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Currently we have a linear model which includes 3 independent variables and the dependent variable "Y" which is the predicted values (range from -0.5 to 2000) from the model. Now we want to leverage the same model by just removing one of the predictor (lets call that as X1).

One of my colleague suggested to run a model by have a new dependent as (Y-X1) against the two predictors. Is this a correct approach or is there any better way like "offset" technique for continuous dependent variable?

I really appreciate your help in advance.

Gopi
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    Setting the new dependent variable to $Y-X_1$ is just equivalent to having a regression for $Y$ and using all three predictors but forcing the coefficient/effect for $X_1$ to be $1$. Further, perhaps it would be useful to know why you want to remove this predictor? –  Jun 11 '14 at 00:42
  • Yes i would like to make the effect of X1 to be 1. X1 is used for one type of product (New Business) and we want to ignore it for renewals which we try to make the effect of X1=1 for the renewals. – Gopi Jun 11 '14 at 00:49
  • Maybe this is a job for moderator/dummy variables? http://stats.stackexchange.com/questions/102902/how-do-you-do-regression-analysis-on-advertising-impact/102909#102909 – pedrofigueira Jun 11 '14 at 00:54
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    You can certainly use an offset if your software supports them (indeed in the case of some GLMs, that may be the only easy way to do it correctly). See the discussion of offset vs subtracting $x_1$ from $y$ here, for example – Glen_b Jun 11 '14 at 02:17

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