State whether true, false, uncertain and reason why: -In the two variable PRF, b

Question

State whether true, false, uncertain and reason why:

-In the two variable PRF, b2 is likely to be a more accuarte estimate of B2 if the disturbances ui follow the normal distribution.

-The OLS estimators b1 and b2 each follow the normal distribution only if ui follows the normal distribution.

-r^2 is the ratio of TSS/ESS

-For a given alpha and d.f, if the computed | t | exceeds the critical value we should accepts the null hypothesis.

-The coefficient of correlation, r, has the same sign as the slope coefficient b2.

-The p value and the level of significance, alpha, mean the same thing.

Explanation / Answer

True (Because the variables may have unequal variability). May be true…… False. (R^2 = ESS/TSS) True (if computed t value is greater than critical value, it means that t is significant i.e the difference between means of two samples is significant and we reject that null hypothesis) False (The coefficient of correlation, r, has the same sign as the slope coefficient b and not b2). False (The level of significance is the threshold value that we measure p values against. I t tells us how extreme observed results must be in order to reject the null hypothesis of a significance test. A p-value is also a probability, but it comes from a different source than alpha. Every test statistic has a corresponding probability or p-value. This value is the probability that the observed statistic occurred by chance alone.)

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