Use the accompanying data file to analyze loyalty (Loyal equals 1 if the member stayed at the gym for at least one year, 0 otherwise). Also included in the file are the member’s age and income (in $1,000s) and whether he/she joined on a single plan (Single equals 1 if on a single plan, 0 otherwise).

a. Estimate the logistic regression model for loyalty, using age and income as the predictor variables, and compute the accuracy rate.
b. Extend the model to include the membership plan (single or family) and compute the resulting accuracy rate.
c. Use the preferred model to predict the loyalty probability for a 50-year-old member with income of $80,000; consider both single and family plans if you pick the model in part b.

 

Loyal	Age	Income	Plan
0	39	134	Single
1	57	120	Family
1	72	75	Single
1	71	143	Single
1	25	75	Single
1	44	149	Single
0	21	113	Family
1	26	87	Family
0	63	44	Family
0	37	44	Single
1	65	138	Family
0	43	138	Family
0	66	96	Family
1	21	91	Family
0	70	59	Single
0	39	31	Single
0	39	50	Single
0	43	85	Family
0	65	53	Single
1	73	119	Single
1	71	63	Family
0	72	51	Single
1	53	108	Single
0	60	46	Family
1	60	119	Single
0	21	41	Single
1	46	100	Family
0	21	55	Family
0	27	127	Single