regression assumptions and OLS assumptions, are they different? Question

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*Is there difference between assumptions of regression and assumptions of Ordinary Least Squares (OLS)?

*To apply OLS (the only regression method that I can use) on data, should my data and OLS meet both assumptions (assumptions of regression and assumptions of OLS)?

*Since 'non-linear' regression is also one kind of a regression, if it meets the assumptions of regression, can I apply non-linear regression? No matter whether it is a linear regression or non-linear regression, if the "assumptions of regression" are met, can I use either of them? Or Should there be another set of assumptions for non-linear regression?

More Details

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*I am studying linear regression, covering Ordinary Least Squares(OLS) so far.


*I have learned the assumptions of regressions which should not be violated. The number of assumptions varies from book to book, but let me refer to that of the popular statistics youtuber "zedstatistics". The 6 assumptions of regression are as follows:

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*Linearity

*Constant Error Variance

*Independent Error Terms

*Normal Errors

*No multi-collinearity between predictors

*Exogeneity





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*I thought if my data and model meets the six assumptions mentioned above, I could apply OLS on the data freely. However, I found on the Internet "assumptions of OLS" on the famous book website 'Econometrics with R'


OLS performs well under a quite broad variety of different circumstances. However, there are some assumptions which need to be satisfied in order to ensure that the estimates are normally distributed in large samples.

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*The Error Term has Conditional Mean of Zero

*Independently and Identically Distributed Data

*Large Outliers are Unlikely



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*Now I am puzzled because it seems like there are two streams of assumptions to be met, in order to use OLS. The 1st assumption is the 'assumptions of regression (the 6 assumptions)' and we also need to check if the 2nd assumption (the 3 assumptions mentioned right above) is met as well.

*Am I correct? Or are the two streams of assumptions saying the same thing, but expressed in a different way?


The assumptions for the regression model are model assumptions to specify the behaviour in the model.  By contrast, use of the OLS estimator is based on specification of the estimation method (which is not so much an assumption as a decision of how you want to do your estimation).  You can either directly specify that you want to use OLS as your estimation method, or you can specify use of the MLE and this reduces down to OLS in the Gaussian regression model, or you can specify another estimator entirely.
