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-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of John Paul Telthorst Sent: Monday, December 21, 2009 1:13 AM To: r-help@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 [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
