Essay
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.
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