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8 January, 01:45

If the formula were used to find the r-value of the following data, what would be the value of to three decimal places?

x y

2 4

5 10

7 14

11 19

15 24

A. 6.940

B. 5.099

C. 4.561

D. 7.759

+2
Answers (1)
  1. 8 January, 02:08
    0
    R = (n∑xy - (∑x) (∑y)) / (sqrt (n (∑x^2) - (∑x) ^2) * sqrt (n (∑y^2) - (∑y) ^2); where n = 5, ∑xy = 2 * 4 + 5 * 10 + 7 * 14 + 11 * 19 + 15 * 24 = 8 + 50 + 98 + 209 + 360 = 725, ∑x = 2 + 5 + 7 + 11 + 15 = 40, ∑y = 4 + 10 + 14 + 19 + 24 = 71, ∑x^2 = 2^2 + 5^2 + 7^2 + 11^2 + 15^2 = 4 + 25 + 49 + 121 + 225 = 424, ∑y^2 = 4^2 + 10^2 + 14^2 + 19^2 + 24^2 = 16 + 100 + 196 + 361 + 576 = 1294

    r = (5 (725) - (40) (71)) / (sqrt (5 (424) - (40) ^2) * sqrt (5 (1294) - (71) ^2) = (3625 - 2840) / (sqrt (2120 - 1600) * sqrt (6470 - 5041)) = 785 / (sqrt (520) * sqrt (1429)) = 0.8936

    r = 0.8936
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