Question

1. 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.)

(a) Interpret this correlation coefficient.
(b) 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

Answer 1

Association between the variables and yes.

Explanation:

Given that 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

The test was done and significant at 1% level

a) the correlation coefficient is the strength of association between the two. Here we have strong negative correlation between the two variables. If correlation coefficient absolute value is nearer to 1, we say strong.

b) Yes . The lower the temperature the higher is the sales this is because of strong negative correlation.