[R] Signif. codes

[Daniel Malter]

No, it does not mean that the numbers have zero chance of being wrong. The
extent to which the estimate can be wrong (which is a very bad and imprecise
expression) is indicated by the standard error.

The p-value close to zero implies that the intercept of the underlying
population from which your sample was drawn is significantly different from
zero with a probability that approaches certainty (One minus p<2e-16).
Remember that your data is assumed to be a random sample drawn from an
underlying, larger population. Thus, the sample can never PERFECTLY
represent the underlying population (only the underlying population itself
can). However, the regression model gives you an estimate for what the
data-generating process in the underlying population was (i.e., it gives you
probability distributions for the true coefficients of the population,
assuming that the assumptions for OLS regression are met). 

So, given the observed mean in your sample (i.e., your data), the
probability that the true mean of the intercept in the underlying population
is zero approaches zero. Another way to look at this is that it would be
extremely unlikely (next to impossible) to draw a random sample from the
population that has a zero intercept.

By the OLS assumptions, the probability density for the true intercept in
the population will be distributed normally around the estimate for the
intercept, with the mean equal to the estimated intercept and standard
deviation equal to the standard error of the intercept.

Daniel

-------------------------
cuncta stricte discussurus
-------------------------
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of John Paul Telthorst
Sent: Monday, December 21, 2009 1:13 AM
To: r-help at r-project.org
Subject: [R] Signif. codes

My question is about the "Signif. codes" and the p-value, specifically, the
output when I run

summary(nameofregression.lm)


So you get this little key:

Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

And on a regression I ran, next to the intercept data, I get '***'

Coefficients:
>
>             Estimate Std. Error t value Pr(>|t|)
>
> (Intercept)  7.95652    0.59993  13.262   <2e-16 ***
>
> day.f2      -0.04348    0.84843  -0.051    0.959
>
> day.f3      -0.13043    0.84843  -0.154    0.878
>
> day.f4      -0.21739    0.84843  -0.256    0.798
>
> day.f5       0.02174    0.84843   0.026    0.980
>
> day.f6      -0.15217    0.84843  -0.179    0.858
>
> day.f7       0.14986    0.84390   0.178    0.859
>
>
Does this mean that these numbers have a 0% chance of being wrong?  Is there
a way to change this to the .05 level of significance?

Thanks,
John

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