Test Yourself — Wins from offence & defence

sports_basketball

The scenario

An NBA analyst models wins from two predictors: points scored per game (PPG, offence) and points allowed per game (OppPPG, defence), over 6 teams.

Team	PPG (x?)	OppPPG (x₂)	Wins (y)
Heat	112	108	41
Bucks	118	110	52
Pistons	109	112	38
Celtics	121	106	58
Wizards	108	114	33
Warriors	115	109	49

Fitted model: ŷ = −137.67 + 1.752·PPG − 0.151·OppPPG R² = 0.980 n = 6 predictors p = 2

aWhat does β̂(PPG) = 1.752 mean?1 mark

bThe defence coefficient is β̂(OppPPG) = −0.151. What does the negative sign say?1 mark

cPredict the wins for a team with PPG = 115 and OppPPG = 109.2 marks

Plug both into the fitted equation.

ŷ wins

ŷ = −137.67 + 1.752×115 − 0.151×109 = 47.3 wins

dCompute the adjusted R². (R² = 0.980, n = 6, p = 2)2 marks

adj = 1 − (1 − R²)(n − 1)/(n − p − 1).

adjusted R²

adj = 1 − (1 − 0.980)·(6−1)/(6−2−1) = 1 − 0.020·5/3 = 0.967

eThe overall F-test gives F = 72.7 on (2, 3) df, p ≈ 0.003. Conclusion?1 mark

emoji_events

5 / 5 — you read the whole model.

Coefficients with the right "holding constant" phrasing, a prediction, adjusted R², and the F-test. That's MLR.

Your turn

The scenario

5 / 5 — you read the whole model.