[R] Re: testing slopes different than a given value

Vito Ricci
Fri, 11 Feb 2005 08:29:57 -0000

Hi,

We know that a regression coefficent fitted by sample
data (under usual linear model hypothesis) b_hat has
mean=b and se=se(b_hat); (b_hat-b)/s(b_hat) is
distributed as Student?s t distribution with df=n-2.
So you can test h0:b=b0 hA:b<>b0 using t test (for
large sample normal distribution is the same of a t
distribution):

x1<-rnorm(100)
x2<-rnorm(100)
e<-rnorm(100)
y<-3+0.6*x1+0.3*x2 +e
fm<-lm(y~x1+x2)

> summary(fm)

Call:
lm(formula = y ~ x1 + x2)

Residuals:
     Min       1Q   Median       3Q      Max
-2.17610 -0.65146 -0.09532  0.54848  2.41966

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  3.04924    0.09661  31.562  < 2e-16 ***
x1           0.55124    0.09930   5.551 2.47e-07 ***
x2           0.23477    0.10534   2.229   0.0281 *
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.'
0.1 ` ' 1

Residual standard error: 0.9492 on 97 degrees of
freedom
Multiple R-Squared: 0.2687,     Adjusted R-squared:
0.2536
F-statistic: 17.82 on 2 and 97 DF,  p-value: 2.561e-07
> b<-coef(fm)
> b
(Intercept)          x1          x2
  3.0492374   0.5512398   0.2347682
you get b_hat standard errors from summary(fm):

se<-c(0.09661,0.09930,0.10534)
> se
[1] 0.09661 0.09930 0.10534

ttest<-(b[2]-0.6)/se[2]

> ttest
        x1
-0.4910391
> 1-pt(ttest,df=97) ##p-value, as df is high we can
use normal distribution
      x1
0.687746

we accept h0 :b1=0.6;

Hoping I helped you.
Best regards,
Vito

You wrote:
In a multiple linear regression with two independent
variables is there any function in R to test for the
coefficients being different than some given values?
Example:
x1<-rnorm(100)
x2<-rnorm(100)
y<-3+0.6*x1+0.3*x2
fm<-lm(y~x1+x2)
Obtain a test for the coefficients for x1 being
different than 0.6 and for x2 different than 0.3
Thanks
Manuel



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