3. (10 points) Answer the following questions: (3 points) What does it mean to s

Question

3. (10 points) Answer the following questions: (3 points) What does it mean to say that the standard error of an estimated regression coefficient is biased? (3 points) For a random variable X, the sample mean X is an estimator of the population mean Is X constant or random? Is ux constant or random? (4 points) Explain how the standard error of regression (SER) relates to R2. In particular, if the R2 of an estimated regression is higher, what must be true (other things equal) about the SER? a. b. c.

Explanation / Answer

(a) The standard error of an estimated regression coefficient is biased means that it does not follow Normal(0, sigma^2) distribution, and is affected by some omitted observations or some multicollinear variable in the model

(b) The sample mean changes with every new sample that is taken up therefore it is random. Population mean does not change and therefore it is constant.

(c) SER is inversely proportinal to R^2 which means that if the R^2 of an estimated regression is higher, (there things being equal) its SER will be smaller.

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