A realtor wanted to find a model that describes the asking price of houses in Greenville, South Carolina. She obtains a random sample of homes from the area.

(a) Find the least-squares regression equation Y̅ = b0 + b1x1 + b2x2 + b3x3, where x1 is square footage, x2 is number of bedrooms, x3 is number of baths, and y is the response variable, asking price.
(b) Use a partial F-test to determine whether number of bedrooms and number of baths do not significantly help to predict the response variable, asking price.
(c) Use either forward selection, backward elimination, or stepwise regression to identify the best model in predicting asking price.
(d) Draw residual plots, a boxplot of residuals, and a normal probability plot of residuals to assess the adequacy of the model found in part (c).
(e) Interpret the regression coefficients for the least-squares regression equation found in part (c).
(f) Construct 95% confidence and prediction intervals for the asking price of a 2600-square foot house in Greenville, South Carolina, with four bedrooms and three baths. Interpret the results.