Without knowing more about your data, my first guess would be that you should consider re-expressing your dependent variable. Appropriate re-expressions (e.g log or square root) often improve both linearity and homoskedasticity. If you tell us more about your data, we may be able to be more specific

Don't use tests to evaluate the normality of residuals or the homoscedasticity. With 156 observations, these tests may have significant results even if the deviation from these assumptions isn't really problematic. Use plots. If you want, post the plots here, and see what people think.

I make that 14 entities that you are repeatedly measuring; is that right (156/ (2021-2010)? It will be difficult to asses 'normality' with that few observations. But what reality matters is outliers.

I agree with Salvatore that you shouldn't use tests for normality and homoscedasticity. Aside from the sample size issues, those are *assumptions* for regression and can't be tested for legitimately.

I also agree that outliers are important--but I doubt that's the issue here.

Please plot your data and try re-expressing your response variable. Show us the plots here and we can help. Tell us what the response variable measures and how, for example.

In general, it is a good idea to back off "testing"--that's not what statistics is about.

It seems as though Prof Jones is the only one thinking of this as panel data. He is correct about the small number of observations. Attached are a few tricks to use for outliers that may be of some help. It is the 14 that you are measuring repeatedly that you should be concentrating on. I'm attaching an ancient paper that discusses outliers. perhaps that may help. Best wishes, David Booth

Oops Forgot to say that Velleman 's book ABCs of EDA still available in the z-library may be helpful here. It concerns outliers. Best wishes, David Booth

Kelvyn pointed out how few entities are involved - I make it 156/(2021-2009) = 13 because 2010 was used - and Sal pointed out the usefulness of plots. Also, as Kelvyn said, an outlier could be very problematic here. Good points.

I'd also say that "...normality of the error terms...," Tekalign Negash, is not a very strict 'requirement.' Also, for heteroscedasticity, are you referring to heteroscedasticity among the 13 each year as what you say "persist(s)" from year to year, or do you mean you just have heteroscedasticity between years, treating each year's 13 cases as homoscedastic? If the former, one expects heteroscedasticity with respect to predicted-y as a size measure.* If the latter, I would not expect homoscedasticity each year, although it might happen.**

*https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity,

with more exactness and further considerations here:

**Knaub, J.R., Jr.(2021), "When Would Heteroscedasticity in Regression Occur?"  Pak. J. Statist., Vol. 37(4), 315-367, https://www.pakjs.com/, 

https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR