Question

Finding the Strength of a Correlation
A 2-column table with 5 rows. The first column is labeled hours spent exercising with entries 2, 4, 3, 4, 5. The second column is labeled hours spent playing video games with entries 16, 7, 5, 15, 8.

Over five different weeks, Irina tracked the hours she spent exercising and the hours she spent playing video games. What is the strength of the correlation between the hours spent exercising and the hours spent playing video games?

weak negative correlation
moderate negative correlation
weak positive correlation
moderate positive correlation

Answer 1

Compute the Pearson r. With x = [2,4,3,4,5], y = [16,7,5,15,8]:

mean(x)=3.6, mean(y)=10.2
Σ(x−x̄)(y−ȳ) = −8.6
Σ(x−x̄)² = 5.2, Σ(y−ȳ)² = 98.8

r = −8.6 / sqrt(5.2·98.8) ≈ −0.38

This is a (moderately) negative correlation. Answer: moderate negative correlation.