Chapter 8 Linear model

8.1 Scatter plot

  • To produce a scatter plot, use plot(<x variable>, <y variable>).
plot(mtcars$mpg,mtcars$wt)
plot(mtcars$mpg,mtcars$wt, xlab="mpg", ylab="weight", main="Scatter plot of weight vs mpg")


8.2 Correlation coefficient

  • To calculate the correlation coefficient, use cor(<x variable>, <y variable>).
cor(mtcars$mpg,mtcars$wt)


8.3 Regression line

  • To produce the regression line, use lm(<y variable>~<x variable>).
lm(mtcars$wt~mtcars$mpg)
#Or
L=lm(mtcars$wt~mtcars$mpg)
L$coeff
#Or
lm(wt~mpg,data=mtcars)
  • Now you can add this line to the scatter plot.
plot(mtcars$mpg,mtcars$wt)
abline(L)


8.4 Residual plot

  • The residual plot helps to detect any pattern not captured by the linear model.

    • If it is a random scatter, then the linear model seems appropriate.
    • If it shows a pattern (eg quadratic), then another model should be considered.

  • To produce a residual plot:

plot(mtcars$mpg,L$residuals, xlab = "mpg", ylab = "Residuals")
abline(h = 0, col = "blue")