[R] Test if beta is different from something other than 0

[Peter Dalgaard BSA]

"Moffet, Corey" <Corey.Moffet at ttu.edu> writes:

> Is there a function/package that will allow you to test the hypothesis beta1
> = x in a
> simple linear regression, where x is a constant?  The AOV tests if beta1 in
> different from
> 0 but what if I want to know if beta1 one is different from 1?

(Slightly unfortunate choice of variable names there.)

Say that y are responses and x the *predictor*:

> x<-1:10 
> y <- x+rnorm(10)
> summary(lm(y~x))

Call:
lm(formula = y ~ x)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.5600 -0.1918  0.2597  0.4870  1.1106 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.3347     0.7225  -0.463    0.655    
x             1.0557     0.1164   9.067 1.76e-05 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 1.058 on 8 degrees of freedom
Multiple R-Squared: 0.9113,     Adjusted R-squared: 0.9002 
F-statistic:  82.2 on 1 and 8 DF,  p-value: 1.755e-05 

> summary(lm(y-x~x))

Call:
lm(formula = y - x ~ x)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.5600 -0.1918  0.2597  0.4870  1.1106 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.33475    0.72250  -0.463    0.655
x            0.05572    0.11644   0.478    0.645

Residual standard error: 1.058 on 8 degrees of freedom
Multiple R-Squared: 0.02782,    Adjusted R-squared: -0.0937 
F-statistic: 0.229 on 1 and 8 DF,  p-value: 0.6451 


-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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