How can one produce many `p-values` in regression analysis? In order to understand ANOVA and regression better, I read this: http://www.theanalysisfactor.com/why-anova-and-linear-regression-are-the-same-analysis/
It seems to make sense for the most part.  The only part that is confusing to me is how to get a p-value for each difference between the intercept and the means of each of the categories. Here is the exact quote that is confusing to me:

A regression reports only one mean(as an intercept), and the differences between that one and all other means, but the p-values evaluate those specific comparisons.

How do I get multiple p-values for a single regression analysis?  The only way I can think to do this is if I assume each coefficient has a certain distribution, and I compute the p-value of the coefficient for that distribution.  Or, is there another way to get p-values that I'm missing?
 A: When you regress on a factor you have an indicator (dummy) variable for each level of the factor bar one (the "baseline" category). 
As a result the p-values of the coefficients represent p-values for the pairwise comparisons with the baseline.
Here's an example in R, a data set on weights of chicks on different feed:

> summary(lm(weight~feed,chickwts))

[... snip ...]

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    323.583     15.834  20.436  < 2e-16 ***
feedhorsebean -163.383     23.485  -6.957 2.07e-09 ***
feedlinseed   -104.833     22.393  -4.682 1.49e-05 ***
feedmeatmeal   -46.674     22.896  -2.039 0.045567 *  
feedsoybean    -77.155     21.578  -3.576 0.000665 ***
feedsunflower    5.333     22.393   0.238 0.812495    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 54.85 on 65 degrees of freedom
Multiple R-squared:  0.5417,    Adjusted R-squared:  0.5064 
F-statistic: 15.36 on 5 and 65 DF,  p-value: 5.936e-10

The last column in the coefficients table is a set of p-values for comparisons with the mean of the baseline (casein) category.
