Download Logistic Regression Problems: Remission in Cancer Patients and Death Penalty and more Exams Statistics in PDF only on Docsity! STA 6127 PRACTICE PROBLEM 3 These problems deal with logistic regression and related issues. 1. This problem studies remission in cancer patients (1=remission, 0=not successful) as a function of the explanatory variable called labelling index (LI). Following is a part ofthe SAS output obtained: ------------------------------------------------------------------- Intercept Intercept and Criterion Only Covariates -2 Log L 34.372 26.073 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio * 1 0.0040 Parameter Estimate Standard Error Chi-Square Pr > ChiSq Intercept -3.7771 1.3786 7.5064 0.0061 li 0.1449 0.0593 * 0.0146 Obs li remiss n pi_hat lower upper 1 8 0 2 0.06797 0.01121 0.31925 2 10 0 2 0.08879 0.01809 0.34010 -------------------------------------------------------------------- (a) State the fitted model in terms of π̂. 1 (b) If a patient has labeling index value 15, predict the odds of that patient having successful remission as opposed to not having successful remission. (c) Now predict the probability π̂ for a person with LI=15. Using this value find out the approximate slope of the curve around LI=15. Does the chance of successful remission increase or decrease with increase in LI? 2 2. This problem deals with a similar data discussed in class to study death penalty as a function of defendants race and vicitims race.(death penalty=1, not death penalty=0, victim’s race=1 if white, =0 for black, defendant’s race=1 if white, 0 if black. Following is a part of SAS output. ----------------------------------------------------------------- Criteria For Assessing Goodness Of Fit Criterion DF Value Deviance 1 0.3798 Pearson Chi-Square 1 0.1978 Log Likelihood -209.4783 Standard Likelihood Ratio Chi- Parameter Estimate Error 95% Conf Limits Square Intercept -3.5961 0.5069 -4.7754 -2.7349 50.33 def -0.8678 0.3671 -1.5633 -0.1140 5.59 vic 2.4044 0.6006 1.3068 3.7175 16.03 LR Statistics Source DF Chi-Square Pr > ChiSq def 1 5.01 0.0251 vic 1 20.35 <.0001 ----------------------------------------------------------------- (a) Write down the fitted model in terms of logit(π̂). 5 (b) Quote two Goodness of fit statistic from the output and check whether they are significant or not. What does it imply, model fits well to data or not? (c) After controlling for victim’s race find the parial odds ratio for death penalty for a white defendant as opposed to a black defendant. 6 (d) After controlling for defendant’s race find the parial odds ratio for death penalty for a white victim as opposed to a black victim. (e) Summarize in words what you think about the death penalty verdict as a function of the defendant’s and victim’s race in the light of your answers to part (c) and (d). 7