The Bayesian Information Criterion ($BIC$) is a criterion for model selection among a finite set of models. For a linear regression model, it is defined as: $BIC = \\frac{RSS + \\log(n)d\\hat{\\sigma}^2}{n\\hat{\\sigma}^2}$ where $RSS$ is the Residual Sum of Squares, $d$ is the number of predictors, $n$ is the number of observations, and $\\hat{\\sigma}^2$ is an estimate of the error variance. A lower $BIC$ value indicates a better model. $BIC$ is closely related to the Akaike Information Criterion ($AIC$), but unlike $AIC$, the $BIC$ formula considers the number of observations ($n$).