Hi Can you be more specific as to what is not clear? Testing the gradient of the regression equation = 0 can be expressed as an ANOVA problem (with k = 2). This is what they have done.
It is just following the method given in section 3 of chapter 14 - but if it helps here is an intuitive approach. We are treating this set of 11 data points as single values (the y's) from 11 treatments (the x's). We are then seeing if these data points are different from the overall mean \(\bar{X}\). If they aren't then that suggests that the regression line is horizontal - they're all roughly the same. We don't reject the \(H_0\). If they are that suggests the line is not horizontal.
