In this chapter, we extend the linear regression model allowing for several explanatory variables. For example, if we have three explanatory variables then, including the intercept, we will have four unknown beta parameters. We will use the symbol k to denote the number of unknown beta parameters. The OLS principle for estimating the beta parameters will still work but the mathematics will become more complicated and is best done using matrices. However, we can always feed data into software and get the OLS estimates from the software. The fundamental assumption, exogeneity, will be discussed and we will conclude that the OLS estimator will be unbiased and consistent under this assumption. Further, the OLS estimator will be best if the error terms are homoscedastic.