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Statistical Probability Testing and Regression

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

[see attachment]

The correlation of x and y is -0.991.

1) Calculate and interpret the coefficients of determination (R-squared xy and R-squared yx).
2) How is the value of the correlation coefficient 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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See attached file for full problem description.

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Solution Preview

Please see the attached file.

1) We know that the correlation is -0.991. That means that the coefficient of determination (R2xy) is equal to (-0.991)2.
(-0.991)2 = 0.982081

You can also do this automatically in Excel: 0.982266865

The numbers are slightly different because the correlation of -0.991 is an approximation.

You can find coefficient of determination (R2yx) in ...

$2.19