## Parameter Estimates

The **Parameter Estimates** table, as shown in
Figure 14.5, displays the parameter estimates
and the corresponding degrees of freedom,
standard deviation, *t* statistic, and *p*-values.
Using the parameter estimates, you can also write out the fitted model:

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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