Case File — Build a two-predictor model

Phase 1 of 4

Frame the problem

Two candidate predictors, one outcome. Is MLR the right tool, and what's what?

Right tool for the job?

Team	Tackles	Inside-50s	Win %
Carlton	62	48	60
Essendon	55	44	48
Brisbane	68	52	70
North Melb	50	40	38
Geelong	72	55	82
Sydney	58	46	52

1 · Is multiple linear regression appropriate here?

2 · Which is the response, Y?

3 · So the two predictors are…

Phase 2 of 4

Two predictors changes how you get — and judge — the model.

What's the play?

4 · How do you get the coefficients for two predictors?

5 · To judge the fit of a 2-predictor model, which number do you quote?

Phase 3 of 4

R has fitted the plane. Use the results to predict and to judge the fit.

Predict & adjust

Fitted: ŷ = −69 + 1.0·tackles + 1.4·inside50s R² = 0.992 n = 6 p = 2

Predict a team with 60 tackles & 48 inside-50s, then adjust R²:

ŷ win %

adjusted R²

ŷ = −69 + 1.0×60 + 1.4×48 = 58.2 adj R² = 1 − (1−0.992)·5/3 = 0.986

Phase 4 of 4

The numbers only matter if you read them correctly.

Read it the MLR way

6 · How do you interpret the tackles coefficient (1.0)?

7 · Inside-50s has a bigger coefficient (1.4 vs 1.0). Does it "matter more"?

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You framed it, chose the matrix approach, judged it with adjusted R², and read the coefficients the MLR way.