Question

Consider the accompanying data file to estimate the logistic 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 $1,000) and whether he/she joined on a single plan (single = 1 if on a single plan, 0 otherwise).

A. Model for predicting loyalty
B. Variables affecting loyalty estimation
C. Predicting membership duration
D. Factors influencing gym retention

Answer 1

In this question, we are estimating the logistic model for predicting loyalty based on age, income, and plan type. The scatter plot, least-squares line, and correlation coefficient are calculated and explained.

Step-by-step explanation:

a. The independent variable is the year, and the dependent variable is the percent of workers paid hourly rates. Draw a scatter plot with year on the x-axis and percent of workers paid hourly rates on the y-axis.

b. From inspection, we can see a negative relationship between the variables. As the years increase, the percent of workers paid hourly rates tends to decrease.

c. The y-intercept, a, represents the predicted percent of workers paid hourly rates when the year is 0. However, in this context, it does not have any practical meaning.

d. To calculate the least-squares line, we need to find the slope (b) and the y-intercept (a) using the given data points. The equation of the line will be ŷ = a + bx.

e. After calculating the least-squares line, we can find the correlation coefficient (r). The correlation coefficient measures the strength and direction of the linear relationship between the variables. If the correlation coefficient is close to -1 or 1, it indicates a strong relationship, whereas if it is close to 0, there is a weak relationship.