5.30 The following are true–false questions.

a. A model for a binary response has a continuous predictor. If the model truly holds, the deviance statistic for the model has an asymptotic chisquared distribution as the sample size increases. It can be used to test model goodness of fit.

b. For the horseshoe crab data, when width or weight is the sole predictor for the probability of a satellite, the likelihood-ratio test of the predictor effect has P-value <0.0001. When both weight and width are in the model, it is possible that the likelihood-ratio tests for the partial effects of width and weight could both have P-values larger than 0.05.

c. For the model, logit[π(x)] = α + βx, suppose y = 1 for all x ≤ 50 and y = 0 for all x > 50. Then, the ML estimate ˆ β = −∞.