For most real-world phenomena, the graphs aren’t that regular nor repeating, so there are more hints about direction and lag.
Yeah, though I think “at fourth glance” stands as it is: in the long run any bounded function will have zero correlation with its derivative.
#3 is a communication failure—we forgot to say “compared to what” when we say “increases” risk of death.
Compared to the control group. People often measure the effect of variable X on variable Y by randomly dividing a population into experiment and control groups, intervening on X in the experiment group, and measuring the difference in Y between groups. Well, I tried to show an example where intervening on X in either direction will increase Y.
Yeah, though I think “at fourth glance” stands as it is: in the long run any bounded function will have zero correlation with its derivative.
Compared to the control group. People often measure the effect of variable X on variable Y by randomly dividing a population into experiment and control groups, intervening on X in the experiment group, and measuring the difference in Y between groups. Well, I tried to show an example where intervening on X in either direction will increase Y.