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.