Question

The board of directors of a professional association conducted a survey of 30 members to assess the effects of several possible amounts of dues increase. X denotes the dollar increase in annual dues posited in the survey interview. Y -1 if the interviewee indicated that the membership will not be renewed at that amount of dues increase and 0 if the membership will be renewed. The output for fitting the logistic regression is below. 95% CI Odds Predictor Coef Constant p-value Ratio Lower Upper SE Coef Z 4.500 0.125 2.655-1.81 0.070 0.0661.87 0.061 1.13 0.99 1.29 Log-Likelihood = -18.732 Test that all slopes are zero: G -3.991, DF -1, P-Value0.046 Write the sample logistic regression equation for predicting the probability of not renewing membership as a function of amount of dues increase. a) b) Use the equation in part a) to predict the probability that a person does not renew membership when amount of dues are increased by 4. c) Write a sentence that interprets the value 1.13 given under "Odds Ratio" in the output.

That is all the information. What specific information do you need?

Answer 1

a)

Therefore, the fitted response function is:

π^i=e^(β0+β1xi)/1+e^(β0+β1xi)

By plugging in β0 = -4.5 and β1 = 0.125, we get the response function:

π^i=e^(0.125xi−4.5)/1+e^(0.125xi−4.5)

Plot Logistic Regression
xx <- with(data.17, seq(min(x), max(x), len = 200))
plot(y ~ x, data.17, pch = 19, col = "gray40", xlab = "The dollar increase in annual dues", ylab = "Fitted Value")
lines(xx, predict(logit.17, data.frame(x = xx), type = "resp"), lwd = 2, col='blue')
a= coef(logit.17)[1]
b= coef(logit.17)[2]
curve(exp(a+b*x)/(1+exp(a+b*x)), from = min(data.17$x), to = max(data.17$x), col='green',add=T)
title("Scatter Plot with Logistic Mean Response Functions")

Scatter Plot with Logistic Mean Response Functions 50 45 40 35 30 The dollar increase in annual dues

b)

cat("the estimated probability that association members will not renew their membership if \n the dues are increased by $4 is", predict(logit.17, type = "response",new data = list(x=4)))

the estimated probability that association members will not renew their membership if 
the dues are increased by $40 is 0.05487487

c)

The e^β1 is 1.133237, which means for every one dollar increase in the annual dues, the odds ratio of getting membership un-renewed (Y=1) versus renewed (Y=0) increase by 1.133237 times.