## 7.5 Comparing the Bayesian and Frequentist Approaches

The frequentist approach works better when the data are normally distributed and the predictors are independent of each other. We showed how to use the least-squares criterion with the conventional analysis to reduce the sum-of-the-squared errors of prediction. This technique enables us to test the null hypotheses that each regression coefficient is 0 in the population and that R-squared (the overall goodness of the model) is also 0 in the population, both of which are based on frequentist thinking.

The Bayesian approach does not require such assumption. We may create a distribution for each regression coefficient (B-weight) and the value of R-squared using the knowledge we have about our outcome and predictors. The center of these distributions can be used to determine the location of each coefficient value, and a highest density interval (HDI) can be created to determine the range of values that are feasible given the limitations of sampling.