Quality Quiz from Professor Cleary
Congratulations:
"A" is correct.
Click here for a more complete video explanation
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 noncorrelated, 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, nm.
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.
Click here to register to win a free Quality Gamebox program.
Copyright 2006 PQ Systems.
Please direct questions or problems regarding this web site to the Webmaster.
