Question

Find the correlation coefficient, r, of the data described below,
Emily is a psychology professor studying the effect of media violence on modern
culture. As part of her research, she analyzed the content of several recent
action movies
For each movie, she noted the running time in minutes), x, and the number of
explosions, y
Explosions
8
12
8
29
21
Running time (in minutes)
80
85
85
88
90
Round your answer to the nearest thousandth,
r =

Answer 1

Answer:

r = 0.7575

Explanation:

Result Details & Calculation

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

X Values

∑ = 78

Mean = 15.6

∑(X - Mx)2 = SSx = 337.2

Y Values

∑ = 428

Mean = 85.6

∑(Y - My)2 = SSy = 57.2

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = 105.2

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 105.2 / √((337.2)(57.2)) = 0.7575

Meta Numerics (cross-check)

r = 0.7575