A study was performed to investigate the relationship betwee family income and ownership of a luxury car. 16 households were randomly selectedand their family income X1 (units of 1000 dollars) and information about luxury car ownership (Y = 1 if family owns at least one luxury car; otherwise Y = 0 were recorded) the data are shown below:
| Y |
X_1 |
Y |
X_1 |
| 1 |
227 |
1 |
225 |
| 1 |
166 |
0 |
164 |
| 0 |
108 |
0 |
133 |
| 0 |
139 |
1 |
156 |
| 1 |
233 |
1 |
229 |
| 0 |
129 |
0 |
117 |
| 0 |
103 |
0 |
118 |
| 0 |
213 |
1 |
165 |
a) Fit a logistic regression model to these data
b) Is the model you fitted in part (a) significant?
c) Interpret the regression coefficient Beta1 in terms of log odds ratio.
d) Determine the estimated probability that a person with family income of $177,000 owns a luxury car.