Econometric Theory/Proofs of properties of β1

< Econometric Theory

LinearityEdit

To be linear,   must be a linear function of  , as shown below

 

where   is a constant, at any given observation 'i'.

ProofEdit

From the deviation-from-means form of the solution of the OLS Normal Equation for  , we have

 

 , since  .

 , where  , which is a constant for any given 'i'-value.