I have a dependent variable that are correlated with the passage of days (1, 2, 3, ...).

But I fitted a linear model without days/time, because I am more interested in other things I can influence somehow. Seems to me that a model with time "steal" influence of other coefficients, and I don't want that.

So I got a reasonable R², low p-values (~0) and a good residuals plot (y = residuals, x = fitted values). As far as I can see, my scatter plot of residuals means that the assumption E(u|X)=0 (OLS/Gauss-Markov) is ok.

After that, I decided to plot fitted values of variations of the original model (more or less variables, transformations of the variables or dummies included) in a time perspective (y = fitted val., x = days).

Even though I have not included time in my models, fitted values "dancing" around the real values, without any visual correlation or bias, proves that I can use that without major concerns?

  • $\begingroup$ The most critical part is that the residuals be consistent with the assumptions on the error term of your model. In particular, they should be white noise. Have you looked at ACF/PACF plots of the residuals? $\endgroup$ – Chris Haug May 28 '18 at 22:52

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