Question

The table shows the average number of hours of daylight per day for the last four months of the year.

A 2-column table with 4 rows. The first column is labeled month of year with entries 9, 10, 11, 12. The second column is labeled average hours of daylight per day with entries 12.37, 11.37, 10.57, 10.
What is the correlation coefficient for the data in the table?

–0.993
–0.791
0.791
0.993

Answer 1

Compute the Pearson r. For x = (9,10,11,12) and y = (12.37,11.37,10.57,10):

mean(x) = 10.5, mean(y) = 11.0775
sum (xi−x̄)(yi−ȳ) = −3.955
sum (xi−x̄)^2 = 5.0, sum (yi−ȳ)^2 = 3.174625

r = [sum (xi−x̄)(yi−ȳ)] / sqrt[sum (xi−x̄)^2 · sum (yi−ȳ)^2]
= −3.955 / sqrt(5·3.174625) ≈ −0.993

Answer: −0.993.