{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework2 Solutions

# Homework2 Solutions - Mehmet Soytas Wednesday Applied...

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

Mehmet Soytas Applied Econometrics I, Summer, 2009 Wednesday, May 21, 2009 (due: Wednesday, May 27, 2009) Homework Assignment 2 1. Show that the OLS formula for the coe¢ cient ° 1 in the multiple regression model Y i = ° 0 + ° 1 X 1 i + ° 2 X 2 i + u i reduces to the OLS formula of ° 1 in the one regressor case if the correlation between X 1 i and X 2 i is zero. The formula for ^ ° 1 in the multiple regression model is ( x 1 i = X 1 i ° ° X 1 , x 2 i = X 2 i ° ° X 2 , y i = Y i ° ° Y ): ^ ° 1 = P n i =1 y i x 1 i P n i =1 x 2 2 i ° P n i =1 y i x 2 i P n i =1 x 1 i x 2 i P n i =1 x 2 1 i P n i =1 x 2 2 i ° ( P n i =1 x 1 i x 2 i ) 2 Correlation between X 1 i and X 2 i is de°ned as : ± X 1 ;X 2 = cov ( X 1 ;X 2 ) p var ( X 1 i ) p var ( X 2 i ) 1 n ° 1 P n i =1 x 1 i x 2 i p 1 n ° 1 P n i =1 x 2 1 i p 1 n ° 1 P n i =1 x 2 2 i If the correlation is equal to zero, ± X 1 ;X 2 = 1 n ° 1 P n i =1 x 1 i x 2 i p 1 n ° 1 P n i =1 x 2 1 i p 1 n ° 1 P n i =1 x 2 2 i = 0 ) 1 n ° 1 P n i =1 x 1 i x 2 i = 0 ) P n i =1 x 1 i x 2 i = 0 If we replace P n i =1 x 1 i x 2 i with 0 in the formula of ^ ° 1 . ^ ° 1 = P n i =1 y i x 1 i P n i =1 x 2 2 i ° P n i =1 y i x 2 i (0) P n i =1 x 2 1 i P n i =1 x 2 2 i ° (0) 2 = P n i =1 y i x 1 i P n i =1 x 2 2 i P n i =1 x 2 1 i P n i =1 x 2 2 i = P n i =1 y i x 1 i P n i =1 x 2 1 i = The formula for ^ ° 1 in the one variable regression model 2. For this question, use the California Testscore Data Set and your regression package (STATA). a. First perform a multiple regression of testscores on a constant, the student-teacher ratio, and the percent of English learners. Record the coe¢ cients. Run reg testscr str el_pct,r Next, do the following three step procedure instead: b. First, regress the testscore on a constant and the percent of English learners. Calculate the residuals and store them under the name resYX2. Run reg testscr el_pct,r generate resYX2=testscr-664.7394-(-0.6711562)el_pct c. Second, regress the student-teacher ratio on a constant and the percent of English learners. Calculate the residuals from this regression and store these under the name resX1X2. Run reg str el_pct,r generate resX1X2=str-19.33432-0.019413el_pct d. Finally regress resYX2 on resX1X2. Explain intuitively why the simple regression coe¢ cient in the last regression is identical to the regression coe¢ cient on the student-teacher ratio in the multiple regression Run

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