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

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following.
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fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
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