This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Lecture 31 31.1 Statistical inference in simple linear regres- sion. Let us first summarize what we proved in the last two lectures. We considered a simple linear regression model Y = + 1 X + where has distribution N (0 , 2 ) and given the sample ( X 1 , Y 1 ) , . . . , ( X n , Y n ) we found the maximum likelihood estimates of the parameters of the model and showed that their joint distribution is described by 1 N 1 , 2 n ( X 2- X 2 ) , N , 1 n + X 2 n ( X 2- X 2 ) 2 Cov( , 1 ) =- X 2 n ( X 2- X 2 ) and 2 is independent of and 1 and n 2 2 2 n- 2 . Suppose now that we want to find the confidence intervals for unknown parameters of the model , 1 and 2 . This is straightforward and very similar to the confidence intervals for parameters of normal distribution. For example, using that n 2 / 2 2 n- 2 , if we find the constants c 1 and c 2 such that 2 n- 2...
View Full Document