Multiple linear regression is an extension of simple linear regression to model the relationship between a scalar dependent variable and two or more explanatory variables.

Here are a few key aspects about multiple regression:

It allows us to analyze the joint relationships and relative influence of multiple independent variables on a single dependent variable.

The regression equation becomes:

y = b0 + b1x1 + b2x2 +…+ bnxn

Where b0 is the intercept, b1 to bn are coefficients of variables x1 to xn.

Both continuous and categorical variables can be used as independents.

It helps determine the individual and partial contribution of each independent variable in explaining the variance in dependent variable.

Interpretation of coefficients is similar to simple linear regression – they indicate the expected change in Y with each one unit increase in the corresponding X, keeping others constant.

Evaluation metrics like R-squared, F-statistic, p-values, etc. are used to assess overall model fit and significance.

Assumptions include linearity, no multicollinearity, homoscedasticity, independence of errors, normality of residuals.

Variable selection techniques help determine the optimal set of predictors.

So in summary, multiple regression extends linear modeling to multiple independent factors simultaneously.