Proportion of Prize Money for Ford in NASCAR Winston Cup Races 19942000 Methodology SLP Ferrari and F CribariNeto 2004 Beta Regression for Modelling Rates and Proportions Journal of Applied Statistics ID: 464471
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Slide1
Beta Regression
Proportion of Prize Money for Ford in NASCAR Winston Cup Races – 1994-2000
Methodology: S.L.P. Ferrari and F.
Cribari-Neto
(2004). “Beta Regression for Modelling Rates and Proportions,”
Journal of Applied Statistics
, Vol. 31, #7, pp. 799-815.
Data:
L. Winner (2006). “NASCAR Winston Cup Race Results for 1975-2003,”
Journal of Statistics Education,
Vol.14,#3, www.amstat.org/publications/jse/v14n3/datasets.winner.htmlSlide2
Data Description
Units: 267 Winston Cup Races for Years 1992-2000
Response: Proportion of Prize Money Won by Ford Cars
Predictor Variables:
Proportion of all Cars that are Fords for the race
Track LENGTH (Miles)
Track Turn BANK (Degrees)
Number of LAPS
Year Dummy Variables (Year1993-Year2000)
Distribution: Beta (Scaled for responses between 0 and 1)
Link Function: Logit: log(
m
/(1-
m
))=
b
0
+
b
1
X
1
+…+
b
P
X
pSlide3Slide4Slide5
Beta Distribution – Likelihood FunctionSlide6
Beta Distribution – Logit LinkSlide7
Beta Distribution – Logit LinkSlide8
Beta Distribution – Logit LinkSlide9
Beta Distribution – Logit LinkSlide10
Variance-Covariance Matrix & Starting Values Slide11
First 6 Races & Preliminary OLS RegressionSlide12
Iterative Results for
qSlide13
Diagnostic MeasuresSlide14
Influence MeasuresSlide15Slide16Slide17Slide18Slide19
R Program
### Fisher Scoring Method
ford <- read.csv("http
://www.stat.ufl.edu/~winner/data/nas_ford_1992_2000a.csv
",header=T)
attach(ford); names(ford)
library(
betareg
)
Year <- factor(Year)
Track_id
<- factor(
Track_id
)
beta.mod1 <-
betareg
(
FPrzp
~
FDrvp
+
TrkLng
+ Bank + Laps + Year)
summary(beta.mod1)
resid
(beta.mod1,type="
pearson
")
resid
(beta.mod1,type="deviance")
cooks.distance
(beta.mod1)
gleverage
(beta.mod1)
hatvalues
(beta.mod1)
par(
mfrow
=c(2,2))
plot(beta.mod1,which=1:4,type="
pearson
")