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Can you interpret coefficients in regression analysis output as if they say something about causes of effect. Or is it always about effect of causes? In other words, can a regression analysis answer why-questions or is it always about what-if questions?

Example: Your dependent variable is income in USD (continuous), your independent variables are education (ordinal), sex (dummy) and age (continuous). You fit your OLS model to your data and the output says:

Education: 10

Sex: -3

Age: -5

Constant: 50

Can you say that because of higher education there is in average higher income while having other IVs constant? Or just if you change education by 1 you get +10 into your income in average while having other IVs constant?

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In your model, it projects that as education goes up one unit (say from education 1 to education 2), income goes up by 10 units. As you have age and sex in the model, these results are adjusted for those variables, so it still goes up by 10 whether you are male or female or whether you are young or old.

The same is true for the other variables. No matter your education and sex, if you are young, you will have a lower income.

If you want to examine the relationship between education, age and sex, you can use interaction terms in your model.

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  • $\begingroup$ Thank you for answer. That is exactly the what-if interpretation of regression coefficients is. It says what happens with your DV in average if certain IV goes up by one unit (while "holding other IVs constant"). What I am trying to get is if it also works for answering backward questions. For example you would ask this: Given the value of DV does this particular IV (for example "education") contributed to the DV? $\endgroup$ – Nothingman Nov 12 '20 at 6:54
  • $\begingroup$ That question can be answered by accessing your statistics software and then doin a regression for y and x, then swapping x and y. Now try adding more variables and swap again. Do coefficients and significance measurements tally to the exact same values? $\endgroup$ – Paze Nov 17 '20 at 6:55

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