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As an example, we discuss the case of two predictors for
the multiple
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regression.
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We can repeat the derivation we perform for the simple linear
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regression to find that the fraction of variance explained by the 2-
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predictors regression (R) is:
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here r
is the correlation coefficient
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We can show that if r2y
is smaller than or equal to a “minimum useful
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correlation” value, it is not useful to
include the second predictor in
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the regression.
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The minimum useful correlation = r1y
* r12
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This is the minimum correlation of x2 with
y that is required to improve
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the R2 given that x2
is correlated with x1.
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