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The principles of multiple linear regression are widely described, however there are still some aspects I don't truly understand why. Specifically speaking I don't understand why heteroscedasticity hinders the possibility to run linear regression models? Why the not uniform dispersion hinders the possibility to estimate?

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  • $\begingroup$ What do you mean that heteroskedasticity hinders the possibility of running a linear regression model? $\endgroup$
    – Dave
    Commented May 24 at 9:54
  • $\begingroup$ That homoscedasticity is a condition that needs to be met to run linear regression $\endgroup$ Commented May 24 at 10:43
  • $\begingroup$ Not quite, homoscedasticity is required for proper interpretation, but you can still run a model and forecast with it. $\endgroup$ Commented May 24 at 10:44
  • $\begingroup$ I don't see the detail $\endgroup$ Commented May 24 at 10:48
  • $\begingroup$ From e.g. stats.stackexchange.com/questions/179111/… you can observe that OLS can still be unbiased even if there is heteroskedasticity $\endgroup$ Commented May 24 at 11:01

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In most cases you can run a linear regression model on any data you like. If you plug in the data the formula (or your statistical program) will provide estimates for beta coefficients and standard errors based on that data. But in lots of cases those estimates will be "bad." For example, you can still run a linear regression model on a nominal dependent variable( like 1=married 2=not married 3=divorced 4=widowed 5=other) but the coefficients you get will be meaningless. The "assumptions" of linear regression are the conditions under which we can expect it to give us "good" answers. For a good example of how violating various assumptions can lead regression to produce bad answers, see Anscombe's quartet.

Homoskedasticity is one of those assumptions, although I think most people would agree that is is not one of the more important ones.

As for why and how it matters: Homoscedasticity is the assumption that the variance of the dependent variable is constant across all values of the independent variables. OLS uses this assumption to estimate the standard errors around the coefficients. Running a model on data where this assumption is violated will not (on its own) bias the model's estimate of the beta coefficients, but it will cause the model to incorrectly estimate the standard error. This might mean that you interpret a variable as statistically significant even when it should not be, or vice versa.

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