Question

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Annual dues. The board of directors of a professional association conducted a random sample survev of 30 members to assess the effects of several possible amounts of dues increase. The sample results follow. X denotes the dollar increase in annual dues posited in the survey interview, and 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 28 49 0 I: 2 29 30 30 0 30 30 0 50 50 L'ogistic regression model (14.20) is assumed to be appropriate. a. Find the maximum likelihood estimates of β0 and β1-State the fitted response function. b. Obtain a scatter plot of the data with both the fitted logistic response function from part (a) and a lowess smooth superimposed. Does the fitted logistic response function appear to fit well? Obtain exp(bi) and interpret this number. What is the estimated probability that association members will not renew their membership if the dues are increased by $40? c. d. e. Estimate the amount of dues increase for which 75 percent of the members are expected not to renew their association membership

Full Data Set:

Y X

0 30

1 30

0 30

0 31

0 32

0 33

1 34

0 35

0 35

1 35

1 36

0 37

0 38

1 39

0 40

1 40

1 40

0 41

1 42

1 43

1 44

0 45

1 45

1 45

0 46

1 47

1 48

0 49

1 50

1 50

0 55

1 55

1 60

0 60

0 65

Answer 1