[R] t-test for regression estimate

[Steven Yen]

Thanks John. Yes, by using verbose=T, I get the value of the hypothesis. 
But tell me again, how would I get the variance (standard error)?

On 6/29/2016 11:56 AM, Fox, John wrote:
> 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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