What exactly does the Significance F represent in this Regression from the
Data Analysis Add-on?

Two replicates of three samples. Regressed on indicator variables
{X1,X2,X3}, such that {1,0,0} is sample 1. No intercept is estimated as the
mean of all three samples are (adjusted to) zero. If the Null hypothesis is
rejected the samples are non-uniform.

Is the Significance F a measure of Beta error? Or is it meaningless because
the intercept is zero.

I would expect the Significance F to be FDIST(13.397,3,3) = 0.03042

ANOVA
df SS MS F Significance F
Regression 3 29.0574 9.685 13.397 0.07025439
Residual 3 2.16890 0.722
Total 6 31.22640461

Thanks,

Arne