A researcher uses binary logistic regression in SPSS to predict whether a student passes a final exam (0 = Fail, 1 = Pass) from Hours Studied (0–20), Tutoring (0 = No, 1 = Yes), and their interaction (HoursStudied×Tutoring). SPSS output (Variables in the Equation) is:
Variables in the Equation
- HoursStudied: B = 0.350, SE = 0.140, Wald = 6.25, Sig = 0.012, Exp(B) = 1.419
- Tutoring (1 vs 0): B = 1.099, SE = 0.540, Wald = 4.14, Sig = 0.042, Exp(B) = 3.001
- HoursStudied×Tutoring: B = -0.200, SE = 0.095, Wald = 4.43, Sig = 0.035, Exp(B) = 0.819 (Constant): B = -4.000
Which interpretation is MOST correct?
For students without tutoring, each additional study hour multiplies the odds of passing by about 1.42 (≈42% increase). For tutored students, the per-hour effect is smaller because the interaction is negative: their per-hour odds multiplier is exp(0.35 − 0.20) ≈ 1.16 (≈16% increase).
Tutoring multiplies the odds of passing by about 3.00 for all students, regardless of how many hours they study, because Exp(B) for Tutoring is 3.001.
Because the interaction coefficient is negative, tutoring makes students less likely to pass overall (i.e., tutoring is harmful at all study-hour levels).
Because Exp(B) for the interaction is 0.819 (< 1), each extra study hour decreases the odds of passing for students who receive tutoring.