The manager is concerned about the attrition rate at her gym. She would like to identify the profile of loyal members who retain the membership for at least one year. The accompanying data file contains information on whether the member has been loyal (Loyal = 1 if the member stayed at the gym for at least one year,
0 otherwise). Also included are the member’s age and income (in $1,000s) and whether he/she joined on a single or a family plan.
a. Estimate the logistic regression model using Loyal as the response variable and Age, Income, and Single (equals 1 if on a single plan, 0 otherwise) as the predictor variables.
b. Predict the probability of being loyal for a 40- and a 60-year-old member with income of $80,000 and on a single plan.
c. Predict the corresponding probabilities for a member on a family plan.

 

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