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When Kohl Minor tried to explain coefficient of
determination to his boss, Hal Zangels, last month, he used the
data below, referring to tons of coal and total cost for his mine.
Kohl used CHARTrunner's
scatter diagram to analyze the data, making total cost the dependent
variable (Y) and total tons produced, the independent variable (X).
This generated the following chart:
The regression line in simple linear regression
is a straight line drawn through the points plotted on the scatter
diagram. The calculation results in an equation where the value
of Y (on the vertical axis) can be predicted from the value of X
(on the horizontal axis). The equation takes the form of
Last month, Kohl explained to his boss, Hal Zangels,
that the coefficient of determination represents the ratio of explained
variance of Y to the total variation of Y. In this case, it is 0.76.
But Hal pressed Kohl for further explanation. He had memorized the
definition from a textbook without fully understanding its application.
To further assure Hal of his competence, Kohl added,
"Well, if you take the square root of this number 0.76^2, you
will have the correlation coefficient, which is 0.87. And of course
you know what that means."
Analyze Hal's competence for yourself, and predict
the scenario to follow:
a) Hal is convinced
that Kohl understands coefficient of determination, since he is
correct in this assertion;
b) Kohl has dug his
own statistical grave, not only with his sarcastic remark but also
the demonstration of his lack of comprehension of the concept.
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