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Find the correlation coefficient, r, of the data described below. Round your answer to the nearest...

Find the correlation coefficient, r, of the data described below.
Round your answer to the nearest thousandth.
r =

Answer

Data:

Months owned (x) Plays (y)
2 52
12 52
13 75
23 88
23 90

To find the correlation coefficient, r, use the formula:

r = Σ((x - mean of x)(y - mean of y)) / sqrt(Σ(x - mean of x)^2 * Σ(y - mean of y)^2)

Calculating step-by-step:

  1. Mean of x = (2 + 12 + 13 + 23 + 23) / 5 = 14.6
  2. Mean of y = (52 + 52 + 75 + 88 + 90) / 5 = 71.4
  3. Σ((x - mean of x)(y - mean of y)) = (2-14.6)(52-71.4) + (12-14.6)(52-71.4) + (13-14.6)(75-71.4) + (23-14.6)(88-71.4) + (23-14.6)(90-71.4) = 447.2
  4. Σ(x - mean of x)^2 = (2-14.6)^2 + (12-14.6)^2 + (13-14.6)^2 + (23-14.6)^2 + (23-14.6)^2 = 394.8
  5. Σ(y - mean of y)^2 = (52-71.4)^2 + (52-71.4)^2 + (75-71.4)^2 + (88-71.4)^2 + (90-71.4)^2 = 1094.8
  6. r = 447.2 / sqrt(394.8 * 1094.8) = 0.899

Answer: r = 0.899

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