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Chapter 10
Question 1
Pearson's correlation coefficient
Evaluate Pearson’s correlation coefficient for the data on sales and advertising
spend in the table below.
Advertising spend ($000) Sales value ($000)
10 1,500
12 2,000
15 2,200
18 2,700
19 2,700
21 2,720
n = 6
2
x y xy x 2 y
10 1,500 15,000 100 2,250,000
12 2,000 24,000 144 4,000,000
15 2,200 33,000 225 4,840,000
18 2,700 48,600 324 7,290,000
19 2,700 51,300 361 7,290,000
21 2,720 57,120 441 7,398,400
95 13,820 229,020 1,595 33,068,400
n ∑ xy – ∑ x ∑ y
r =
2
2
(n ∑ x -( ∑ x) )(n ∑ y -( ∑ y) )
2
2
2
2
r = (6 × 229,020 – 95 × 13,820)/√[(6 × 1,595 – 95 ) (6 × 33,068,400 – 13,820 )]
r = 61,220/√[545 × 7,418,000]
r = 61,220/63,583 = 0.96
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