Business Analytics > Predictive Modelling > Multiple Linear Regression

Multiple linear regression

When a linear regression model is with more than one independent variable is called a multiple linear regression model. Simple linear regression is just a special case of multiple linear regression. A multiple linear regression model has the form

where Y is the dependent variable, X₁,…, X_k are the independent (explanatory) variables, b₀ is the intercept term, b₁, …. , b_k are the regression coefficients for the independent variables, and e is the error term.

The partial regression coefficients represent the expected change in the dependent variable when the associated independent variable is increased by one unit while the values of all other independent variables are held constant.

Thus, b₁=2.5  would represent an estimate of the change in the advertizinge for a unit increase in the Sales while holding all other variables constant.

Multiple R and R Square (or R²) are called the multiple correlation coefficient and the coefficient of multiple determination, respectively, in the context of multiple regression. They indicate the strength of association between the dependent and independent variables. Similar to simple linear regression, R² explains the percentage of variation in the dependent variable that is explained by the set of independent variables in the model.

 

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