Assignment:
The board of directors of a professional association conducted a random sample survey of 30 members to assess the effects of several possible changes in membership dues. The predictor Xi denotes, in dollars, the change in annual dues from the previous year posited in the survey interview to the i-th subject, so, for example, if Xi = 10, then the board is proposing a $10 increase in dues, if Xi = 0, then there is no change. The response is binary with Yi = 1 if the interviewee indicated that the membership will NOT be renewed at that amount of change in dues and Yi = 0 if the membership will be renewed. The output for ?tting the logistic regression model is given below. Use this to answer the following questions.
a) Write the estimated equation, as a function of X, for:
i. The log-odds of not renewing membership;
ii. The odds of not renewing membership;
iii. The probability of not renewing membership.
b) Estimate the probability that someone does not renew membership when annual dues increase $22.
c) Estimate the odds that someone does not renew when the annual dues increase by $22.
d) Estimate the odds that someone DOES renew when annual dues increase $22.
e) Estimate the increase in annual dues for which 75% of the members are expected to not renew their association membership.
Conduct a Wald test to determine whether an increase in dues is related to the probability of membership renewal. In your answer, state the null and alternative hypotheses, the test statistic, p-value, and conclusion based on (1) α = 0.05 and (2) α = 0.1.