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I try to do a linear regression of a positive continuous dependent variable (outcome) with several independent variables (all of them are categorical / binary). I had many troubles to get Gaussian residuals (the distribution of my outcome variable is not Gaussian itself).

I tried a lot of transformations for the outcome: log, square root, inverse... and the best one is Box-Cox with a parameter: $\lambda = -3$. The regression is correct, the residuals are Gaussian, and homoscedastic. But I have found the Box-Cox is not the easiest thing to interpret. The original outcome represent a delay and there is no way to interpret the transformed outcome with a mix of power and inverse. And when I want to come back to my original outcome, I have cube root (or power 1/3).

My questions are:

  • How is the change of a given binary variable modality on my original outcome, knowing the corresponding coefficient?
  • Can I do the same thing with the confidence interval (2.5% and 97.5% limits) of the regression coefficients?
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Why use Box-Cox here at all? Consider using a generalised linear model with power link. That way you get predictions on the scale of the original variable automatically.

Why sacrifice all on the altar of Gaussian residuals? If you use a generalised linear model, you can use other error families.

If I understand you correctly, your outcome is delay, i.e. some lapse measured in time units. Reciprocal links (or transformations) are often natural for such variables, as the reciprocal of a time is some kind of rate (e.g. a speed of processing, or some such).

I don't understand the question on "change of a given binary variable modality".

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    $\begingroup$ I understand for the power link with a GLM, we will try it. About using other error families, we tried Gamma regression but we didn't know anything about residuals analysis of this regression (and find few bibliography). In our Gamma regression model, the residuals are distributed like a Gamma distribution and not like a gaussian distribution. Is that correct ? Do you know more, or have references about residuals diagnosis on Gamma regression ? $\endgroup$
    – Marco
    Commented May 14, 2013 at 20:41
  • $\begingroup$ It's not much different from any other error family. Best to have a quantile-quantile plot for gamma rather than for Gaussian. There are some specific comments in McCullagh and Nelder crcpress.com/product/isbn/9780412317606 $\endgroup$
    – Nick Cox
    Commented May 15, 2013 at 16:13

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