Category:Gujarati -> Chapter 07
Question:
07.02 State with brief reasons whether the following statements are true, false, or uncertain.
a. OLS in an estimating procedure that minimizes the sum of the errors squared, .
b. The assumptions made by the classical linear regression model (CLRM) are not necessary to compute OLS estimators.
c. The theoretical justification for OLS is provided by the Gauss-Markov theorem
d. In the two-variable PRF, b2 is likely to be a more accurate estimate of B2 if the disturbances ui follow the normal distribution.
e. The OLS estimators b1 and b2 each follow the normal distribution only if ui follows the normal distribution.
f. r² is the ratio of TSS / ESS.
g. For a given alpha and d.f., if the computed ItI exceeds the critical t value, we should accept the null hypothesis.
h. The coefficient of correlation, r, has the same sign as the slope coefficient b2.
i. The p value and the level of significance, α, mean the same thing.

Answers:

07.02 a
False. It minimuzes the sum of residuals squared, that is, it minimizes .

07.02 b
True.

07.02 c
True.

07.02 d
False. The OLS does not require any probabilistic assumption about the error term in estimating the parameters.

07.02 e
True. The OLS estimators are linear functions of ui and will follow the normal distribution if it is assumed that ui are normally distributed. Recall that any linear function of a normally distributed variable is itself normally distributed.

07.02 f
False. It is ESS / TSS.

07.02 g
False. We should reject the null hypothesis.

07.02 h
True. The numerator of both coefficients involves the covariance between Y and X, which can be positive or negative.

07.02 i
Uncertain. The p value is the exact level of significance of a computed test statistic, which my be different from an arbitrarily chosen level of significance, α.

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