A researcher predicts final exam score (Y) from Hours Studied (X1) and Test Anxiety (X2) using multiple linear regression. Below is a simplified SPSS output.
Correlations (zero-order):
- r(Y, Hours) = .62
- r(Y, Anxiety) = −.28
- r(Hours, Anxiety) = −.79
Model Summary: R = .71, R² = .50, Adjusted R² = .49
Coefficients (DV = Exam Score):
- Constant: B = 42.10, p < .001
- Hours Studied: B = 5.80, SE = 1.10, Beta = .82, t = 5.27, p < .001, Tolerance = .18, VIF = 5.56
- Test Anxiety: B = 3.20, SE = 1.25, Beta = .41, t = 2.56, p = .013, Tolerance = .18, VIF = 5.56
Which statement is most defensible based on these results?
Because B for Test Anxiety is positive and significant (p = .013), we can conclude that higher anxiety causes higher exam scores.
The positive coefficient for Test Anxiety is likely a suppression/multicollinearity artifact given the strong correlation between predictors and the high VIF; interpret the unique effect of anxiety cautiously.
Since Test Anxiety is significant and Hours Studied is also significant, multicollinearity is not a concern here; the coefficients can be interpreted normally.
Because Beta for Hours Studied (.82) is larger than Beta for Test Anxiety (.41), Hours Studied explains 82% of the variance in exam scores.