Bayesian linear regression

In Chapter 3, More Than Just One Predictor – MLR, we have seen that the general Multiple Linear Regression (MLR) model for n variables is of the form:

Here, x₁, x₂,.. x_n are the n predictors and y is the only response variable. The coefficients β measure the change in the y value associated with a change of x_i, keeping all the other variables constant.

In order to estimate β, we minimized the following term:

The general linear regression model can be expressed using a condensed formulation:

Here, β =[β₀, β₁, β₂,…, β_n]. To determine the intercept and the slope through the least squares method, we have to solve the previous equation with respect to β, as follows (we must estimate the coefficients with the normal equation):

To predict a new value of the response variable, given some new predictors data, we simply multiply the components of the new predictors by the associated β coefficients. So, in estimating a new observation, the β coefficients are treated as fixed values...