# Significance Tests in Multiple Regression (2 of 2)

Following the general formula for significance testing using the standard error of a statistic,

where b is the regression coefficient, sb 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 sb is beyond the scope of this text. However, all standard statistical packages compute sb 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.