For the Crabs data file at the text website, fit the logistic regression model for the probability of a satellite (y = 1) using x = weight as the sole explanatory variable.

a. Report the ML prediction equation. At the mean weight value of 2.437 kg, give a linear approximation for the estimated effect of (i) a 1-kg increase in weight. This represents a relatively large increase, so convert this to the effect of (ii) a 0.10-kg increase, (iii) a standard deviation increase in weight (0.58 kg).

b. Find and interpret the average marginal effect of weight per 0.10-kg increase.

c. Construct the classification table using the sample proportion of y = 1 as the cutoff. Report the sensitivity and specificity. Interpret.

d. Construct an ROC curve, and report and interpret the area under it.