13.86 Logistic versus linear For binary response variables, one reason that logistic regression is usually preferred over straight-line regression is that a fixed change in x often has a smaller impact on a probability p when p is near 0 or near 1 than when p is near the middle of its range. Let y refer to the decision to rent or to buy a home, with p = the probability of buying, and let x = weekly family income. In which case do you think an increase of $100 in x has greater effect: when x = 50,000

(for which p is near 1), when x = 0 (for which p is near 0), or when x = 500? Explain how your answer relates to the choice of a linear versus logistic regression model.