The correlation coefficient between the given variables is determined as 0.771 (three decimal places).
Correlation coefficient between the variables
The correlation coefficient between the variables is calculated as follows;
[tex]r = \frac{n\Sigma xy - \Sigma x\Sigma y}{\sqrt{[n\Sigma x ^2 \ - (\Sigma x)^2][n\Sigma y^2- (\Sigma y)^2]} }[/tex]
∑xy = (40 x 6) + (29 x 5) + (108 x 11) + (35 x 7) + (62 x 14) + (50 x 10) + (8 x 2)
∑xy = 3202
n∑xy = 7(3202)
n∑xy = 22,414
∑x = 40 + 29 + 108 + 35 + 62 + 50 + 8 = 332
∑y = 6 + 5 + 11 + 7 + 14 + 10 + 2 = 55
∑x∑y = 332 x 55 = 18,260
∑x² = 40² + 29² + 108² + 35² + 62² + 50² + 8² = 21,738
n∑x² = 7(21,738) = 152,166
(∑x)² = (332)² = 110,224
∑y² = 6² + 5² + 11² + 7² + 14² + 10² + 2² = 531
n∑y² = 7(531) = 3,717
(∑y)² = (55)² = 3,025
Correlation coefficient
[tex]r = \frac{22,414-18,260}{\sqrt{(152,166-110,224) (3,717 - 3025)} } \\\\r = \frac{4154}{\sqrt{29,023,864} } \\\\r = 0.771[/tex]
Thus, the correlation coefficient between the given variables is determined as 0.771 (three decimal places).
Learn more about correlation coefficient here: https://brainly.com/question/4219149
