15.38.* For the logistic regression model, from the linear approximation /4 for the rate of change in

15.38.* For the logistic regression model, from the linear approximation β/4 for the rate of change in the probability at the x-value for which P(y = 1) = 0.50, show that 1/|β| is the approximate distance between the x-values at which P(y = 1) = 1/4 (or P(y = 1) = 3/4) and at which P(y = 1) = 1/2. Thus, the larger the value of |β|, the less the x-distance over which this change in probability occurs.