State with brief reasons whether the following statements are true (T), false (F), or uncertain (U).
a. The adjusted and unadjusted R2s are identical only when the unadjusted R2 is equal to 1.
b. The way to determine whether a group of explanatory variables exerts significant influence on the dependent variable is to see if any of the explanatory variables has a significant t statistic; if not, they are statistically insignificant as a group.
c. When R2 = 1, F = 0, and when R2 = 0, F = infinite.
d. When the d.f. exceed 120, the 5% critical t value (two-tail) and the 5% critical Z (standard normal) value are identical, namely, 1.96.
*e. In the model Yi, = B1 + B2X2i + B3X3i ui, if X2 and X3 are negatively correlated in the sample and B3 > 0, omitting X3 from the model will bias b12 downward [i.e., E(b12) < B2] where b12 the slope coefficient in the regression of Y on X2 alone.
f. When we say that an estimated regression coefficient is statistically significant, we mean that it is statistically different from 1.
g. To compute a critical t value, we need to know only the d.f.
h. By the overall significance of a multiple regression we mean the statistical significance of any single variable included in the model.
i. Insofar as estimation and hypothesis testing are concerned, there is no difference between simple regression and multiple regression.
j. The d.f. of the total sum of squares (TSS) are always (n - 1) regardless of the number of explanatory variables included in the model.