Question

1. Give an example of correlation and causation in which the explanatory variable directly causes a change in the response variable.

2. Next, give an example of correlation and non-causation in which the two variables are correlated but no direct cause-and-effect relationship exists between the two variables.

Answer 1

Answer

(1) An example of correlation and causation in which the explanatory variable directly causes a change in the response variable is "smoking causes lung cancer" where response variable is risk of lung cancer and explanatory variable is smoking. Here smoking directtly causes the risk of having lung cancer.And increasing the frequency of smoking increse the risk of lung cancer So the two variables are positively correlated and causation also exist.

(2) Consider an example where data collected on the sales of ice cream cones and air conditioners. One found that when ice cream sales were low, air conditioner sales tended to be low and that when ice cream sales were high, air conditioner sales tended to be high. So one can conclude that sales of ice cream cones and air conditioner are positively correlated. But one can't conclude that selling more ice cream cones causes more air conditioners to be sold. It is likely that the increases in the sales of both ice cream cones and air conditioners are caused by a third factor, an increase in temperature.

Hence there is no direct cause-and-effect relationship exists between the two variables considered here.