# multiple linear regression

#### xbender

##### New Member
Hello,
I have an econometric model using multiple linear regression.
lets say Q=alpha+beta*P1+gamma*P2+residuals
I would like to ask if the absolute values of P1 matter in estimating the correct coefficients. If I would run the regression with P3 (P3=P1-x; x being a real number) instead of P1, would I get the same result and just a different alpha, or would the estimate itself be different?

#### BGM

##### TS Contributor
$$P_1 = P_3 + x$$
$$\Rightarrow Q = \alpha + \beta(P_3 + x) + \gamma P_2 + \epsilon = (\alpha + \beta x) + \beta P_3 + \gamma P_2 + \epsilon$$

So you should get a new $$\alpha ' = \alpha + \beta x$$

#### xbender

##### New Member
this makes sense, so the estimation of the coefficient is the same and just the alpha changes, that is what I have expected ...

one more thing...how would it work if the model was in log version? how do you cope with the logarith of the sum/difference? alpha+beta*log(P1+x) or eventually alpha+beta*log(P1-x)

... I guess that cannot be rewritten, so I would end up with a different estimate of the coefficient since the independent variable itself has changed...

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