Question

Let’s consinder a mortgage application using HMDA (The Home Mortgage Disclosure Act). Here is a sample from 30 mortgage applications:

ID	loanamt	income	hprice
1	109	63	155
2	185	137	264
3	121	53	128
4	125	78	125
5	119	37	149
6	153	65	171
7	380	188	484
8	100	58	125
9	110	78	158
10	41	31	116.5
11	115	54	128
12	248	117	280
13	126	60	157.5
14	260	192	325
15	90	40	145
16	50	36	230
17	125	45	125
18	125	55	145
19	158	62	175
20	130	29	209
21	204	77	260
22	30	28	150
23	114	60	143
24	188	91	253
25	187	85	285
26	84	44	105
27	450	265	650
28	108	49	120
29	100	53	125
30	53	24	66

loanamt = Amount of Mortgage Loan Application (in $1000)

income = Applicant’s Annual Income (in $1000)

hprice = House Price to buy (in $1000)

Regression Analyis

Let’s consider the following regression model. Estimate the model using Minitab and answer the questions using the output.

Loanamti = b0 + b1 * incomei + et

Write the equations for the following statistics, find or calculate them from the Minitab output, and explain the meanings of the statistics (2 points each)

1) Estimated intercept

2) Estimated slope coefficient

3) SST (Total Sum of Square), SSR (Regression Sum of Square), and SSE (Error Sum of Square)

4) r2 and r, t test for the correlation coefficient

5) Standard Error of b

6) t test for the coefficient of income (Ho: B1 = 0 )

7) F statistics and perform the test for the model

8) Variance of et

9) According to the model what are the predicted loan amount if applicants have annual income of $50,000, $100,000, and $200,000 and their confidence intervals?

10) List and explain the assumptions you made for a simple regression model

Answer 1

Regression Analysis: loanamt versus income

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	1	210817	210817	188.83	0.000
income	1	210817	210817	188.83	0.000
Error	28	31261	1116
Lack-of-Fit	25	30856	1234	9.14	0.046
Pure Error	3	405	135
Total	29	242078

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
33.4135	87.09%	86.63%	84.30%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	29.4	10.5	2.81	0.009
income	1.556	0.113	13.74	0.000	1.00

Regression Equation

loanamt

=

29.4 + 1.556 income

Fits and Diagnostics for Unusual Observations

Obs	loanamt	Fit	Resid	Std Resid
14	260.0	328.1	-68.1	-2.26	R
27	450.0	441.7	8.3	0.34		X

R Large residual
X Unusual X