Consider the accompanying data file to estimate the logistic regression model for predicting loyalty (Loyal equals 1 if the member stayed at the gym for at least one year, 0 otherwise). Predictor variables include 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. Use the estimated model to predict the loyalty odds for a 50-year-old member with income of $80,000 and on a single plan.
b. Predict the corresponding odds for a member on a family plan.
c. Interpret the percentage change in the loyalty odds when each predictor variable increases by one unit, holding the other variables constant.

 

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