Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).
Bayesian linear regression uses probabilities to model relationships between variables, aiming to estimate the probability of the relationship between a dependent variable and independent variables, allowing for predictions about the dependent variable based on observed values of the independent variables.