Linear regression analysis

• Consider the auto dataset, auto.csv (you can download it on the Internet)

I hope to build a multiple linear regression for predicting mpg as y variable. ( R or SAS, or anything else)

1) Fit a multiple linear regression model using all variables (displacement, horsepower, weight, acceleration, origin as x variables) except cylinder and model year.

Carry out regression diagnostics (including plot of absolute residuals). Clearly state each assumption (linearity, normality, homoscedasticity, outliers), the diagnostic tools used to check it (specifically, Q-Q plot and residual plots), and the conclusion.

2) Use the principle of extra sum of squares (type I and III SS) to determine which variables can be removed from the model (try removing one variable - the least significant one at a time). Once a tentative final model is obtained, compare it with the initial model using appropriate extra sum of squares.

Clearly state at each step the hypotheses being tested, the appropriate extra sum of squares, test statistic, p-value, and conclusion.