Multiple Linear Regression
A mortgage department of a large bank is studying its recent loans. Of particular 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 = 0) 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 |
Mortgage |
|||||
|
($ thousands) |
($ thousands) |
Education |
Age |
Payment |
Gender | |||
|
$190 |
14 |
53 |
$230 |
1 | ||||
|
$40.30 |
121 |
15 |
49 |
370 |
1 | |||
|
39.6 |
161 |
14 |
44 |
397 |
1 | |||
|
40.8 |
161 |
14 |
39 |
181 |
1 | |||
|
40.3 |
179 |
14 |
53 |
378 |
0 | |||
|
40 |
99 |
14 |
46 |
304 |
0 | |||
|
38.1 |
114 |
15 |
42 |
285 |
1 | |||
|
40.4 |
202 |
14 |
49 |
551 |
0 | |||
|
40.7 |
184 |
13 |
37 |
370 |
0 | |||
|
40.8 |
90 |
14 |
43 |
135 |
0 | |||
|
37.1 |
181 |
14 |
48 |
332 |
1 | |||
|
39.9 |
143 |
15 |
54 |
217 |
1 | |||
|
40.4 |
132 |
14 |
44 |
490 |
0 | |||
|
38 |
127 |
14 |
37 |
220 |
0 | |||
|
39 |
153 |
14 |
50 |
270 |
1 | |||
|
40.6 |
145 |
14 |
50 |
279 |
1 | |||
|
40.3 |
174 |
15 |
52 |
329 |
1 | |||
|
40.1 |
177 |
15 |
47 |
274 |
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 R2? 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 test to determine whether any of the independent variables can be dropped.
e) If variables are dropped, recomputed the regression equation and R2.
