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I have a five-variable regression equation, and I added any constant (fixed value, say 100) to all the observations of variable $A$, another (or same) fixed value in variable $B$, while the other three variables are unchanged, what will be the interpretation of the Betas of variable $A$ & $B$ (A & B are Independent variables).

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  • $\begingroup$ If I read you correctly you are asking how the coefficients change if you add a constant value to all the observations of one of the variables in multiple regression. Is that correct? $\endgroup$ – Antoni Parellada Apr 30 '16 at 17:18
  • $\begingroup$ Dear Antoni, Yes. My point is if I have independent variable (A) and I transformed A by adding constant in all its observation and new variable is A*. Now I regress the multiple regression and use A* instead of A. How I can interpret the coefficient of A*. Remember I am interested in coefficient of A not A*. Thanks $\endgroup$ – Muhammad Husnain May 1 '16 at 4:53
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    $\begingroup$ What is the reason you want to add that constant? $\endgroup$ – Metariat May 1 '16 at 8:05
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If you transform one of the regressors by adding a constant, this shift will not influence the actual slope or estimated coefficient $\hat \beta_i$ of the regressor. Instead, it will be absorbed in the estimated intercept, which will be displaced because all the points in the data cloud will shift accordingly. As an example, here is the plot of a multiple regression with only one regressor plotted together with the OLS regression line including the intercept and the slope of the plotted regressor. After shifting the explanatory variable $20$ units up, the slope stays unchanged, but the intercept is shifted accordingly:

enter image description here

If instead, you transformed the variable in question by multiplying it by a scalar value, there would not be any translation of the data cloud, but the slope would change. You would be doing the equivalent of a change of units in the explanatory variable:

enter image description here

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