State with reason whether the following statements are true, false, or uncertain:

a. Despite perfect multicollinearity, OLS estimators are BLUE.

b. In cases of high multicollinearity, it is not possible to assess the individual significance of one or more partial regression coefficients.

c. If an auxiliary regression shows that a particular R²_i is high, there is definite evidence of high collinearity.

d. High pair-wise correlations do not suggest that there is high multicollinearity.

e. Multicollinearity is harmless if the objective of the analysis is prediction only.

f. Ceteris paribus, the higher the VIF is, the larger the variances of OLS estimators.

g. The tolerance (TOL) is a better measure of multicollinearity than the VIF.

h. You will not obtain a high R² value in a multiple regression if all the partial slope coefficients are individually statistically insignificant on the basis of the usual t test.

i. In the regression of Y on X₂ and X₃, suppose there is little variability in the values of X₃. This would increase var (β̂₃). In the extreme, if all X₃ are identical, var (β̂₃) is infinite.