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

(a) If predictors are collinear, then removing one variable will have no influence on the point estimate of another variable's coefficient.

(b) Suppose a numerical variable x has a coefficient of b₁ = 2:5 in the multiple regression model. Suppose also that the first observation has x₁ = 7:2, the second observation has a value of x₁ = 8:2, and these two observations have the same values for all other predictors. Then the predicted value of the second observation will be 2.5 higher than the prediction of the first observation based on the multiple regression model.

(c) If a regression model's first variable has a coefficient of b1 = 5:7, then if we are able to influence the data so that an observation will have its x₁ be 1 larger than it would otherwise, the value y₁ for this observation would increase by 5.7.

(d) Suppose we fit a multiple regression model based on a data set of 472 observations. We also notice that the distribution of the residuals includes some skew but does not include any particularly extreme outliers. Because the residuals are not nearly normal, we should not use this model and require more advanced methods to model these data.