linear regression the most basic regression model involves linear relationship between the response and single explanatory variable in particularwe have measurements ( )(xn yn that lie approximately on straight lineas in figure - - - - figure data from simple linear regression model following the general scheme captured in ( ) simple model for these data is that the {xi are fixed and variables {yi are random such that yi xi ei ( for certain unknown parameters and the {ei are assumed to be independent with expectation and unknown variance the unknown line { ( ( bis called the regression line thuswe view the responses as random variables that would lie exactly on the regression linewere it not for some "disturbanceor "errorterm represented by the {ei the extent of the disturbance is modeled by the parameter the model in ( is called simple linear regression this model can easily be extended to incorporate more than one explanatory variableas follows regression line simple linear regression model definition multiple linear regression model in multiple linear regression model the response depends on -dimensional explanatory vector [ xd ]via the linear relationship bd xd ewhere and var ( multiple linear regression model