7. Consider the uswages data in the Faraway package. (20 Points) (a) Create a new predictor called region which takes values "NE", " MW" ,"WE" , and "SO", and summarizes the variables ne, mw, we, and so in the data set. (b) Turn region into a factor variable with "NE" as the baseline. Fit the regression model with region as the predictor and wage as the outcome. Summarize the fit of the model and use an F-test to determine if region is significantly associated with wages (take n = 0.05). Take special care to interpret what each of the betas represents. (c) Now use "SO" as the baseline and redo (b). Contrast the results. (d) Keep "SO" as the baseline. Now use an F-test to determine if region is still significant after correcting for education. Use n = 0.1. (e) Keep "SO" as the baseline. Now fit a model with eduction, region, and their interaction. Summarize of the fit of the model (paying attention to how to inter-pret the betas) and use an F-test to determine if the interaction effect is, overall, significant. (f) Plot the results from (e) by creating a scatter plot of wage vs education. Color code the points by region and plot the regression lines for each region (make sure the color of the regression line matches the color of the points).