Question

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

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

Homework Answers

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

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