[R] t-test for regression estimate

[Fox, John]

Dear Steven,

OK -- that makes sense, and there was also a previous request for linearHypothesis() to return the value of the hypothesis and its covariance matrix. In your case, where there's only 1 numerator df, that would be the value and estimated sampling variance of the hypothesis.

I've now implemented that, using (at least provisionally) attributes in the development version of the car package on R-Forge, which you should be able to install via install.packages("car", repos="http://R-Forge.R-project.org"). Then see ?linearHypothesis for more information.

Best,
 John

> -----Original Message-----
> From: Steven Yen [mailto:syen04 at gmail.com]
> Sent: June 28, 2016 3:44 PM
> To: Fox, John <jfox at mcmaster.ca>
> Cc: R-help <r-help at r-project.org>
> Subject: Re: [R] t-test for regression estimate
> 
> Thanks John. Reason is I am doing linear transformations of many coefficients
> (e.g., bi / scalar). Of course I can uncover the t-statistic from the F statistic and
> then the standard error. Simply scaling the estimated coefficients I can also
> transform the standard errors. I have since found deltaMethod from library
> "car" useful. Its just that, if linearHypothesis had provide the standard errors
> and t-statistics then the operation would have been easier, with a one-line
> command for each coefficient. Thank you again.
> 
> 
> On 6/28/2016 6:28 PM, Fox, John wrote:
> 
> 
> 	Dear Steven,
> 
> 	The reason that linearHypothesis() computes a Wald F or chisquare
> test rather than a t or z test is that the (numerator) df for the linear hypothesis
> need not be 1.
> 
> 	In your case (as has been pointed out) you can get the coefficient
> standard error directly from the model summary.
> 
> 	More generally, with some work, you could solve for the the SE for a 1
> df linear hypothesis in terms of the value of the linear function of coefficients
> and the F or chisquare. That said, I'm not sure why you want to do this.
> 
> 	I hope this helps,
> 	 John
> 
> 	-----------------------------
> 	John Fox, Professor
> 	McMaster University
> 	Hamilton, Ontario
> 	Canada L8S 4M4
> 	Web: socserv.mcmaster.ca/jfox
> 
> 
> 
> 		-----Original Message-----
> 		From: R-help [mailto:r-help-bounces at r-project.org] On Behalf
> Of Steven Yen
> 		Sent: June 28, 2016 9:27 AM
> 		To: R-help <r-help at r-project.org> <mailto:r-help at r-
> project.org>
> 		Subject: [R] t-test for regression estimate
> 
> 		test option for linearHypothesis in library(car) include "Chisq"
> and "F". I prefer
> 		a simple t-test so that I can retrieve the standard error.
> 		Any options other than linearHypothesis to test the linear
> hypothesis (with 1
> 		restriction/degree of freedom)?
> 
> 		 > summary(ols1)
> 
> 		Coefficients:
> 		             Estimate Std. Error t value Pr(>|t|)
> 		(Intercept) -0.20013    0.09199  -2.176   0.0298 *
> 		age          0.04054    0.01721   2.355   0.0187 *
> 		suburb       0.01911    0.05838   0.327   0.7435
> 		smcity      -0.29969    0.19175  -1.563   0.1184
> 		---
> 		Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> 		 > linearHypothesis(ols1,"suburb")
> 		Linear hypothesis test
> 
> 		Hypothesis:
> 		suburb = 0
> 
> 		Model 1: restricted model
> 		Model 2: polideo ~ age + suburb + smcity
> 
> 		   Res.Df    RSS Df Sum of Sq      F Pr(>F)
> 		1    888 650.10
> 		2    887 650.02  1  0.078534 0.1072 0.7435
> 
> 
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> 
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