[R] retrieving p-values in lm

[Gavin Simpson]

On Fri, 2005-12-09 at 14:19 +0100, Patrick Kuss wrote: 
> Dear list,
> 
> I want to retrieve the p-value of a two-polynomial regression. For a
> one-polynomial lm I can easily do this with:
> summary(lm(b~a, data=c)[[4]][[8]].
> 
> But how do I find the final p-value in the two-polynomial regression? Under
> $coefficients I don't find it
> 
> Any suggestions?

Judging from your code, you mean p-value of the F-statistic for the
whole model - this isn't stored anywhere, see:

getAnywhere(print.summary.lm)

In particular this section:

 cat("\nResidual standard error:", format(signif(x$sigma,
        digits)), "on", rdf, "degrees of freedom\n")
    if (!is.null(x$fstatistic)) {
        cat("Multiple R-Squared:", formatC(x$r.squared, digits = digits))
        cat(",\tAdjusted R-squared:", formatC(x$adj.r.squared,
            digits = digits), "\nF-statistic:", formatC(x$fstatistic[1],
            digits = digits), "on", x$fstatistic[2], "and", x$fstatistic[3],
            "DF,  p-value:", format.pval(pf(x$fstatistic[1],
                x$fstatistic[2], x$fstatistic[3], lower.tail = FALSE),
                digits = digits), "\n")
    }

The relevant bit being:

format.pval(pf(x$fstatistic[1],
                x$fstatistic[2], x$fstatistic[3], lower.tail = FALSE)

The reason this works for the first model is that with one covariate the
value in $coefficients is the overall model p-value, in that case. With
two covariates, the things in $coefficients relate to these, not to the
overall model - your assumption was wrong in the first usage, you just
lucked out that it gave the same result.

So,

p1 <- pf(lm.res$fstatistic[1],
         lm.res$fstatistic[2], lm.res$fstatistic[3], 
         lower.tail = FALSE)

p2 <- pf(lm.res.2$fstatistic[1],
         lm.res.2$fstatistic[2], lm.res.2$fstatistic[3], 
         lower.tail = FALSE)

Gives you the p-values:

> p1
     value
0.01368545
> p2
    value
0.0461472

HTH

G
> 
> Patrick
> 
> alt <-(2260,2183,2189,1930,2435,
> 2000,2100,2050,2020,2470,
> 1700,2310,2090,1560,2060,
> 1790,1940,2100,2250,2010)
> 
> H <- c(0.2034,0.1845,0.2053,0.1788,0.2196,
> 0.2037,0.1655,0.2176,0.1844,0.2033,
> 0.1393,0.2019,0.1975,0.1490,0.1917,
> 0.2180,0.2064,0.1943,0.2139,0.1320)
> 
> X <- data.frame(alt,H)
> 
> lm.res <- summary(lm(H~alt,data=X))
> lm.res
> p1 <- lm.res[[4]][[8]]
> p1
> 
> lm.res.2 <- summary(lm(H~alt+I(alt^2),data=X))
> lm.res.2
> str(lm.res.2) # where is p
> 
> p2 <- lm.res.2[[???]][[????]]
> 
> --
> Patrick Kuss
> PhD-student
> Institute of Botany
> University of Basel
> SchÃ¶nbeinstr. 6
> CH-4056 Basel
> +41 61 267 2976
> 
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Gavin Simpson                     [T] +44 (0)20 7679 5522
ENSIS Research Fellow             [F] +44 (0)20 7679 7565
ENSIS Ltd. & ECRC                 [E] gavin.simpsonATNOSPAMucl.ac.uk
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