[R] t-test for regression estimate

[Steven Yen]

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>
>> 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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