Answer to Question #161469 in Statistics and Probability for Mahnoor

Question #161469

Calculate the pearson correlation coefficient for the following data

X 7 2 8 4 5

Y 4 4 7 6 7


1
Expert's answer
2021-02-08T17:27:23-0500

The Pearson correlation coefficient formula is given below,

r=n(ΣXY)(ΣX)(ΣY)[nΣX2(ΣX)2][nΣY2(ΣY)2]r=\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n\Sigma X^2-(\Sigma X)^2][n\Sigma Y^2-(\Sigma Y)^2]}}, where n=n= sample size

To find Pearson correlation coefficient of the given data, we first calculate the following table



Here n=5n=5 .

\therefore r=n(ΣXY)(ΣX)(ΣY)[nΣX2(ΣX)2][nΣY2(ΣY)2]r=\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n\Sigma X^2-(\Sigma X)^2][n\Sigma Y^2-(\Sigma Y)^2]}} =(5×151)(26×28)[(5×158)(26)2].[(5×166)(28)2]=\frac{(5×151)-(26×28)}{\sqrt{[(5×158)-(26)^2].[(5×166)-(28)^2]}} =275244=0.37=\frac {27}{\sqrt {5244}}=0.37 (approximately)



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