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in the context of regression, determine wether the following statement is true or false. If there...

in the context of regression, determine wether the following statement is true or false.
If there is a very strong correlation between x and y, the amount of unexplained variation should be relatively large.

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Answer #1

If there is a very strong correlation between x and y, the amount of unexplained variation should be relatively large.

This is true.

Consider an example; we are given with the two variables having correlation coefficient, r = 0.912, which is a very strong correlation between x and y. Now, we know that the explained variation, r2 is the square of the correlation coefficient. Therefore, r2 = 0.9122 = 0.8317. Therefore, the amount of unexplained variation = 1 - 0.8317 = 0.1683.

Thus, we can say that if there is a very strong correlation between x and y, the amount of unexplained variation should be relatively large.

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