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Woodworth and Baldus of the University of Iowa collected ext

Woodworth and Baldus of the University of Iowa collected extensive data on death penalty sentencing… Show more Woodworth and Baldus of the University of Iowa collected extensive data on death penalty sentencing in Georgia. The information was presented for defendant McClesky in the 1988 law case, McClesky vs. Zant. Table 1 provides information on a subset of their data, in constellation format. It consists of 362 death penalty cases. For each case, the following variables were collected: y = death penatly (yes, no) x_1 = aggravation level (1,2,3,4,5,6) x_2 = race of victim (1, if white; 0, if black) Aggravation level 1 comprises those involving bar room brawls, liquor-induced arguments, and lovers’ quarrel; level 6 comprises the most vicious, cruel, cold-blooded, unprovoked crimes. a) Briefly interpret the estimated odds ratio=6.03 for aggravation level 1 in Table 1. b) Fit the logit model $pi^*(x_1, x_2) = beta_0 + beta_1 x_1 + beta_2 x_2$ . Interpret the fitted model obtained, specifically, what do the odds ratios mean? c) Test for adequacy of the fitted model. (State Ho vs. Ha, test statistic, p-value, and conclusion) d) Is there evidence to indicate that aggravation level is a significant predictor of death penalty? What about race of the victim? Justify your answer e) Find a 95% confidence interval for the predicted probability of a death penalty when the aggravation level is 4 and the victim is white. Interpret this confidence interval. f) For each constellation, give two estimates of $pi(x_1, x_2)$=probability of a death penalty: (i) based on the saturated or full model (denote this by p($x_1,x_2$)) and (ii) based on the logistic or reduced model (denote this by $hat{pi} (x_1,x_2)$). Test for goodness of fit of the logistic model. • Show less

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