what is multiple linear regression mlr 
multiple linear regression mlr also known simply as multiple regression is a statistical technique that uses several explanatory variables to predict the outcome of a response variable the goal of mlr is to model the linear relationship between the explanatory independent variables and response dependent variables in essence multiple regression is the extension of ordinary least squares ols regression because it involves more than one explanatory variable formula and calculation of multiple linear regression mlr y i 0 1 x i 1 2 x i 2 p x i p where for i n observations y i dependent variable x i explanatory variables 0 y intercept constant term p slope coefficients for each explanatory variable the model s error term also known as the residuals begin aligned y i beta 0 beta 1 x i1 beta 2 x i2 beta p x ip epsilon textbf where for i n textbf observations y i text dependent variable x i text explanatory variables beta 0 text y intercept constant term beta p text slope coefficients for each explanatory variable epsilon text the model s error term also known as the residuals end aligned yi 0 1 xi1 2 xi2 p xip where for i n observations yi dependent variablexi explanatory variables 0 y intercept constant term p slope coefficients for each explanatory variable the model s error term also known as the residuals 1