Let be distributed N(0, ),i.e. ,the errors are distributed normally with a constant variance (homoskedasticity).This results in being distributed N(β1, ),where .Statistical inference would be straightforward if was known.One way to deal with this problem is to replace with an estimator .Clearly since this introduces more uncertainty,you cannot expect to be still normally distributed.Indeed,the t-statistic now follows Student's t distribution.Look at the table for the Student t-distribution and focus on the 5% two-sided significance level.List the critical values for 10 degrees of freedom,30 degrees of freedom,60 degrees of freedom,and finally ∞ degrees of freedom.Describe how the notion of uncertainty about can be incorporated about the tails of the t-distribution as the degrees of freedom increase.

Question

Let  be distributed N(0,  ),i.e. ,the errors are distributed normally with a constant variance (homoskedasticity).This results in  being distributed N(β1,  ),where  .Statistical inference would be straightforward if  was known.One way to deal with this problem is to replace  with an estimator  .Clearly since this introduces more uncertainty,you cannot expect  to be still normally distributed.Indeed,the t-statistic now follows Student's t distribution.Look at the table for the Student t-distribution and focus on the 5% two-sided significance level.List the critical values for 10 degrees of freedom,30 degrees of freedom,60 degrees of freedom,and finally ∞ degrees of freedom.Describe how the notion of uncertainty about  can be incorporated about the tails of the t-distribution as the degrees of freedom increase.

Quizplus · Accepted Answer

The Answer of Let  be distributed N(0,  ),i.e. ,the errors are distributed normally with a constant variance (homoskedasticity).This results in  being distributed N(β1,  ),where  .Statistical inference would be straightforward if  was known.One way to deal with this problem is to replace  with an estimator  .Clearly since this introduces more uncertainty,you cannot expect  to be still normally distributed.Indeed,the t-statistic now follows Student's t distribution.Look at the table for the Student t-distribution and focus on the 5% two-sided significance level.List the critical values for 10 degrees of freedom,30 degrees of freedom,60 degrees of freedom,and finally ∞ degrees of freedom.Describe how the notion of uncertainty about  can be incorporated about the tails of the t-distribution as the degrees of freedom increase.

Let Be Distributed N(0, ),I