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Multiple Regression |
The t statistic is used to test the null
hypothesis that a parameter is 0 in the model.
In this example, only the coefficient for HSM appears
to be statistically significant (p 0.0001).
The coefficients for HSS and HSE are not significant,
partly because of the relatively high correlations
among the three explanatory variables.
Once HSM is included in the model, adding HSS and
HSE does not substantially improve the model fit.
Thus, their corresponding parameters are not
statistically significant.
Two other statistics, tolerance and variance inflation,
also appear in the Parameter Estimates table.
These measure the strength of interrelationships
among the explanatory variables in the model.
Tolerances close to 0 and large variance inflation factor
values indicate strong linear association or collinearity
among the explanatory variables (Rawlings 1988, p. 277).
For the GPA data, these statistics signal no problems of
collinearity, even for HSE and HSS, which are the two
most highly correlated variables in the data set.
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