In 1997, Ms. Susan Oh conducted a survey of n = 831 faculty and staff concerning their willingness to switch insurance p

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In 1997 Ms Susan Oh Conducted A Survey Of N 831 Faculty And Staff Concerning Their Willingness To Switch Insurance P 1 (302.19 KiB) Viewed 29 times

In 1997, Ms. Susan Oh conducted a survey of n = 831 faculty and staff concerning their willingness to switch insurance plans from that currently used (Blue Cross/Blue Shield) to an alternative Health Maintenance Organization (HMO) plan. Generally speaking, premiums for HMO plans are lower, but the insured person has less options with respect to choice of doctors and treatments. It was somewhat believed that those who are older, richer, and set in their ways would be less likely to want to switch. The response variable of primary interest in this study is ISW, where ISW = 1 if the respondent is willing to switch plans (from BC/BS to HMO) and ISW = 0 if the respondent is not willing to switch plans. Below are listed several variables (among nine investigated) that were believed to be associated with ISW: • INCOME (on a l 5 scale, where l=Poor Respondent and 5=Rich Respondent); 1 • IHMOP 0 1 variable; 1=Prior use of HMO by responsdent; (=No prior use of HMO); • INWH (0 1 variable; 1=Respondent is Non-White; 0=Respondent is White); • IOLD (0 1 variable; 1=Respondent is 44+ years old; 0=Respondent is < 44). For example, below is the 2 x 2 table classifying the respondents by ISW (0 or 1) and IOLD, where IOLD = 0) if the respondent is < 41 years old and IOLD = 1 if the respondent is 44 or older. (44 was chosen since it is approximately the median age of the survey respondents). Similar tables could be made for ISW vs. the other three potential explanatory variables. IOLD=0) IOLD=1 Total ISW = 0 270 353 623 ISW=1 148 60 208 Total 418 413 831 The dataset 'soh.csv' consisted of 831 lines of data, with much information on each respondent being displayed in each row. The models (I-A, 1-B, I-C, I-D, II) which we will consider in this problem are shown below. Model # Variables (I-A) INCOME (I-B) IHMOP (I-C) INWH (I-D) IOLD (II) INCOME, IHMOP, INWH, IOLD

(5 pts) Based on the result in part (a) Model II, which of the 40 combinations of (INCOME, IHMOP, INWH, IOLD) are predicted to be most favorable by logistic regression, least favorable, and most typical for switching? Fill in the table below with the predicted and observed probabilities of switching for these three combinations. INCOME IHMOP INWH IOLD PRE. P(SW=1) OBS. P(SW=1) MOST TYPICAL LEAST Attention: The most favorable combinations correspond to the highest possible predictor levels for variables with positive coefficients, and the lowest possible levels for those with negative coefficients. The least favorable is the opposite. To find the 'typical' case, note that overall 208 of 831 respondents, or 25.03% of the respondents wished to switch. So, we should compare the 40 predicted probabilities with 0.2503 to find the one whose predicted probability is closest to 0.2503. (5 pts) Predict the response variable based on the Model II using linear discrimi- nant analysis. Compare the prediction result with Logistic Regression using 5-fold cross validation.