Exercise $9-17$ Algo

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$$s age and income $($in $$1,000)$ and whether he$/$she joined on a single or a family plan.

Click here for the Excel Data File

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.

Note: Negative values should be indicated by a minus sign. Round your answers to $2$ decimal places.

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.

Note: Do not round intermediate calculations and round final answers to $2$ decimal places.

Predict the corresponding probabilities for a member on a family plan.

Note: Do not round intermediate calculations and round final answers to $2$ decimal places.