Question

Consider the following study: Researchers recorded the temperatures at The Fashion Mall at Keystone in Indianapolis during 40 random days in November and December 2013, then again in June and July 2014. For these same days, they recorded the mall sales. The correlation coefficient between these variables was -0.884 and it was significant at the 1% level. (Though we do not cover it in our course, the significance of the correlation coefficient can be tested with a t test.) Does this correlation show that colder temperatures cause sales at malls to increase, or is something else the cause? (Hint: Consider the months during which the temperatures were recorded.) Briefly explain your answer using an interpretation of this correlation coefficient.

Answer 1

The correlation coefficient between the given two variables temperature and sales at mall is given as -0.884. This means there is a strong negative linear relationship or association exists between the given two variables. This means, when the temperature increases, the sale at mall decreases and when the temperature decreases, the sale at mall increases. This correlation does not exactly show colder temperatures causes sales at malls to increase, although there is a statistical relationship between two variables. We know the concept of correlation and causation. Causation always implies correlation but correlation does not always imply causation. There would be something else cause or you may say that there is some confounding variable which play the role for this correlation. If we see the months November and December, there are more holidays and due to holidays, more peoples came at mall and this fact is responsible for increasing sales. Also, there would be some other confounding variables which are responsible for this correlation.