ABSTRACT
In the preceding chapters, the approach typically taken to solve the regression problem was characterized as classical or frequentist in nature, e.g., under the assumptions of the strong classical linear regression model, the method of maximum likelihood enabled us to determine point estimators for β0 and β1 (denoted β0 and β1, respectively), which coincided with OLS estimators for these parameters. Moreover, by virtue of these assumptions, the (unknown) sampling distributions of these estimators are normally distributed. (Remember that these sampling distributions describe the behavior of the relative frequencies of these estimators under hypothetical repeated sampling from the same population.) In this regard, any particular estimate of, say, β1, is treated as having been generated via a random drawing from β1’s sampling distribution, and the use of β1 as a point estimator of β1 is legitimized by the fact that β1 has certain desirable properties, e.g., β1 is BLUE for β1, among others.
