regression assumptions and OLS assumptions, are they different? Question

*

*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

*

*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:

*

*Linearity

*Constant Error Variance

*Independent Error Terms

*Normal Errors

*No multi-collinearity between predictors

*Exogeneity





*

*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.

*

*The Error Term has Conditional Mean of Zero

*Independently and Identically Distributed Data

*Large Outliers are Unlikely



*

*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 OLS assumptions are incomplete, since they are missing the constant error variance and lack of multi-collinearity.
Moreover, the assumptions of OLS follow from the six assumptions listed by zedstatistics:

*

*Error term with conditional mean of zero, means the same as exogenity

*IID follows from the independent errors (independence) and from the normal errors (identically distributed).

*Large outliers are unlikely, follows from the normally distributed errors, as the tails of the normal distribution decay quickly.

