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 30 times

In 1997 Ms Susan Oh Conducted A Survey Of N 831 Faculty And Staff Concerning Their Willingness To Switch Insurance P 2 (76 KiB) Viewed 30 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

(10 pts) Using all the observations, predict the response variable based on the models shown in the above table using logistic regression and report the fitting results. (10 pts) Show how you could have deduced the values of 0 and 1 in Model (I-D) just from the 2 x 2 table above without even running a program. Attention: Based on the table, when IOLD=0, p = 148/418 and 1 - p = 270/418. Thus, In(p/1 - p) = Bo + B1 x 0 = Bo = In(p/1 - p), so this gives you Bo. When IOLD=1, p = 60/413 and 1-p=353/413. Thus, In(p/1 - p) = Bo+Bı x1= B = ln(p/1-P) - Bo. Verify if ß, and ß, agree with the coefficient estimates shown for Model (I-D).