ABSTRACT
First, suppose for m = 1, we let βˆ1 represent the OLS estimator for the regression slope a1, whereas β1 is a slightly biased estimator for the same with a variance that is small relative to the variance of βˆ1. The sampling distributions of these estimators appear in Figure 14.1. Clearly, β1 has a small bias and is much more precise relative to the unbiased OLS estimator βˆ1. Hence, β1 is the preferred estimator because it has a higher probability of being close
to a1 than does βˆ1. The estimates obtained from the sampling distribution of β1 are more stable relative to those obtained from the sampling distribution of βˆ1.
