Using Regression to Study Recent Loans of a Large Bank

A mortgage department of a large bank is studying its recent loans. Of particualr interest is how such factors as the value of the home (in thousands of dollars), education level of the head of the household, age of the head of the household, current monthly mortgage payment (in dollars), and gender of the head of the household (male = 1, female = 2) relate to the family income. Are these variables effective predictors of the income of the household? A random sample of 25 recent loans is obtained.

Income Value Years of Age Mortgage Gender
($thousands) ($thousands) Education Payment
$40.3 $190 14 53 $230 1
39.6 121 15 49 370 1
40.8 161 14 44 397 1
40.3 161 14 39 181 1
40.0 179 14 53 378 0
38.1 99 14 46 304 0
40.4 114 15 42 285 1
40.7 202 14 49 551 0
40.8 184 13 37 370 0
37.1 90 14 43 135 0
39.9 181 14 48 332 1
40.4 143 15 54 217 1
38.0 132 14 44 490 0
39.0 127 14 37 220 0
39.5 153 14 50 270 1
40.6 145 14 50 279 1
40.3 174 15 52 329 1
40.1 177 15 47 247 0
41.7 188 15 49 433 1
40.1 153 15 53 333 1
40.6 150 16 58 148 0
40.4 173 13 42 390 1
40.9 163 14 46 142 1
40.1 150 15 50 343 0
38.5 139 14 45 373 0

a) Determine the regression equation.

b) What is the value of R squared? Comment on the value.

c) Conduct a global hypothesis test to determine whether any of the independent variables are different from zero.

d) Conduct individual hypothesis tests to determine whether any of the independent variables can be dropped.

e) If variables are dropped, recompute the regression equation and R squared.