Lecture_9_Prof._Arkonac's_Slides_(Ch_7.3_-_8.3)

Lecture_9_Prof._Arkonac's_Slides_(Ch_7.3_-_8.3) - Multiple...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Multiple Regression (cont’) Confidence Intervals in Multiple Regression. Nonlinear Regression I (Fall 2010) Lecture 9 Prof: Seyhan Arkonac, PhD PS #3 is due NOW! Solutions will be posted on Oct. 6 th after 9pm. PS#4 will be posted today after class. 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
TA Information: Naihobe Gonzalez E-mail: ndg2109@columbia.edu Office Hours: Thurs 12-1 (Uris Library), Recitation: Thurs 11-11:50 (PUP 424) TA Information: Ju Hyun Kim E-mail: jk3201@columbia.edu Office Hours: Recitation: Fri 2:10-3PM(PUP 424), Office Hours: Fri 3:10-4:10PM(Lehman) TA Information: WooRam Park E-mail: wp2135@columbia.edu Office Hours: Office hours : Thurs 2:00~3:00 IAB 1006A Recitation Thurs 3:10~4:00 IAB 403 TA Information: Ran Huo E-mail: rh2346@columbia.edu Office Hours: Recitation: Thursday 12:00-12:50 404IAB; Office Hour: Wednesday 1-2 1006A IAB TA Information: Shreya Agarwal E-mail: sa2628@columbia.edu Office Hours: Mon 12:30pm - 1:30 pm (Uris Library Common Area) Recitation: Fri 12:00pm - 12:50pm (Schermerhorn Extension 558) 2
Background image of page 2
3 Testing Single Restrictions on Multiple Coefficients (SW Section 7.3) Y i = 0 + 1 X 1 i + 2 X 2 i + u i , i = 1,…, n Consider the null and alternative hypothesis, H 0 : 1 = 2 vs. H 1 : 1 2 This null imposes a single restriction ( q = 1) on multiple coefficients – it is not a joint hypothesis with multiple restrictions (compare with 1 = 0 and 2 = 0).
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 Testing single restrictions on multiple coefficients, ctd. Here are two methods for testing single restrictions on multiple coefficients: 1. Rearrange (“transform”) the regression Rearrange the regressors so that the restriction becomes a restriction on a single coefficient in an equivalent regression; or, 2. Perform the test directly Some software, including STATA, lets you test restrictions using multiple coefficients directly
Background image of page 4
5 Method 1: Rearrange (“transform”) the regression Y i = 0 + 1 X 1 i + 2 X 2 i + u i H 0 : 1 = 2 vs. H 1 : 1 2 Add and subtract 2 X 1 i : Y i = 0 + ( 1 2 ) X 1 i + 2 ( X 1 i + X 2 i ) + u i or Y i = 0 + 1 X 1 i + 2 W i + u i where 1 = 1 2 W i = X 1 i + X 2 i
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 Rearrange the regression, ctd. (a) Original system : Y i = 0 + 1 X 1 i + 2 X 2 i + u i H 0 : 1 = 2 vs. H 1 : 1 2 (b) Rearranged (“transformed”) system : Y i = 0 + 1 X 1 i + 2 W i + u i where 1 = 1 2 and W i = X 1 i + X 2 i so H 0 : 1 = 0 vs. H 1 : 1 0 The testing problem is now a simple one: test whether 1 = 0 in specification (b).
Background image of page 6
Does ACT and bgfriend have the same effect on colGPA ? . reg colGPA hsGPA ACT bgfriend skipped,r Linear regression Number of obs = 141 F( 4, 136) = 11.12 Prob > F = 0.0000 R-squared = 0.2446 Root MSE = .32832 ------------------------------------------------------------------------------ | Robust colGPA | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hsGPA | .4186377 .0987409 4.24 0.000 .2233717 .6139038 ACT | .0140484 .0110336 1.27 0.205 -.0077711 .035868 bgfriend | .0780312 .0554459 1.41 0.162 -.0316163 .1876788 skipped | -.0825624 .0256374 -3.22 0.002 -.1332619 -.0318629 _cons | 1.344903 .3590842 3.75 0.000 .6347917 2.055014 ------------------------------------------------------------------------------ 7
Background image of page 7

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

View Full DocumentRight Arrow Icon
Are hsGPA and ACT jointly significant? . test hsGPA ACT ( 1) hsGPA = 0 ( 2) ACT = 0 F( 2, 136) = 12.95 Prob > F = 0.0000 Are hsGPA and bgfriend jointly significant? . test hsGPA bgfriend ( 1) hsGPA = 0 ( 2) bgfriend = 0 F( 2, 136) = 9.27 Prob > F = 0.0002 Then “transform” the regression to test H 0 : β ACT = β bgfriend 8
Background image of page 8
Does ACT and bgfriend have the same effect on colGPA ?
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 44

Lecture_9_Prof._Arkonac's_Slides_(Ch_7.3_-_8.3) - Multiple...

This preview shows document pages 1 - 10. Sign up to view the full document.

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