{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch._5_Exercise_Solutions

# Ch._5_Exercise_Solutions - Sol 1 Chapter 5 Solutions 1...

This preview shows pages 1–2. Sign up to view the full content.

Sol - 1 Chapter 5 Solutions 1. Suppose the columns of X are orthogonal. Show that the estimate of β j , the coefficient of x j , is not dependent on which are columns of X are included in the model. Suppose we have a model that includes x j and any other columns of X . We can write the model as y U r = + α . Note that the columns of U are also orthogonal so that U U is diagonal and the diagonal element corresponding to t β j is x x . Hence the diagonal element of ( corresponding to j t j ) U U t 1 β j is 1 and since ( / x x j t j ) U U t 1 is also diagonal, we have \$ β j j t j t j x y x x = independent of all the other explanatory variates 2. Show that c for the full model that includes all p explanatory variates. p p = + 1 By definition if there are k explanatory variates in the model (plus a constant term), then c k p = estimated residual sum of squares 2 \$ ( ) n + + σ 2 1 . If we fit the full model with p explanatory variates, we get c n p p n p p = + + = ( - - ) 2 2 1 2 1 \$ \$ ( ) + 1 σ σ as required. 3. The file ch6Exercise3.txt contains a response variate y and 10 explanatory variates x x 1 ,..., 10 for 100 cases. These data were created artificially for practice. The model

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

View Full Document
This is the end of the preview. Sign up to access the rest of the 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