This can be a good start for the multivariate regression.
First of all, you need a mathematical model like this:
$y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \varepsilon$.
Basically you have a mathematical equation were the $y$ is your response variable and the $X$ matrix has 2 columns, your explanatory variables, the regressors. The $\varepsilon$ is a vector that concern all the things that are not explained with the $X$, the remainder; usually is an $iid$ process with $0$ mean and $\sigma^2$ costant variance.
Assume that you estimate the coefficients with the $OLS$ and so you get th classic Gaussian Multivariate Model.
Shortly, the $\beta$ coefficients are the effects of the two $x$ variables on the response $y$. You can interpret this effect with the Ceteris Paribus:
- $\beta_1$ is the effect on the $y$ by an increment of 1 unit of the $X_1$, with $X_2$ constant.
- The same for $\beta_2$ but in the inverse order.
- $\beta_0$ is the intercept, the mean value of the $y$ when all the $x$ variables (and so their effects) are null.
