1. Indicate whether the following statements are true or false. If the statement is false, alter it so that the statement becomes true.
a. If we would like to approximate the relationship between a response and two continuous predictors, we would need a plane.
b. In linear regression, while the response variable is typically continuous, it may be categorical as well.
c. In general, for a multiple regression with m predictor variables, we would interpret coefficient as follows: “the estimated change in the response variable for a unit increase in variable xi is bi.”
d. In multiple regression, the residual is represented by the vertical distance between the data point and the regression plane or hyperplane.
e. Whenever a new predictor variable is added to the model, the value of always goes up.
f. The alternative hypothesis in the F-test for the overall regression asserts that the regression coefficients all differ from zero.
g. The standard error of the estimate is a valid measure of the usefulness of the regression, without reference to an inferential model (i.e., the assumptions need not be relevant).
h. If we were to use only the categorical variables as predictors, then we would have to use analysis of variance and could not use linear regression.
i. For use in regression, a categorical variable with k categories must be transformed into a set of k indicator variables.
j. The first sequential sum of squares is exactly the value for SSR from the simple linear regression of the response on the first predictor.
k. The VIF has a minimum of zero, but no upper limit.
l. A variable that has been entered into the model early in the forward selection process will remain significant, once other variables have been entered into the model.
m. The variable selection criteria for choosing the best model account for the
multicollinearity among the predictors.
n. The VIFs for principal components using varimax rotation always equal 1.0.