0
$\begingroup$

When I tried to fit a regression model to my data to predict a power variable using steam at entry and steam at exit variables in a thermal power plant, after taking care of outliers, etc... I fit the regression model but the problem came in, when I tried to run diagnostics, my residuals seem to have a 0 mean but with high spread around 0.6, so they are not normally distributed, I really don't know how to address this problem if someone could help please, BTW I'm thinking about running a regression using medians but still hesitant, here is the plot of densities below.

Note : The output is bimodal

Density of residuals vs standard normal distribution

$\endgroup$
3
  • 4
    $\begingroup$ "*after taking care of outliers etc *" That's always a concerning phrase. $\endgroup$
    – Galen
    Commented Aug 7, 2023 at 18:18
  • 1
    $\begingroup$ 1. What do you mean by "high spread around 0.6"? 2. The plot doesn't show as much detail as you'd probably like to show; try adjusting the range of the x-axis to say +/- 2 for more granularity. 3. Your residuals don't need to follow a Normal distribution, that's an oft-repeated myth. $\endgroup$
    – jbowman
    Commented Aug 7, 2023 at 18:18
  • 1
    $\begingroup$ @Galen Oh yes. I agree. I missed that. $\endgroup$
    – Peter Flom
    Commented Aug 7, 2023 at 18:21

1 Answer 1

3
$\begingroup$

You wrote

my residuals seem to have a 0 mean but with high spread around 0.6 , so they are not normally distributed

Residuals always have a mean of 0, OLS regression forces that.

The SD around 0.6 doesn't have anything to do with normality, and whether it is high or low depends on context.

And your plot of the residuals looks pretty normal, too, although it's hard to tell. The standard normal is irrelevant. Try a Quantile normal plot. Or a density plot of the residuals without the standard normal. (The standard normal has a mean of 0 and SD of 1; your residuals don't have these, so they won't look like the standard normal, but they may still be normal).

EDIT: Also, the output is not bimodal.

$\endgroup$
4
  • 1
    $\begingroup$ Hello thank's for your clarifications , i used also a QQPlot , but it didn't fit pretty well on the 45 ° line , and i've used also the test of shapiro wilk , and it confirms that it not normally distributed $\endgroup$ Commented Aug 7, 2023 at 18:27
  • $\begingroup$ Then you could try robust regression or quantile regression. $\endgroup$
    – Peter Flom
    Commented Aug 7, 2023 at 18:35
  • 1
    $\begingroup$ You could also try using a different link function for a generalized linear model, or more broadly model the joint distribution over the variables. If you can put justifiable priors on the parameters, you might opt for a Bayesian inference. $\endgroup$
    – Galen
    Commented Aug 7, 2023 at 18:38
  • $\begingroup$ Okey i'll try to do this , thank you so much for your time, that's so kind from you ! $\endgroup$ Commented Aug 7, 2023 at 18:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.