Say you have an independent variable, $x$, and two dependent variables $y_1$ and $y_2$. I want to calculate whether these two variables have a significantly different slope. I can do it by calculating separate regressions, and then using he method mentioned at Test a significant difference between two slope values.
I was wondering, would be equivalent to testing for the significance of the slope of the series $(y_1-y_2)$ [e.g. null hypothesis slope=0]? I tried it with a couple of hundred independent series, and the results look very similar (similar distribution of p-values), but I'd think if it were that easy, more people would use it, as the computation is simpler. So, why is it not the same?