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.