3

It seems that three common assumptions for the using classical linear regression with OLS is that:

  1. Error terms follow a normal distribution
  2. Homoskedasticity
  3. Error terms are uncorrelated

Can somebody provide me with some real life examples where error terms are correlated?

Farellia
  • 85
  • 1
  • 7
  • 3
    One typically makes two assumptions: that the error is uncorrelated with the included explanatory variables (this screws up the coefficients) and that the errors from different observations are uncorrelated with each other (this screws up the standard errors). Which ones do you need explained? – dimitriy Jun 08 '16 at 20:36
  • Look at almost any [tag:time-series]. – whuber Jun 08 '16 at 21:01
  • @Dimitriy The first case. – Farellia Jun 08 '16 at 22:09
  • Related: http://stats.stackexchange.com/questions/144826/what-is-the-difference-between-conditioning-on-regressors-vs-treating-them-as-f/192746#192746 http://stats.stackexchange.com/questions/173660/definition-and-delimitation-of-regression-model?lq=1 http://stats.stackexchange.com/questions/173365/residuals-in-regression-should-not-be-correlated-with-another-variable/173391#173391 – kjetil b halvorsen Jun 09 '16 at 06:34

1 Answers1

3

Suppose that you regress­ wage on years of education, but lack an ability variable to include in the regression. People with higher ability will earn more than others with the same years of education, so they will tend to have high positive error terms; but because they have higher ability they may find it easier (or more fun) to spend additional time in school. This creates correlation between the error term and the explanatory variable years of education, so the schooling coefficient will pick up both the fact that schooling makes you more productive (which is what you want), but also some of the effect of ability (which you don't want).

dimitriy
  • 31,081
  • 5
  • 63
  • 138