Econometric Theory/Proofs of properties of β1

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Linearity[edit]

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

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

Proof[edit]

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.