What is the actual importance of an intercept term in a regression equation? If regressors include variables like age, height, weight and gender(1= male, 0= female), should the equation have an intercept term?
-
1"*should the equation have an intercept term?*" --- yes, definitely. – Glen_b Aug 30 '14 at 11:19
-
1If you drop the intercept in your model, then the R-squared and many of the inferences will do funny things. – Michael M Aug 30 '14 at 14:27
1 Answers
To visualize what happens, first think about the case where there are two predictors, say height and weight. Then your regression mod,el fits a plane to the data. If you exclude the intercept, you are forcing that plane to pass through the origin, which can tilt it considerably from what it would be if the intercept is included. So by omitting the intercept, you are giving a lot of leverage to the origin, which is often very remote from the data (like height 0 and weight 0).
The same ideas apply with 1 predictor, only it's a line -- and with 3 or more predictors, where it's just harder to visualize.
And note also with the gender variable you mention included, omitting the intercept from the model has the consequence that the predicted plane for females passes through the origin, while the predicted plane for males does not. And the reverse would be true if you had coded gender the other way. That's an additional reason that it almost always makes sense to include the intercept.

- 15,161
- 20
- 53
-
-
1Well, you didn't say that in your original question. But if all the variables, both predictors and response, are centered, then you don't need the intercept term. Instead, you take away 1 df for residual because of centering the response variable. Once you have done all that, it is equivalent to *including* the intercept in the model where the variables are not centered. – Russ Lenth Aug 31 '14 at 19:24
-
Shouldn't the intercept be still there if only the predictors are centered? – user53740 Aug 31 '14 at 19:34
-
Yes, the intercept should be included if the response is not centered – Russ Lenth Aug 31 '14 at 20:31