12.45 Housing Prices II Refer to Exercise 12.44 and data set EX1244.

a. Estimate the average increase in the price for an increase of 1 m for houses sold in the city. Use a 99% confidence interval. Interpret your estimate.

b. A real estate salesperson needs to estimate the average sales price of houses with a total of 185.8 m of heated space. Use a 95% confidence interval and interpret your estimate.

c. Calculate the price per square metre for each house and then calculate the sample mean. Why is this estimate of the average cost per square metre not equal to the answer in part a? Should it be? Explain.

d. Suppose that a house with 165.4 m of heated floor space is offered for sale. Construct a 95% prediction interval for the price at which the house will sell.