Problem 2: Multiple Choice Choose the statement that is true about the estimator

Question

Problem 2: Multiple Choice Choose the statement that is true about the estimators for the slope and intercept of a regression line. Assume the conditions of the linear model holo. a. The estimators of the slope and intercept of a regression line are unbiased. b. The sampling distributions of the estimators will follow the Normal distribution if the Normal condition of the error terms is met. c. The sampling distributions of the estimators will be approximately Normal if the Nor- mal condition of the error terms is not met but the sample size is large. d. All of the above are true. e. None of the above are true.

Explanation / Answer

Solution: Here option (a) is correct.

The estimator of the slope and intercept of a regression line are unbiased.

Reason: We know by using Guass-Markov theorem, in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator(BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.

That means using OLS we can find Unbiased estimator / BLUE of coefficients.

Done

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