Case File — The Dodgers & the heat

Phase 1 of 4

Frame the problem

Before any maths: is this even 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 — the thing you're trying to explain?

3 · So which is the predictor, X?

Phase 2 of 4

You decided: SLR, with Y = runs and X = temperature. Now choose each move yourself — no checklist.

What's the play?

4 · What's your first move?

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

6 · You've got the line. The coach asks "how good is it?" What do you compute?

Phase 3 of 4

We've done the tedious sums (you drilled those already). Apply the formulas and check yourself.

Slope, intercept, prediction

x̄ (mean temp)82.13

ȳ (mean runs)5.50

Sxx610.9

Sxy142.5

Compute the line, then predict a 90°F game:

β̂₁ (slope)

β̂₀ (intercept)

ŷ at 90°F

β̂₁ = Sxy / Sxx = 142.5 / 610.9 = 0.233 β̂₀ = ȳ − β̂₁·x̄ = 5.50 − 0.233 × 82.13 = −13.66 ŷ(90) = −13.66 + 0.233 × 90 = 7.3 runs

Fitted line: ŷ = −13.66 + 0.233 × temp. Each +1°F is worth about a quarter of a run.

Phase 4 of 4

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

So what do you tell them?

7 · The forecast says next season averages 10°F warmer. Best estimate of the extra runs per game?

extra runs

Δŷ = β̂₁ × 10 = 0.233 × 10 = 2.33 runs

A 10°F warmer season is worth roughly 2.3 extra runs per game, on average.

8 · Would you trust the model's prediction for a 105°F game?

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