slide13 - Hypothesis tests in linear regression Slope: ^ ^...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Hypothesis tests in linear regression ± Slope: ± H 0 : β 1 = β 1,0 ± H 1 : β 1 ≠β 1,0 ± Reject H 0 : β 1 = β 1,0 if |t 0 |>t α /2,n-2 ± Intercept: ± H 0 : β 0 = β 0,0 ± H 1 : β 0 0,0 ± Reject H 0 : β 1 = β 1,0 if |t 0 |>t α /2,n-2 ) ˆ ( se ˆ S / ˆ ˆ T 1 0 , 1 1 xx 2 0 , 1 1 0 β σ = = ) ˆ ( se ˆ S x n 1 ˆ ˆ T 0 0 , 0 0 xx 2 2 0 , 0 0 0 = + = 2 Hypothesis tests in linear regression ± Special case: ± H 0 : β 1 = 0 ± H 1 : β 1 0 ± Fail to reject H 0 : β 1 = 0 is equivalent to concluding that there is no linear relationship between x and Y.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3 Example: Sales vs. Advertising Advertising (mil.$) Sales (mil.$) 1.2 120 1.6 130 1.8 140 2.2 150 2.6 130 3.1 140 3.4 120 3.6 150 4.0 140 4.2 130 80 90 100 110 120 130 140 150 160 012345 4 Analysis of variance ± Test for significance of regression. ± Analysis of variance identity ± Symbolical equation = = = + = n 1 i 2 i i n 1 i 2 i n 1 i 2 i ) y ˆ y ( ) y y ˆ ( ) y y ( E R T SS SS SS + = squares of sum Error : SS squares of sum gression Re : SS squares of sum correct Total : SS E R T
Background image of page 2
5 Analysis of variance ± Test statistics ± Reject H 0 : β 1 = 0, if f 0 >f α ,1,n-2 E R E R 0 MS MS ) 2 n /( SS 1 / SS F = = 6 Confidence intervals ± Confidence interval on the slope
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

Page1 / 4

slide13 - Hypothesis tests in linear regression Slope: ^ ^...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online