Notes say that When H0 is true SS(TOT)/(n-1) is the overall sample variance But won't this be true whether or not beta=0 ?
You are absolutely right SS_TOT/(n-1) is the sample variance (even if beta is having a shower ). And you are right that the text is quite misleading. The point of beta = 0 is the independence of SS_REG and SS_RES (and so to fulfill the F distribution requirements).
