1

I'm struggling to understand why the following is true: MLR5 assumption in multiple regression

$\text{var}(u|x_1,\ldots,x_n)=\sigma^2$

implies that $\text{var}(u|x_i)=\sigma^2$ for every $i$, where $u$ is the error term. Would you, please, explain?

Frans Rodenburg
  • 10,376
  • 2
  • 25
  • 58
Andrey Gaidin
  • 13
  • 2
  • 1
    Welcome to crossvalidated @Andrey Gaidin, the way you've phrased the question is a bit unclear. Something that would help answer is the context, for example, who is $u$ and what are the multiple regression assumptions you are working with in the statement here? – Lucas Roberts Dec 03 '19 at 01:00
  • Lucas, u is the error term, MLR5 is homoskedasticity assumption. – Andrey Gaidin Dec 03 '19 at 01:07
  • Your question says "why is this true?" but that question doesn't make sense about an assumption. The assumption could be false, but then it would indicate not to do OLS regression on the data set (at least, not without modification). – Peter Flom Dec 03 '19 at 12:04

1 Answers1

3

Welcome to the site.

This assumption is called homoscedasticity, or constant variance: No matter the value of the predictor $x$, the residual variance should remain the same. What this means is that as you move along $x$, the spread of the observations around the regression model should not change.

You are asking why this is true, but that question is categorically wrong: This is one of the assumptions to obtain valid standard errors from the model. It need not be true at all. In fact, this is one of the reasons to perform model diagnostics. You can pick up problematic deviations from this assumption with a scale-location plot.

Frans Rodenburg
  • 10,376
  • 2
  • 25
  • 58