# Linear regression's (OLS) coefficient interpretation with heteroscedasticity

To use OLS for inference, is it necessary in all cases that the premise of homoscedasticity is met?

I need to check the influence of some features (eg age, income...) on a variable y (whether or not I bought a property) in a real case. I thought about using linear regression interpreting the coefficients and I know that if there is heteroscedasticity it affects the reliability of the significance tests and confidence intervals are incorrect. But I'm not sure it would affect the regression coefficients as well.

Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on them, such as p-values and confidence intervals) are incorrect. It doesn't affect the interpretation of the regression coefficients, which depends not the on estimation procedure or assumption but on the structure of the model. That is, if you specify $$E[Y|X] = \beta_0 + \beta_1 x_1 + ... + \beta_k x_k$$ the usual regression model, it doesn't matter how you estimate the coefficients or whether the assumptions are valid. The model itself tells you that for two observations that differ in $$x_1$$ by one unit but are the same on the other predictors, the expected difference in their outcomes is $$\beta_1$$. You might use a terrible method for estimating the coefficients, but that doesn't change their interpretation.