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In an experiment, the participants were asked to allocate 100% of their budget to three categories in different scenarios. Now, I am analyzing the allocation to one particular category via OLS regression, where the dependent variable is the allocation to said good in a range from 0-100.

I have used the linear probability model (as requested by my instructor) (i.e., normal regress functions in Stata). Now, one coefficient that measures study hours amounts to -1.19, and I'm uncertain of the correct interpretation.

Analyzing the other two categories, I had coefficients of 0.67 and 0.91, which I interpreted as "the increase of one additional study hour is associated with a 67 / 91 percentage point increased allocation to the good.

As my dependent is restricted to a range of 0 -100 (as we did not allow borrowing additional money), I thought that the coefficient of the first category above 1 was a limitation of the normal regression, and I should rather use logit instead.

The logit coefficient amounts to -.2383773, and the odds ratio is .7879054.

I would be most grateful if anyone could tell me how to interpret the -1.19.

Thank you in advance!

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  • $\begingroup$ I'd just write the interpretation of the coefficients as percentage point increase/decrease per additional minute of studying. $\endgroup$
    – VARulle
    Commented Feb 27 at 8:23

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For some regressor values, you can get feasible fitted values of the dependent variable even when the regression coefficients are quite large (positive or negative). It may be that you can still interpret the coefficients in the usual way as long as the regressor values stay close to their averages.

  • If you set the regressor values to their averages, do you obtain a feasible value of the dependent variable? (Hopefully, you do.)
  • How far can you vary the variable associated with the coefficient -1.19 (keeping the other regressors at their means) so that the dependent variable stays within its allowable range?

The idea is, we know the model is fundamentally flawed as it can produce values of the dependent variable that are outside the feasible range. However, perhaps it can be useful locally (for some "typical" values of $X$s).

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