[R] F-test where the coefficients in the H_0 is nonzero

[John]

Hi,

   I try to run the same f-test by lm (with summary) and the function
"linearHypothesis" in car package. Why are the results (p-values for the
f-test) different?


> df1<-data.frame(x=c(2,3,4), y=c(7,6,8))
> lm1<-lm(y~x, df1)
> lm1

Call:
lm(formula = y ~ x, data = df1)

Coefficients:
(Intercept)            x
        5.5          0.5

> summary(lm1)

Call:
lm(formula = y ~ x, data = df1)

Residuals:
   1    2    3
 0.5 -1.0  0.5

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    5.500      2.693   2.043    0.290
x              0.500      0.866   0.577    0.667

Residual standard error: 1.225 on 1 degrees of freedom
Multiple R-squared:   0.25, Adjusted R-squared:   -0.5
F-statistic: 0.3333 on 1 and 1 DF,  p-value: 0.6667

> linearHypothesis(lm1, c("(Intercept)=0", "x=0"))
Linear hypothesis test

Hypothesis:
(Intercept) = 0
x = 0

Model 1: restricted model
Model 2: y ~ x

  Res.Df   RSS Df Sum of Sq      F Pr(>F)
1      3 149.0
2      1   1.5  2     147.5 49.167 0.1003

2018-08-03 13:54 GMT+08:00 Annaert Jan <jan.annaert using uantwerpen.be>:

> You can easily test linear restrictions using the function
> linearHypothesis() from the car package.
> There are several ways to set up the null hypothesis, but a
> straightforward one here is:
>
> > library(car)
> > x <- rnorm(10)
> > y <- x+rnorm(10)
> > linearHypothesis(lm(y~x), c("(Intercept)=0", "x=1"))
> Linear hypothesis test
>
> Hypothesis:
> (Intercept) = 0
> x = 1
>
> Model 1: restricted model
> Model 2: y ~ x
>
>   Res.Df     RSS Df Sum of Sq      F Pr(>F)
> 1     10 10.6218
> 2      8  9.0001  2    1.6217 0.7207 0.5155
>
>
> Jan
>
> From: R-help <r-help-bounces using r-project.org> on behalf of John <
> miaojpm using gmail.com>
> Date: Thursday, 2 August 2018 at 10:44
> To: r-help <r-help using r-project.org>
> Subject: [R] F-test where the coefficients in the H_0 is nonzero
>
> Hi,
>
>    I try to run the regression
>    y = beta_0 + beta_1 x
>    and test H_0: (beta_0, beta_1) =(0,1) against H_1: H_0 is false
>    I believe I can run the regression
>    (y-x) = beta_0 +beta_1‘ x
>    and do the regular F-test (using lm functio) where the hypothesized
> coefficients are all zero.
>
>    Is there any function in R that deal with the case where the
> coefficients are nonzero?
>
> John
>
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>
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