[R] Significance of slopes

[Petr PIKAL]

Hi


r-help-bounces at r-project.org napsal dne 09.12.2008 23:21:17:

> Hi Christian,
> please give always reproducible code,
> so we can see what have done
> and  give you the best answer.
> 
> lm function, generally 
> as in this  example form lm man page ( ?lm)
> 
> 
> > trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
> >ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
> >reg=lm(trt~ctl)
> >summary(reg)
> 
> Call:
> lm(formula = trt ~ ctl)
> 
> Residuals:
>      Min       1Q   Median       3Q      Max 
> -1.09389 -0.33069 -0.15249  0.05128  1.45497 
> 
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|) 
> (Intercept)   7.7957     2.1661   3.599  0.00699 **
> ctl          -0.6230     0.4279  -1.456  0.18351 
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 
‘ ’ 1 
> 
> Residual standard error: 0.7485 on 8 degrees of freedom
> Multiple R-squared: 0.2095,    Adjusted R-squared: 0.1106 
> F-statistic:  2.12 on 1 and 8 DF,  p-value: 0.1835 
> 
> 
> Returns you all the  answer (almost) for the  questions that you ask;
> the p-value of the intercept line, is the p-value from the 
> test( t test)  if the intercept is  different form zero. 
> the ctl line has also the same interpretation, regarding the value 
returned.
> Meaning no is not significantly different form zero.
> 
> If you want to test if the  estimates ( slopes or intercept) are
> different from a specific value as in your case different for 0.5
> you can apply a test. 

Or use offset

test for slope == -1
reg=lm(trt~ctl+offset(-1*ctl))
summary(reg)

Call:
lm(formula = trt ~ ctl + offset(-1 * ctl))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.09389 -0.33069 -0.15249  0.05128  1.45497 

Coefficients:
            Estimate Std. Error t value Pr(>|t|) 
(Intercept)   7.7957     2.1661   3.599  0.00699 **
ctl           0.3770     0.4279   0.881  0.40391 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.7485 on 8 degrees of freedom
Multiple R-squared: 0.2095,     Adjusted R-squared: 0.1106 
F-statistic:  2.12 on 1 and 8 DF,  p-value: 0.1835 

test for slope == 0.5 
reg=lm(trt~ctl+offset(0.5*ctl))

Regards
Petr


> Type on R 
> ?t.test 
> and you can find the  all the information you need.
> 
> Hope this helps
> 
> Best Regards
> 
> Anna
> 
> Anna Freni Sterrantino
> Ph.D Student 
> Department of Statistics
> University of Bologna, Italy
> via Belle Arti 41, 40124 BO.
> 
> 
> 
> 
> ________________________________
> Da: Christian Arnold <chrarnold at web.de>
> A: r-help at r-project.org
> Inviato: Martedì 9 dicembre 2008, 21:54:23
> Oggetto: [R] Significance of slopes
> 
> Hello R community,
> 
> I have a question regarding correlation and regression analysis. I have 
two 
> variables, x and y. Both have a standard deviation of 1; thus, 
correlation and
> slope from the linear regression (which also must have an intercept of 
zero) are equal.
> I want to probe two particular questions:
> 1) Is the slope significantly different from zero? This should be easy 
with 
> the lm function, as the p-value should reflect exactly that question. If 
I am 
> wrong, lease correct me.
> 2) Is the slope significantly different from a non-zero value (e.g. 
0.5)? How 
> can I probe that hypothesis? Any ideas?
> 
> I apologize if this question is too trivial and already answered 
somewhere, 
> but I did not find it.
> 
> [[elided Yahoo spam]]
> Christian
> 
> ______________________________________________
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> 
> 
> 
> 
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> 
> ______________________________________________
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