9252012 p kolm 17 estimating the error variance s 2

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: VER. 9/25/2012. © P. KOLM 17 Estimating the Error Variance s 2 One issue: We assumed that the error variance is known. In practice that is not the case. It needs to be estimated We know that s 2 = E (u 2 ) , so if we could observe the true errors, ui , errors we 1n 2 ˆ would estimate s = å ui . But ui are not known n i =1 2 ˆ Instead, we estimate s 2 using the residuals, ui , 1n2 SSR ˆ s= ui = å n - 2 i =1 n -2 2 Fact: This estimator is unbiased (For you: Verify!) s = s 2 is also referred to as the standard error of the regression VER. 9/25/2012. © P. KOLM 18 The Sampling Distribution Finally, if we assume u | x N (0, s 2 ) Then, we have ˆ b1 N (b1, s 2 / SSTx ) n æ ˆ N çb , s 2n -1 å x 2 / SST b0 ç0 i x ç è i =1 ö ÷ ÷ ÷ ÷ ø VER. 9/25/2012. © P. KOLM 19 Statistical Inference Now, as we know the sampling distribution for the classical linear regression model in the two-variable case we can go ahead and perform statistical inference (hypothesis testing, confidence intervals, etc.) However, we will defer this discussion for linear regression when we discuss the multiv...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online