Simple Linear Regression

NFL Point Spreads – 2007

Background

• Las Vegas Bookmakers provide a point spread for each game

• The spread reflects how many points the home team “gets” from the visiting team (negative values mean the home team “gives” points to visitor)

• If bookmakers are accurate, on average the actual difference should equal prediction

• Accurate ? How variable ?

Statistical model

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Summary Statistics / Regression Equation

Mean Std Dev

Spread -2.72 6.23

Actual -1.69 15.37

Regression StatisticsMultiple R 0.4803R Square 0.2307Adjusted R Square 0.2277Standard Error 13.5602Observations 256

ANOVAdf SS MS F P-value

Regression 1 14008.25 14008.25 76.18 0.0000Residual 254 46705.23 183.88Total 255 60713.48

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Intercept -0.2023 0.9008 -0.2245 0.8225 -1.9763 1.5718Open Spread (HT) 1.0778 0.1235 8.7282 0.0000 0.8346 1.3209

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Testing accuracy in mean

• H0:

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• Fit Model UnDer H0: Y*=X

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full model (HA).

Testing for Accuracy

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