When interest rates decline, Patriot Bank has found that they get inundated with requests to refinance home mortgages. To better plan its staffing needs in the mortgage processing area of its operations, Patriot wants to develop a regression model to help predict the total number of mortgage applications (Y) each month as a function of the prime interest rate (X1). The bank collected the data shown in the file Dat9-14.xls on your data disk representing the average prime interest rate and total number of mortgage applications in 20 different months.

a. Prepare a scatter plot of these data.

b. Fit the following regression model to the data:

Ŷi = b0 + b1X1i

Plot the number of monthly mortgage applications that are estimated by this model along with the actual values in the sample. How well does this model fit the data?

c. Using the previous model, develop a 95% prediction interval for the number of mortgage applications Patriot could expect to receive in a month in which the interest rate is 6%. Interpret this interval.

d. Fit the following regression model to the data:

Ŷi = b0 + b1X1i + b2X2i

Where X2i = X12i. Plot the number of monthly mortgage applications that are estimated by this model along with the actual values in the sample. How well does this model fit the data?

e. Using the previous model, develop a 95% prediction interval for the number of mortgage applications that Patriot could expect to receive in a month in which the interest rate is 6%. Interpret this interval.

f. Which model would you suggest that Patriot Bank use, and why?