Let me see if I can explain this the way I understand it. I could be wrong and misleading then hopefully someone will correct me.

In a linear regression,

These models try to model the relationship between two variables. You are trying to see how an Independent variable explains a dependent variable. In order to use linear regression, there should be a linear relationship.

A good example online is say you are trying to model the relationship between income and age group. You find that people under the age of 20 often earn minimum wage so there is no variability in their earnings. If you were to model this relationship, you decide that a linear regression is fitting.

Now, you have to model this relationship for people age 20 - 30. From there, you now start to see that there’s no clear picture. Heck of a lot of variability. The IV is no longer much of a predictor of the DV. When you plot your points on a graph and you draw a line, you are not seeing a relationship.

Approach it in this way, If I am to use a linear regression, the variance of the error terms must be constant. If I find that is not the case, then my results may mean there’s a problem with my data or I must use a different model. Think of this as a real world scenario where you have the data and are trying to figure out what model to use.

Hope, this is what you are asking…

I hope someone corrects me here if this is a flawed example as I am also lowkey struggling through quant.