Linear regression analysis

• Consider the auto dataset below.

I want to build a simple linear regression predicting mpg as a y variable (R or SAS or STATA, please).

Assume that I have to choose the weight as a x variable.

(a) Make scatterplots of mpg vs other variables (put all plots in one page). Based on these plots, choose one numerical variable that you think may be used effectively to predict mpg. (b) Fit a simple linear regression model and carry out regression diagnostics. The analysis should include an assessment of the degree to which the key regression assumptions are satisfied. Clearly state each assumption, the diagnostic tools used to check it, and the conclusion. (c) If an assumption is not met, attempt to remedy the situation. Explain the steps used to obtain the final model. Comment on the fit the final model using appropriate tests and statistics.(d) Use the final model to obtain 95% interval estimates for the mean response for the entire range of predictor and plot them against the predictor values. Where is the interval narrowest and why? In the same plot, add the corresponding interval estimates for mpg of future observations. Compare the two sets of intervals. (e) Construct a 95% confidence ellipse for the regression coefficients and plot it. Use the plot to test if they are all equal to 0 at 5% level of significance. (f) Construct 95% simultaneous confidence bands for the entire regression line and add it to the plot of confidence interval of mean response obtained in (d) (the intervals on future observations may be omitted for this plot). Which set of intervals is wider and why