Quality Quiz from Professor Cleary

Congratulations:
"A" is correct.

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Everyone gets lucky sometimes, and that was the case with Kohl Minor's guess at the solution to last month's dilemma. His response, however, is not particularly useful to someone who might be trying to understand the coefficient of determination.

The above figure appears in nearly every statistics textbook, in chapters relating to regression. It offers an excellent approach to gaining insight about the coefficient of determination. The formula for is:

The easiest way to understand this figure is to start with a value of X, in this case. If X were equal to and X and Y were completely non-correlated, the best estimate of Y would be . Using the regression equation = a + bx, the best estimate of Y is . Thus
- is the explained difference of the mean of y() and the predicted value of y(). Sum these values and divide that by the appropriate degrees of freedom, m. The total variance is the difference between each observation ( ) and the average value for y( ), or - divided by the appropriate degrees of freedom, n-m.

The coefficient of determination is indeed the ratio of explained variation to total variation. Finally, the square root of happens to be equal to r, or the correlation coefficient. So this time, Kohl Minor was correct in his assertion, even though he may not have a justification for it.

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