Question

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?

 

 

Answer 1

a.

Interest Rate	Int Rate ^ 2	Applications
4.0%	0.2%	3098
4.3%	0.2%	2785
4.3%	0.2%	2515
4.7%	0.2%	2180
4.7%	0.2%	1873
5.2%	0.3%	1794
5.6%	0.3%	1450
5.7%	0.3%	1177
6.1%	0.4%	822
6.2%	0.4%	886
6.2%	0.4%	740
6.8%	0.5%	740
7.1%	0.5%	722
7.6%	0.6%	540
8.3%	0.7%	375
8.9%	0.8%	425
9.4%	0.9%	360
9.5%	0.9%	389
9.7%	0.9%	339
9.8%	1.0%	336

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.882531994
R Square	0.77886272
Adjusted R Square	0.766577316
Standard Error	431.048903
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	11779437.38	11779437.38	63.39740177	2.62133E-07
Residual	18	3344456.821	185803.1567
Total	19	15123894.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3847.933481	348.9861725	11.02603422	1.9468E-09	3114.740172	4581.12679	3114.74017	4581.12679
X Variable 1	-39830.47697	5002.415685	-7.962248537	2.62133E-07	-50340.17047	-29320.78347	-50340.17	-29320.783
	6.00%
LCL	613.2490129
UCL	2302.960712

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.98585571
R Square	0.97191148
Adjusted R Square	0.96860694
Standard Error	158.078141
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1.5E+07	7349543	294.115	6.5E-14
Residual	17	424808	24988.7
Total	19	1.5E+07
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9663.16885	553.003	17.474	2.7E-12	8496.43	10829.9	8496.43	10829.9
X Variable 1	-220032.29	16771.8	-13.119	2.5E-10	-255418	-184647	-255418	-184647
X Variable 2	1287725.57	119132	10.8092	4.9E-09	1036378	1539073	1036378	1539073
	6.00%
LCL	787.210553
UCL	1406.87687

Scatter Plot (a)

 

 

b.	R2 = 0.778. Approximately 77.8% of the total variation in the number of mortgage applicants is accounted for using this model.
c.	Lower confidence limit = 613.24
	Upper confidence limit = 2302.96
d.	R2 = 0.972. Approximately 97.2% of the total variation in the number of mortgage applicants is accounted for using this model.
e.	Lower confidence limit = 787.21
	Upper confidence limit = 1406.88
f.	The quadratic model appears to be much more accurate.