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Re: re: re: st: Simple regression and Multiple regression?
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[email protected]
To
statalist<[email protected]>
Subject
Re: re: re: st: Simple regression and Multiple regression?
Date
Mon, 15 Mar 2010 14:18:19 +0800
Dear Kit and Eric,
Thank you very much for your help, which really helps a lot!
What about the constant? Is there an existing relationship between simple regression and multiple regression?
By the way, I found the standard errors of turn were not the same in "reg epsp epst" and "reg price mpg weight turn". Just a decimal difference which can be ignored?
. reg price epst
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 1, 72) = 7.23
Model | 57963155.7 1 57963155.7 Prob > F = 0.0089
Residual | 577102240 72 8015308.9 R-squared = 0.0913
-------------+------------------------------ Adj R-squared = 0.0786
Total | 635065396 73 8699525.97 Root MSE = 2831.1
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
epst | -395.1902 146.957 -2.69 0.009 -688.1436 -102.2368
_cons | 6165.257 329.1124 18.73 0.000 5509.183 6821.33
------------------------------------------------------------------------------
. reg epsp epst
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 1, 72) = 10.68
Model | 57963155.7 1 57963155.7 Prob > F = 0.0017
Residual | 390780961 72 5427513.34 R-squared = 0.1292
-------------+------------------------------ Adj R-squared = 0.1171
Total | 448744116 73 6147179.68 Root MSE = 2329.7
------------------------------------------------------------------------------
epsp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
epst | -395.1902 120.929 -3.27 0.002 -636.2578 -154.1226
_cons | 1.21e-12 270.8224 0.00 1.000 -539.8746 539.8746
------------------------------------------------------------------------------
. reg price mpg weight turn
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 3, 70) = 14.59
Model | 244284435 3 81428145.1 Prob > F = 0.0000
Residual | 390780961 70 5582585.15 R-squared = 0.3847
-------------+------------------------------ Adj R-squared = 0.3583
Total | 635065396 73 8699525.97 Root MSE = 2362.7
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | -72.86501 81.29538 -0.90 0.373 -235.0035 89.27351
weight | 3.524339 .8171395 4.31 0.000 1.894605 5.154072
turn | -395.1902 122.6444 -3.22 0.002 -639.7968 -150.5836
_cons | 12744.24 4760.102 2.68 0.009 3250.519 22237.97
------------------------------------------------------------------------------
Thank you for any help.
Best regards,
Rose
----- Original Message -----
From: Kit Baum <[email protected]>
To: [email protected]
Subject: re: re: st: Simple regression and Multiple regression?
Date: 2010-3-15 02:32:07
<>
Rose said
By the way,"Frisch-Waugh-Lovell theorem says that the coefficient of turn should be the same in multiple regression or in a regression
of price on turn, with the effects of other regressors partialled-off from both." In Woodbridge's book, the effect of other regressors is only partialled-off from the concerned regressor, not from the dependent variable.
It is also OK, right?
What I tried in stata told me it was OK.
No, if you fail to partia-offl the other regressors from the dependent variable, you get the same point estimate but a different standard error, t-stat, , R^2, RMS Error, etc. Check the example I gave for
reg epsp epst
versus the regression
reg price epst
You will see that they are not the same.
Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html
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