In a class of 50 students, a logistic regression is performed of course grade (pass or fail) on midterm exam score (continuous values with mean 60 and standard deviation 15). The fitted model is...

In a class of 50 students, a logistic regression is performed of course grade (pass or fail) on midterm exam score (continuous values with mean 60 and standard deviation 15). The fitted model is Pr(pass) = logit⁻¹
(−24 + 0.4x).

(a) Graph the fitted model. Also on this graph put a scatterplot of hypothetical data consistent with the information given.

(b) Suppose the midterm scores were transformed to have a mean of 0 and standard deviation of 1. What would be the equation of the logistic regression using these transformed scores as a predictor?

(c) Create a new predictor that is pure noise (for example, in R you can create newpred <->