OLS assumption

[Pita Fouta]

Hi everyone,

I would like to have your opinion:

According to me in the picture attached, the assumption of linearity is respected because the residuals have no trend and are around 0. However, I can't find on the internet, a graph looking like mine to compare. I wanted to know if you find that this graph respects the assumption of linearity of OLS?

Thanks in advance.

[Ken Chui]

It'd be better to use some additional device to check it rather than with naked eyes alone. For example, you may overlay a LOWESS curve on it and see if there could be other relationship inside. Here is a demonstration:

sysuse auto, clear
reg price mpg

predict yhat
predict sres, rstandard
twoway scatter sres yhat ///
    || lowess sres yhat, bwidth(0.6) ///
    || lfit sres yhat

My guess is that it's probably a very mild inverted U-shape.

In addition, with one-predictor model being the exception, we cannot assess linearity assumption by looking at residual plot. For instance, if there are two continuous predictors, then it will have to be two different "component plus residual" plots. To learn more, check out -help cprplot-.

Lastly, I am not sure what the residual's unit is, but I'd suggest check the influence of the ones with residual < -5.

[Fei Wang]

If you would like to test whether the model omits higher order terms of regressors, you may also use Ramsey test ( -estat ovtest- ) after regression.

[Pita Fouta]

Hello guys Ken Chui and Fei Wang

Thanks for your answers.


I did these additional tests to check for homoscedasticity:


In the white test, I can conclude that there is no heterosckedacity but with the other test yes..... (I m a little bit confused)



I did also the estate ovtest, and I can conclude that there is no omitted variables.


What do you think guys ?

Thanks in advance

[Fei Wang]

B-P and White are two different ways of testing for heterosk, and it's not unusual to see inconsistent results. These testing results are practically unimportant, and one should directly go with robust standard errors.

[Pita Fouta]

Thank you very much Fei Wang

I use the robust command for robust standard errors, and I saw that some of my coefficients are more significant than before.

[Pita Fouta]

Hi Fei Wang ,

Could you tell me how do I know that the result of my regression is correct by using the robust command? Is it enough to say that my analysis will be correct?

Also is the omitted variable test still valid with the robust command in the regression ( -estat ovtest-) ?


Thanks in advance.

[Fei Wang]

Your estimation results would be robust to heterosk if you use robust standard errors, and your regression will be fine -- That's why it's called "robust". The "robust" option does not pass on to the Ramsey test. But the test only examines whether you omit higher order terms of the regressors, if you care about this specific issue (like what you said in the OP). It's not a general test for variable omission, so the Ramsey test, radically speaking, is unnecessary in most practical cases.

[Pita Fouta]

Thank you very much Fei Wang for your explanations