Determine which of the following statements are true and false. For each statement that is false, explain why it is false.

(a) Suppose we consider the first two observations based on a logistic regression model, where the first variable in observation 1 takes a value of x₁ = 6 and observation 2 has x₁ = 4. Suppose we realized we made an error for these two observations, and the first observation was actually x₁ = 7 (instead of 6) and the second observation actually had x₁ = 5 (instead of 4). Then the predicted probability from the logistic regression model would increase the same amount for each observation after we correct these variables.

(b) When using a logistic regression model, it is impossible for the model to predict a probability that is negative or a probability that is greater than 1.

(c) Because logistic regression predicts probabilities of outcomes, observations used to build a logistic regression model need not be independent.

(d) When fitting logistic regression, we typically complete model selection using adjusted R².