Final answer:
The question addresses whether the estimator βb is biased for the parameter β in linear regression, given a predictor variable x. Without additional context, it's difficult to determine bias. Generally, in simple linear regression using OLS, e(βb) = β, making it unbiased.
Step-by-step explanation:
The question is concerned with the expectation of a parameter estimate, βb, given a predictor variable, x, within the context of linear regression. The expectation of βb is denoted as e(βb|x). In the context of linear regression, an estimator βb is biased if the expected value of that estimator is not equal to the true value of the parameter β it is estimating; that is, e(βb) ≠ β. To determine if βb is biased or unbiased for β, we would typically calculate the expected value of the estimator and compare it to the true parameter value.
In this case, without further information or context such as the underlying model, it is impossible to give a definitive answer. For a simple linear regression model, the ordinary least squares (OLS) estimator is unbiased, meaning that e(βb) = β. However, if there are omitted variables that correlate with both the dependent and independent variables or if there is measurement error in the independent variables, the estimator may be biased.