Question

Suppose the researcher somehow discovers that the values of the population slope (,), the standard deviation of the regressor (x), the standard deviation of the error term (O), and the correlation between the error term and the regressor (Pxu) are 0.48, 0.58, 0.34, 0.53, respectively. As the sample size increases, the value to which the slope estimator will converge to with high probability is (Round your answer to two decimal places.) In this case, the direction of the omitted variable bias is positive Assume father's weight is correlated with his years of eduction, but is not a determinant of the child's years of formal education. Which of the following statements describes the consequences of omitting the father's weight from the above regression? O A. It will not result in omitted variable bias because the omitted variable, weight, is not a determinant of the dependent variable. OB. It will not result in omitted variable bias because the omitted variable, weight, is uncorrelated with the regressor. O c. It will result in omitted variable bias the father's weight is a determinant of the dependent variable. OD. It will result in omitted variable bias because the omitted variable, weight, is correlated with the father's years of education.

Answer 1

As the sample size increases, the value to which the slope estimator will converge to with high probability is 0. 48.

The consequences of omitting the father's weight from the above regression is D. It will result in omitted variable bias because the omitted variable, weight, is correlated with the father's years of education.

How to describe the sample size increase?

Given the population slope (β) is 0.48, as the sample size increases, the slope estimator will converge to this value with high probability. Thus, the value to which the slope estimator will converge is 0.48.

The direction of the omitted variable bias in regression analysis depends on the sign of the correlation between the omitted variable and the dependent variable, and the sign of the correlation between the omitted variable and the included regressor.

Option D suggests that there will be an omitted variable bias if the father's weight, which is correlated with the regressor (years of education), is not included in the model.

This correlation can induce bias in the estimated effect of the father's education on the child's education, even if the father's weight does not directly affect the child's education.