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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

The formula for s

b sAs 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._{b}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

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