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Coefficient of Determination
R2
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P. 227 43,44,47
P. 2239 49,50,53
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Gas chromatography is a technique used to
detect very small amounts of a substance, for
example, a contaminant in drinking water.
Laboratories use regression to calibrate such
techniques. The data below show the results of
five measurements for each of four amounts of
the substance being investigated. The
explanatory variable x is the amount of the
substance in the specimen, measure in
nanograms (10 -9 gram). The response variable is
the reading from the gas chromatograph.
S
Amount
Reading on
(mg)
Chromatograph
.25
6.25
7.98
6.54
6.37
7.96
1.00
29.7
30.0
30.1
29.5
29.1
5.00
211
204
212
213
205
20.00
929
905
922
928
919
Percent Change = (a – b) /a
Difference Between R and R2
R measures strength and direction of a linear relationship. R is used
to decide how well a linear model fits the data.
R2 measures the percent of variation in the observed y-values that
is explained by the linear regression of (y-values) on (x-values).
R2 is used to measure how well the least squares regression lines
does at predicting values of the response variable y.