggplot2)

Discussion 11

For this weeks discussion I selected base R dataset called “mtcars” which is based on Motor Trend Car Road Tests.

# load and review the dataset
head(mtcars)
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1
help(mtcars)
## starting httpd help server ... done

Visualize Data

# looking at linear correlation between mpg and hp(horsepower)
theme_set(theme_bw())
ggplot(mtcars, aes(mpg, hp))+
  geom_point()+
  geom_smooth(method = "lm", se=F)+
  labs(title = "Motor Trend Car Road Tests",
       x= "Miles Per Gallon",
       y= "Horsepower",
       subtitle="Linear Model")

Linear Model Function

lm <- lm(mpg ~ hp, data=mtcars)
lm
## 
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
## 
## Coefficients:
## (Intercept)           hp  
##    30.09886     -0.06823
summary(lm)
## 
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.7121 -2.1122 -0.8854  1.5819  8.2360 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 30.09886    1.63392  18.421  < 2e-16 ***
## hp          -0.06823    0.01012  -6.742 1.79e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.863 on 30 degrees of freedom
## Multiple R-squared:  0.6024, Adjusted R-squared:  0.5892 
## F-statistic: 45.46 on 1 and 30 DF,  p-value: 1.788e-07

Based on the p value, we can say this this is a good model.

qqnorm(resid(lm))
qqline(resid(lm))

The residuals are normally distributed. Overall this is a good linear model.