Interpreting Intercept in OLS

[Marie Sofie]

Hello! I have a simple OLS model, where my predictor is a dichotomous variable (treatment, no treatment). I have run an OLS model, and have the intercept with a big coefficient and statistically significant. Does it mean something? Does it tell me something about the model? Thank you.

[Clyde Schechter]

The intercept in the model is just the expected value of the outcome variable when all of the predictors are zero. If I understand your post correctly, your model has only one predictor, treatment vs no-treatment. So the intercept is just the expected value of the outcome variable in whichever of those groups is coded as 0. (If neither is coded as 0 then the intercept is utterly meaningless.) Generally speaking, this just reflects the overall location of the outcome variable distribution, which is usually a consequence of the particular way in which it is measured or defined. Significance tests of whether the expected outcome in one of the groups is zero are usually not of any interest, unless that was an explicit goal of the research.

[Bruce Weaver]

Marie, here are some examples that illustrate some of what Clyde said in #2. Enjoy!

clear *
sysuse auto
ttest mpg, by(foreign)
regress mpg foreign, noheader
regress mpg i.foreign, noheader
margins foreign
margins a.foreign, contrast(nowald effects)
margins ar.foreign, contrast(nowald effects)
regress mpg ib(first).foreign, noheader
regress mpg ib(last).foreign, noheader
* help fvvarlist // Uncomment this line for more info about factor variables

[Marie Sofie]

These are helpful, thank you so much!

[Richard Williams]

As a sidelight, the intercept can sometimes (albeit not in your case) be a more or less meaningless number because it is impossible for all the Xs to equal zero. For example, nobody is zero years old, nobody weighs zero pounds, nobody gets a zero on a scale that runs from 400 to 1200. People therefore sometimes like to center the independent variables, i.e. subtract the mean from each case. The constant then becomes the predicted score for a person who has average scores on the Xs. This is discussed in more detail at

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[Nick Cox]

For a riff on the theme of origins, see https://www.stata-journal.com/articl...article=st0394 (which will be readable by all when SJ 18(2) is published, in about a month's time).