Refer to Table 4.2. Using weight as the predictor, fit the logistic regression model for the probability of a satellite.

a. Report and plot the ML fit, and find predicted probabilities at the values 1.20, 2.44, and 5.20 kg of weight, which are the sample minimum, mean, and maximum.

b. Find the weight at which the predicted probability equals .5. At that value, give a linear approximation for the estimated effect of a 1-kg increase in weight. This represents a relatively large increase, so interpret in terms of (i) a 0.1-kg increase, (ii) a standard deviation increase in weight.

c. Provide an odds interpretation for the association. Construct a 95% confi- dence interval to describe the effect of weight on the odds of a satellite.

d. Using a Wald test, find the P-value for the hypothesis that weight has no effect. Perform also a likelihood-ratio test for the effect. Interpret.