A researcher predicts first-year university GPA using hierarchical (blockwise) multiple regression in SPSS.
Block 1 (Model 1): Age, Gender (0 = female, 1 = male), High-school GPA Block 2 (Model 2): Study Hours/week, Test Anxiety
Key SPSS output (abridged):
Model Summary / Change Statistics
- Model 1: R = .47, R² = .22, Adj. R² = .20
- Model 2: R = .55, R² = .30, Adj. R² = .26
- R² Change = .08, F Change(2, 93) = 5.45, Sig. F Change = .006
Coefficients (Model 2)
- Age: B = 0.01, p = .34
- Gender: B = -0.18, p = .04
- High-school GPA: B = 0.41, p < .001
- Study Hours/week: B = 0.02, p = .08
- Test Anxiety: B = -0.05, p = .003
Which interpretation is the MOST correct?
Because Study Hours/week is not significant (p = .08), Block 2 does not significantly improve prediction beyond Block 1, so Model 2 should be rejected.
Block 2 significantly improves the model (ΔR² = .08, p = .006), but in the final model only Test Anxiety is a statistically significant unique predictor among the Block 2 variables.
R² = .30 in Model 2 means the Block 2 variables (Study Hours/week and Test Anxiety) explain 30% of the variance in GPA above and beyond Block 1.
Since Adj. R² drops from .30 to .26 in Model 2, adding Block 2 worsens the model and indicates overfitting.