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Understanding Pearson Correlation Coefficient Calculation

This chapter delves into computing Pearson correlation coefficient with detailed formulas and examples. Learn how to analyze and interpret correlations in statistical data analysis.

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Understanding Pearson Correlation Coefficient Calculation

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  1. Chapter 9, #7 and #9 Computing r

  2. #7 Pearson r • r = n(Σxy) – (Σx)(Σy) [n(Σx2) – (Σx)2] [n(Σy2) – (Σy)2] n = 7

  3. Pearson r • r = n(Σxy) – (Σx)(Σy) [n(Σx2) – (Σx)2] [n(Σy2) – (Σy)2] n = 7 • r = 7(6284) – (215)(181) = [7(7511) – (215)2] [7(5363) – (181)2]

  4. Pearson r • r = 7(6284) – (215)(181) = • [7(7511) – (215)2] [7(5363) – (181)2] • r = 43988 – 38915 = • [52577 – 46225] [37541 – 32761] • r = 5073 = • [6352] [4780] • r = 5073 = 5073 = 0.921 • 30362560 5510.22

  5. #9 Pearson r • r = n(Σxy) – (Σx)(Σy) [n(Σx2) – (Σx)2] [n(Σy2) – (Σy)2] n = 5

  6. Pearson r • r = n(Σxy) – (Σx)(Σy) [n(Σx2) – (Σx)2] [n(Σy2) – (Σy)2] n = 7 • r = 5(5090) – (250)(100) = [5(12750) – (250)2] [5(2040) – (100)2]

  7. Pearson r • r = 5(5090) – (250)(100) = • [5(12750) – (250)2] [5(2040) – (100)2] • r = 25450 – 25000 = • [63750 – 62500] [10200 – 10000] • r = 450 = • [1250] [200] • r = 450 = 450 = 0.900 • 250000 500

  8. #9 Pearson r definition formula • r = Σ(zxzy) = 4.48 = .900 n 5 n = 5

  9. Pearson r • r = n(Σxy) – (Σx)(Σy) [n(Σx2) – (Σx)2] [n(Σy2) – (Σy)2] n = 7 • r = 5(5090) – (250)(100) = [5(12750) – (250)2] [5(2040) – (100)2]

  10. Pearson r • r = 5(5090) – (250)(100) = • [5(12750) – (250)2] [5(2040) – (100)2] • r = 25450 – 25000 = • [63750 – 62500] [10200 – 10000] • r = 450 = • [1250] [200] • r = 450 = 450 = 0.900 • 250000 500

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