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coefficient of determinations and correlation coefficient

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A sample of eight observations of variables x and y is shown below:

x 5 3 7 9 2 4 6 8
y 20 23 15 11 27 21 17 14

Also, Correlation of x and y = -0.991

i) Calculate and interpret the coefficient of determinations (Rxy2 and Ryx2 )

ii) How is the value of the correlation coefficient ryx affected in each of the following cases?

a) Each x value is multiplied by 3.
b) Each x value is switched with the corresponding y value.
c) Each x value is increased by 4.

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The solution shows the relationship between the coefficient of determinations and correlation coefficient. It also explains how the correlation coefficient is affected by x values of the data.

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