General Linear Model (GLM)

Coefficients

  

Use the p-values to determine which coefficients in the model are significantly different from zero (no effect).

For categorical factors, the coefficients table lists the estimated coefficients for each level of each factor. The table also lists all combinations of factor levels for interaction effects. Before you look at the effects for specific levels in the coefficients table, you should look first in the analysis of variance table at the p-value for each term. After you identify a significant set of effects (for example main effects, or interaction effects), use the coefficients table to evaluate the individual effects.

If the analysis of variance table suggests significant higher-order or interaction effects, you should look at them first because they will influence how you interpret the main effects. To use the p-value, you need to:

·    Identify the p-value for the effect you want to evaluate.

·    Compare this p-value to your a-level. A commonly used a-level is 0.05.

-    if the p-value is less than or equal to a, conclude that the effect is significant.

-    if the p-value is greater than a, conclude that the effect is not significant.

·    Assess the VIF values. If the VIF values are all close to 1, this indicates that the predictors are not correlated. VIF values greater than 5 suggest that the regression coefficients are poorly estimated.

Example Output

Coefficients

 

Term               Coef  SE Coef  T-Value  P-Value   VIF

Constant         2.7275   0.0245   111.29    0.000

Subject

  1             -0.5775   0.0443   -13.04    0.000  1.87

  2              0.0792   0.0380     2.08    0.045  1.44

  3              0.3858   0.0418     9.23    0.000  1.60

Degree

  1             -0.3400   0.0373    -9.11    0.000  1.85

  2             -0.2600   0.0355    -7.33    0.000  1.92

Subject*Degree

  1 1           -0.0100   0.0676    -0.15    0.883  3.53

  1 2            0.0600   0.0666     0.90    0.374  3.42

  2 1           -0.0167   0.0561    -0.30    0.768  2.14

  2 2           -0.0267   0.0532    -0.50    0.619  2.03

  3 1           -0.0233   0.0660    -0.35    0.726  2.80

  3 2           -0.0033   0.0576    -0.06    0.954  2.42

Interpretation

For the salary data, the results can be summarized as follows:

·    Subject is significant at all three levels (p= 0.000, 0.045, and 0.000)

·    Degree is significant at both levels (P = 0.000).

·    The interaction between Subject and Degree is not significant for any combination of factor levels. All interaction p-values are greater than an a-level of 0.05. Consequently, the effect of one predictor does not depend on the value of the other predictor.

·    The VIFs are all close to 1, which indicates that the predictors are not highly correlated.