Which assumptions do I need to test?

Question

I am currently doing an OLS regression where my dependent variable is a Likert scale going from 0 to 10 and my independent variables are factor variables such as gender, ethnicity etc. Now, I know that OLS might not be the best type of regression but my supervisor wants me to do it and treat my dependent variable as a continuous one. My question is: which OLS assumptions do I need to test after having done the regression. The book Introduction to Econometrics by Woolbridge presents 6 assumptions for classical linear model assumptions:

1- Linearity in parameters

2- Random Sampling

3- No perfect collinearity

4- Zero conditional mean

5- Homoskedasticity

6- Normality of residuals

Do I need to run diagnostic tests for each of them in my case? Also my sample size is 1900 observations

Answer 1

You should consider and discuss the assumptions of your model, but you don't (or might not be able to) run diagnostic tests on every single assumption. For example, random sampling is an assumption of a lot of different models, but unless you have access to the data collection apparatus/people, measuring directly whether or not you had random sampling might not be possible. However, if you knew how the data was gathered, you could most likely assess whether or not it was collected in a way that wouldn't bias the results.

Of the assumptions you have listed, you can and should test the collinearity of your independent variables, the variance of your residuals (as it relates to homoskedascity), and the normality of residuals. There are not only simple tests and visualizations to help you determine if the assumptions are correct, but if one of these assumptions is violated, the precision and accuracy of your model's coefficients may be incorrect. If you are planning to do any other statistical tests, than this could obviously have an impact.