Significance Tests in Multiple Regression (2 of 2)
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Following the
general formula for significance testing
using the standard error of a statistic,
where b is the regression coefficient, s
b is the
standard error of the regression coefficient, N is the number of
subjects, and k is the number of predictor variables. The resulting
t is on N - k - 1 degrees of freedom.
The
formula for s
b is beyond the scope of this text. However,
all standard statistical packages compute s
b and
significance tests for the regression coefficients.
Returning to the problem of predicting college GPA, the regression
coefficients and associated significance tests are shown below:
b sb t p
HS GPA 0.3764 0.1143 3.29 0.0010
SAT 0.0012 0.0003 4.10 0.0001
Letters 0.0227 0.0510 0.44 0.6570
As can be seen, the regression coefficients for High School GPA and SAT are
both highly significant. The coefficient for Letters of recommendation
is not significant. This means that there is no convincing evidence that the quality
of the letters adds to the predictability of college GPA once High School
GPA and SAT are known.
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