Question: A study was conducted attempting to relate home ownership to family income. Twenty households were selected and family income was estimated, along with information concerning home ownership (y = 1 indicates yes and y = 0 indicates no). The data are shown below.
| Household |
Income |
Home Ownership Status |
Household |
Income |
Home Ownership Status |
| |
|
|
|
|
|
| 1 |
38,000 |
0 |
11 |
38,700 |
1 |
| 2 |
51,200 |
1 |
12 |
40,100 |
0 |
| 3 |
39,600 |
0 |
13 |
49,500 |
1 |
| 4 |
43,400 |
1 |
14 |
38,000 |
0 |
| 5 |
47,700 |
0 |
15 |
42,000 |
1 |
| 6 |
53,000 |
0 |
16 |
54,000 |
1 |
| 7 |
41,500 |
1 |
17 |
51,700 |
1 |
| 8 |
40,800 |
0 |
18 |
39,400 |
0 |
| 9 |
45,400 |
1 |
19 |
40,900 |
0 |
| 10 |
52,400 |
1 |
20 |
52,800 |
1 |
a. Fit a logistic regression model to the response variable y. Use a simple linear regression model as the structure for the linear predictor.
b. Does the model deviance indicate that the logistic regression model from part a is adequate?
c. Provide an interpretation of the parameter B1 in this model.
d. Expand the linear predictor to include a quadratic term in income. Is there any evidence that this quadratic term is required in the model?