Case File — Threes & wins · Low Stakes Stats

Phase 1 of 4

Frame the problem

Before any maths: is this a regression job, and what plays the role of X and Y?

Is this an SLR job?

1 · Is this a simple linear regression problem?

2 · Which variable is the response, Y?

3 · So which is the predictor, X?

Phase 2 of 4

You decided: SLR, with Y = wins and X = 3-point %. Choose each move yourself.

What's the play?

4 · What's your first move?

5 · Means done. What do you need before the slope?

6 · You've got the line. "How good is it?" — compute…?

Phase 3 of 4

The tedious sums are done for you. Apply the formulas and check yourself.

Slope, intercept, prediction

x̄36.24

ȳ46.62

Sxx27.3

Sxy114.6

Compute the line, then predict a team shooting 37%:

β̂₁ (slope)

β̂₀ (intercept)

ŷ at 37%

β̂₁ = Sxy / Sxx = 114.6 / 27.3 = 4.192 β̂₀ = ȳ − β̂₁·x̄ = 46.62 − 4.192 × 36.24 = -105.29 ŷ(37%) = -105.29 + 4.192 × 37% = 49.8 wins

Fitted line: ŷ = -105.29 + 4.192 × 3PT%. Each +1 percentage point is worth about 4.192 wins.

Phase 4 of 4

The stats only matter if they answer the real question. Two calls to make.

So what do you tell them?

7 · A team lifts its three-point shooting by 2 percentage points over a season. Best estimate of the extra wins?

extra wins

Δŷ = β̂₁ × 2 = 4.192 × 2 = 8.38 wins

8 · Would you trust the model's prediction for a team shooting 45%?

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You framed it, planned it, crunched it, and made the call — SLR as a problem-solving tool, not a recipe.