Assumptions under which ordinary least square estimates are valid.
1. Model is Linear in Parameters.
It means model should be in the form of
Y=B0 + B1X1 + B2X2
it should not be of the form
Y = B0 + B1²X1 + B2²X2
2. The data are a random sample of the population.
The errors are not co- related , they are statistically independent from one another.
3. The Expected values of errors is always zero.
Average of errors is zero.
4. Independent variables are not too strongly collinear.
Independent variables should not be highly co-related among themselves. Independent variables should not be co-related among themselves. As collinearity between variables brings very less additional information coming from 2nd variable.
5. Independent variables are measured precisely.
X variables (Independent variables) are measured precisely.
6. Residuals have constant variance – homoscedasticity.
Variance of the error should be constant.
7. Errors are normally distributed with mean = 0 .
To check take the residuals and generate a histogram.
8. Model is correctly specified.
Meaning we are using correct variable in the right type and we are not missing on any information.
If all these conditions hold, then OLS estimators are BLUE – Best Linear Unbiased Estimators.