Question

what are the assumption of classical linear regression model? Are these assumption useful for identifying characteristics of OLS

Answer 1

Like many statistical analyses, ordinary least squares (OLS) regression has underlying assumptions. When these classical assumptions for linear regression are true, ordinary least squares produces the best estimates.

Assumptions-

1.

The regression model is linear in the coefficients and the error term

2.

The error term has a population mean of zero

3.

All independent variables are uncorrelated with the error term.

4.

Observations of the error term are uncorrelated with each other.

5.

The error term has a constant variance (no heteroscedasticity)

6.

No independent variable is a perfect linear function of other explanatory variables

7.

The error term is normally distributed (optional).

Yes ,these assumptions are useful for identifying characteristics of OLS.If these assumptions hold true, the OLS procedure creates the best possible estimates. In statistics, estimators that produce unbiased estimates that have the smallest variance are referred to as being “efficient.”

Another benefit of satisfying these assumptions is that as the sample size increases to infinity, the coefficient estimates converge on the actual population parameters.

If your error term also follows the normal distribution, you can safely use hypothesis testing to determine whether the independent variables and the entire model are statistically significant. You can also produce reliable confidence intervals and prediction intervals.