Unformatted text preview: at
can be “explained” by the linear
relationship between x and y).
relationship Coefficient of Determination, r
Coefficient 2 r2 is useful because: iit gives the proportion of the variance
t
(fluctuation) of one variable that is
predictable from the other variable
predictable explains how much of the variability in
explains
the y''s can be explained by the fact that
s
they are related to x Let’s look at a formula
Let’s We find the total variation in y (SSTotal)
SSTotal = Σ(yi – ybar)²
SSTotal
ybar)² Is also called SSM (Sum of Squares about the
Is
mean)
mean) Is the variation around the mean…looks like
Is
variance
variance Formula continued
Formula We then find the Sum of Squared
We
Residuals (SSR)
Residuals
SSR = Σ(yi – ŷi)²
SSR Is also called SSE or “sum of squares of error” This is sometimes referred to as a measure of
This
the “unexplained” variation. Or the amount of
variation in y that cannot be attributed to the
linear relationship between x and y
linear Formula continued This gives us
r² = 1 – (SSR / SSTotal) If I multiply by 100, I get the percentage of
If
y variation attributable to the approximate
linear rel...
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This document was uploaded on 03/30/2014 for the course MATH AP Statist at Richard Montgomery High.
 Winter '13
 Jessell
 Coefficient Of Determination

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