Residential community housing prices. A paper published in the Journal of Physics: Conference Series (2020) studied the factors that affect house prices in a residential community in Jinan. A model was determined to predict the average sales price (PRICE) based on local general public budget revenue (REV), local general public budget expenditure (EXP), total population at the end of the year (POP), equivalent sound level of road traffic dB(A) (TRA), equivalent sound level of ambient noise (AMB), and an explanatory variable of sound level (LEV). Stepwise regression was used to find the best subset of predictors. The final stepwise model yielded the following results: PRICE = 24539.33 - 10.841311REV2 + 21.652071EXP2 - 64.510951POP2 + 259.20421LEV2, R2 = 0.9927, F = 412.7018 with p-value 6 0.00.

a. Determine the number of t-tests performed in step 1 of the stepwise regression.

b. Determine the number of t-tests performed in step 2 of the stepwise regression.

c. Give a full interpretation of the final stepwise model regression results.

d. Explain why it is dangerous to use the final stepwise model as the “best” model for predicting PRICE.

e. Using the independent variables selected by the stepwise routine, write a complete second-order model for PRICE.

f. Refer to part

e. How would you determine if the terms in the model that allow for curvature are statistically useful for predicting PRICE?