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How can I interpret the negative constant of -40348.86 on the following model?

π’€π’Š = π’ƒπŸŽ + π’ƒπŸπ‘ΏπŸπ’Š + π’ƒπŸπ‘ΏπŸπ’Š + 𝒃3𝑿3π’Š + πœΊπ’Š

Income= π’ƒπŸŽ + π’ƒπŸAge + π’ƒπŸHeight + 𝒃3Sex + πœΊπ’Š

Income= -40348,806 + 1891,185 age + 423,238 height +12215,847 sex

Sex has been coded as male=1 and female=0

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The intercept of -40348,806 is the prediction if all predictors have a value of zero.

Thus, a woman (sex = 0) of age 0 and height 0 would be predicted to have a negative income of -40348,806.

This is obviously completely irrelevant, since you presumably have no newborn girls of zero height in your sample. It illustrates that models often are nonsensical when extrapolating outside observed predictor settings.

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    $\begingroup$ Bang on, but I would add positive advice to work with log income not income. If you use a generalized linear model with logarithmic link, that (1) tolerates some freak zero or even negative values (2) yields predicted (mean) values that are positive. $\endgroup$
    – Nick Cox
    Jun 24 at 11:39
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    $\begingroup$ @NickCox: completely correct comment, of course, as always. I just wonder how useful the suggestion of a GLM is to an OP who is confused about a negative intercept in a straightforward linear regression... $\endgroup$
    – Stephan Kolassa
    Jun 24 at 14:20
  • $\begingroup$ Indeed. indeed/ $\endgroup$
    – Nick Cox
    Jun 24 at 17:14

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