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

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