Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING State with

Question

Econometrics: MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING

State with brief reasons whether the following statements are true (T), false (F), or uncertain (U). The adjusted and unadjusted R^2s are identical only when the unadjusted R^2 is equal to 1. 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. When R^2 = 1, F = 0, and when R^2 = 0, F = infinite. 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 Y_i = B_1 + B_2 X_2, + B_3 X_3i + u_i, if X_2 and X3 are negatively related in the sample and B_3 > 0, omitting X_3 from the model will bias b_12 downward [i.e., E(b_12)

Explanation / Answer

True; Adjusted R square is usually less than unadjusted R square except for when it is equal to 1. True; The independent variables need to explain the dependant variable. They successfully do so if the t-statistic lies out of the confidence interval. Uncertain. False True; since X3 is not used in the regression at all, the effect of X3 is captured in b12 and hence it is biased downward. True

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