On solving the provided question we can say that - correlation coefficient of the question is r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.
[tex]S_{xx} =[/tex]∑[tex]x^2[/tex] - (∑x[tex])^2[/tex] /n = 19300- ((420)^2 /10)= 1660
[tex]S_{yy} =[/tex] ∑[tex]y^2[/tex] (∑y[tex])^2[/tex]/n = 7454- ((270)^2 /10) = 164
[tex]S_{xy} =[/tex]∑[tex](xy)^2[/tex]/n -475
The correlation coefficient is:
r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
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