ABSTRACT
Statistical models involve the interpretation and application of probability on some scale. In both frequentist and Bayesian approaches, basic probability distributions are used to link observed data to the population characteristics of interest. As both Bayesian and frequentist approaches can be sensitive to large sample arguments, it is worthwhile to review briefly the likelihood function arising in the case of the normal distribution. The properties of the likelihood function or likelihood surface in nonlinear settings affect the stability of the usual likelihood based test statistics. For both the t-test and F-test, the assumption of normality of the errors is necessary or a larger sample supporting application of central limit theorems. The use of centering in linear regression is often justified as a way to lower the observed correlation among the explanatory variables. Eigenvalues and related principal components play an important role in the theory and interpretation of linear models and data matrices.
