Simple Linear Regression NFL Point Spreads – 2007.
-
Upload
laura-alexander -
Category
Documents
-
view
223 -
download
1
Transcript of Simple Linear Regression NFL Point Spreads – 2007.
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
1 and 0 average),(on accurate are oddsmakers If
n)(Assumptio 0,NID~
Predictedin Increaseper Unit Difference Actualmean in Change
)em"'Pick (" 0 Difference Predicted when Difference ActualMean
Team) Home - Team(Away Difference Predicted
Team) Home - Team(Away Difference Actual
:where
10
2
1
0
10
X
Y
XY
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
Testing normality of errors (I)
2,...,3
221
22
582633.3682633.5752461.1293762.0042981.0
706056.2434685.4071190.2147981.0221157.0
:a"-Weights" eapproximatObtain
1 and :c"-Weights"Obtain
25.0
375.0 :nobservatioeach for scores NormalObtain
... :ErrorsOrder
1993) Royston, (see 5)(n Method Francia-Shapiro
~~
1
~
2
~~
1
~
2
1
~2~
2
1
~2~
1
2~
543211
~
5432~
1
2~
~
1~
)()1()2()1(
nim
a
aaaa
aa
mmm
uuuuuca
uuuuuca
nu
m
mc
n
im
eeee
ii
nn
nn
nn
n
i
i
nn
nn
n
j
j
i
i
i
nn
Testing normality of errors (Ii)
'value-
)ln(
2))ln(ln(26758.00308.1
,)ln())ln(ln(0521.12725.1
),'1ln()'( :where
)'(' : wherestatistic,- Za toConverted
' :StatisticTest
ddistributenormally not are Errors :H
ddistributenormally are Errors :H
1
2
)(
2
1)(
~
A
0
ZZPP
nn
nn
WWg
WgZ
ee
ea
W n
ii
n
iii
Example – NFL Spread errors
0.866367'value-
0.475945)ln(
2))ln(ln(26758.00308.1
,-5.30441)ln())ln(ln(0521.12725.1
,-5.83241)'1ln()'( :where
-1.10938)'(
' : wherestatistic,- Za toConverted
0.997069 46705.23
46568.34 ' :StatisticTest
ddistributenormally not are Errors :H
ddistributenormally are Errors :H
1
2
)(
2
1)(
~
A
0
ZZPP
nn
nn
WWg
WgZ
ee
ea
W n
ii
n
iii
Testing accuracy in mean
• H0:
• HA: ≠and/or≠
• Fit Model UnDer H0: Y*=X
• Obtain error sum of squares under Y*• Compare with error sum of squares from
full model (HA).
Testing for Accuracy
1,0 that hypothesis null reject thenot Do
7359.0307.0 :value-P
307.0183.879
385.56
25446705.23
2)46705.2346818(
)2()(
2)()( :StatisticTest
46818)( :)(H Model Reduced
46705.23)(1.0778-0.2023 :)(H Model Full
10
254,2
2
1
^^
A
2
1
^^
A
FP
nFSSE
FSSERSSEF
YYRSSEXY
YYFSSEXY
obs
n
i
R
iii
R
i
n
i
F
iii
F
i