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Linear Regression Analysis – Interpreting the Intercept in a Regression Model

By Futli @futlim

The intercept (often labeled the constant) is the expected mean value of Y when all X=0.

Start with a regression equation with one predictor, X.

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If X sometimes = 0, the intercept is simply the expected mean value of Y at that value.

If X never = 0, then the intercept has no intrinsic meaning. In scientific research, the purpose of a regression model is to understand the relationship between predictors and the response.  If so, and if X never = 0, there is no interest in the intercept. It doesn’t tell you anything about the relationship between X and Y.

You do need it to calculate predicted values, though.  In market research, there is usually more interest in prediction, so the intercept is more important here.

When X never =0 is one reason for centering X. If you rescale X so that the mean or some other meaningful value = 0 (just subtract a constant from X), now the intercept has a meaning. It’s the mean value of Y at the chosen value of X.

If you have dummy variables in  your model, though, the intercept has more meaning.  Dummy coded variables have values of 0 for the reference group and 1 for the comparison group. Since the intercept is the expected mean value when X=0, it is the mean value only for the reference group (when all other X=0).

This is especially important to consider when the dummy coded predictor is included in an interaction term.  Say for example that X1 is a continuous variable centered at its mean.  X2 is a dummy coded predictor, and the model contains an interaction term for X1*X2.

The B value for the intercept is the mean value of X1 only for the reference group.  The mean value of X1 for the comparison group is the intercept plus the coefficient for X2.

Linear Regression Analysis – Interpreting the Intercept in a Regression Model

And now I would like to invite you to learn more about interpreting regression coefficients, including centered predictors, interactions, and more, in one of my FREE monthly Analysis Factor Teleseminars: “Interpreting Linear Regression Coefficients: A Walk Through Output.” Visit http://www.analysisfactor.com/learning/teletraining4.html to get started today.

© 2008 Karen Grace-Martin — Statistical Consultant and founder of The Analysis Factor

Karen Grace-Martin has helped social science researchers practice statistics for 9 years, as a statistical consultant at Cornell University and at The Analysis Factor. She knows the kinds of resources and support that researchers need to practice statistics confidently, accurately, and efficiently, no matter what their statistical background. To get answers, advice, and a list of resources to help you learn and apply appropriate statistics to your data, visit http://www.analysisfactor.com

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