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 YÌ… = 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.

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Square Footage Bedrooms Baths Asking Price ($ thousands) 3800 4 3.5 498 2600 4 3 449 2600 3.5 435 2250 4 400 3300 3 379 2750 3 2.5 375 2200 3 2.5 356 3000 4 2.5 350 2300 3 340 2600 4 2.5 332 2300 298 2000 4 3 280 2200 3 2.5 260