Linear Regression is highly useful when it comes to a tool for inferential analysis. It's often used as predictive tools and for that, we don't need many statistical assumptions to do a great job. When we use it for inferential, we need to check some statistical properties of the model.
These are the assumptions of the linear regression model:
- Observations are independent.
- Errors have constant conditional variance. We call this "Homoskedacity".
- Errors are normally distributed.
The inferential results of the regression model depends on these statistical assumptions, and they are correct only if these assumptions hold at least approximately.
The predictions of the linear regression model are not dependent on these assumptions, so if the goals are purely predictive, these assumptions are not strong concerns.
We need to understand p-values associated with beta coefficients and then interpret them to gain insight into the relationship between variables.