Linear or logistic regression for discrete data: Simulate continuous data from the regression model, z = a + bx + error. Set the parameters so that the outcomes z are positive about half the time and negative about half the time.

(a) Create a binary variable y that equals 1 if z is positive or 0 if z is negative. Fit a logistic regression predicting y from x. (b) Fit a linear regression predicting y from x: you can do this, even though the data y are discrete. (c) Estimate the average predictive comparisonthe expected difference in y, corresponding to a unit difference in xbased on the fitted logistic regression in (a). Compare this average predictive comparison to the linear regression coefficient in (b).