{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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

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

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

View Full Document
TA Information: Naihobe Gonzalez E-mail: [email protected] Office Hours: Thurs 12-1 (Uris Library), Recitation: Thurs 11-11:50 (PUP 424) TA Information: Ju Hyun Kim E-mail: [email protected] Office Hours: Recitation: Fri 2:10-3PM(PUP 424), Office Hours: Fri 3:10-4:10PM(Lehman) TA Information: WooRam Park E-mail: [email protected] 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: [email protected] Office Hours: Recitation: Thursday 12:00-12:50 404IAB; Office Hour: Wednesday 1-2 1006A IAB TA Information: Shreya Agarwal E-mail: [email protected] Office Hours: Mon 12:30pm - 1:30 pm (Uris Library Common Area) Recitation: Fri 12:00pm - 12:50pm (Schermerhorn Extension 558) 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).

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

View Full Document
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
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

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

View Full Document
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).
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

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

View Full Document
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
Does ACT and bgfriend have the same effect on colGPA ?

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 ]}

### 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
Ask a homework question - tutors are online