In the previous lecture an example problem has been solved using the method of least squares. It is necessary to know whether the estimates obtained using the OLS method are close to the population parameters. In other words, it is necessary to know the precision of these estimates. It is also necessary to know the overall suitability of the sample regression function in representing the population data that are being studied.
Since the  and the  are estimated from the sample data it can be said that these two are the statistics. Two know the precision of these estimates it is necessary to know their sampling distributions and the corresponding parameters. Based on the assumptions on the error term, the parameters of the sampling distribution are as shown below;

Since the value of σ is not known an estimate of the same can be obtained as given below;

 

Where,  is the estimated error equals to is the degrees of freedom.  is known as the standard error of the regression.
Once the sampling distributions are known, as already discussed in the previous lectures, it is easy to get the confidence intervals for the estimated parameters. It is also possible to formulate the hypotheses on the parameters to further know the suitability of the corresponding variables. Hypotheses-testing on one of the parameters is shown in the following example.