Quality Quiz from Professor Cleary
"B" is correct.
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Kohl is too quick to comment without considering the real meaning of the statistic, and is wrong about Coefficient of Determination's implications.
Coefficient of Determination is a statistic that
indicates the percent of variation in Y (the dependent variable)
that can be explained by X (the independent variable). Examining
the scatter diagram below, one can see that the Coefficient of Determination
is equal to 1. In other words, X explains 100% of the variation
In this case, X is a perfect predictor of Y. Knowing
what X's value is, and putting that value into the regression equation
(e.g., X = 2), Y = 0 +2X, or Y = 0+2(2), you will derive 4, the
predicted value of Y, given an X of 2.
Looking again at Kohl's regression analysis:
A relationship between X and Y is clear from this chart.
Finally, in an example where X has little or nothing to do with Y:
It is clear that there is no close pattern. Observations
appear to be randomly placed. There continues to be a regression
line (Y = 6.13 + 0.02 X), that offers the best fit, even if that
fit is not especially good.
Recall that last month we learned how to test the goodness of fit by using the t statistic to examine the hypothesis that B = 0. If you were to go through the four steps, what do you think the conclusion would be?
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