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Chapter 10

Question 2

Pearson's correlation coefficient

Evaluate Pearson’s correlation coefficient for the data below.

2
2
n = 6, ∑x = 21, ∑y = 482, ∑xy = 2,213, ∑x = 91, ∑y = 60,514
∑ ∑ ∑
r =

∑ ∑ ∑ ∑
2
2
r = (6 × 2,213 – 21 × 482)/√[(6 × 91 – 21 ) (6 × 60,514 – 482 )]
r = 3,156/√[105 × 130,760]

r = 3,156/3,705 = 0.85

Question 3

Coefficient of determination

If the Pearson’s correlation coefficient is 0.96, calculate the coefficient of
determination

2
2
r = 0.96 = 0.92
92% of the variation in dependent y values can be explained by changes in the
independent x values

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