{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# R2 - n p 1 n-1-1 R 2-p n-1 n-1 n p 1 ˆ σ 2 = 1-adjR 2 Syy...

This preview shows pages 1–5. Sign up to view the full content.

STAT5044: Regression and Anova Inyoung Kim

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

View Full Document
Outline 1 More on R 2
R 2 R 2 : the coefficient of multiple determination R 2 is not an estimate of a population quantity unless the data is multivariate normal R 2 can be drametically changed by how the x ’s are selected. R 2 does not capture non-linear relationship R 2 usually can be made larger by including a larger number of predictor variables

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

View Full Document
Adjusted R 2 Let p variables in model Definition of adj R 2 = 1 - SSE / ( n - ( p + 1 )) SSTO / ( n - 1 ) adj R 2 is found as adj R 2 = ( R 2 - p n - 1 )( n - 1 n - ( p + 1 ) ) What is the rationale for adj R 2 ? If we use p terms that are unrelated to y , the average R 2 is p n - 1 To correct for this, our first adjustment is R 2 - p n - 1 However this reduction R 2 too much. If we have p X’s that perfectly predict y , this adjustment will only give 1 - p n - 1 = n - ( p + 1 ) n - 1 , but in this case we should get a value of 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: [ n-( p + 1 ) n-1 ]-1 , ( R 2-p n-1 )( n-1 n-( p + 1 ) ) ˆ σ 2 = [ 1-adjR 2 ] Syy n-1 , ˆ σ 2 = RSS ( n-( p + 1 )) = MSE As adj R 2 increases ˆ σ 2 decrease. Comments Let p variables in model R 2 can viewed as a coefﬁcient of simple determination between the response Y i and the ﬁtted values ˆ Y i A large value of R 2 does not necessarily imply that the ﬁtted model is useful one. ⇒ Despite a high R 2 , the ﬁtted model may not be useful if most predictions require extrapolations outside the region of observations. Again even though R 2 is large, MSE may still be too large for inferences to be useful when high precision is required....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern