baseball <- read.csv("baseball.csv")
str(baseball)'data.frame': 1232 obs. of 15 variables:
$ Team : chr "ARI" "ATL" "BAL" "BOS" ...
$ League : chr "NL" "NL" "AL" "AL" ...
$ Year : int 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 ...
$ RS : int 734 700 712 734 613 748 669 667 758 726 ...
$ RA : int 688 600 705 806 759 676 588 845 890 670 ...
$ W : int 81 94 93 69 61 85 97 68 64 88 ...
$ OBP : num 0.328 0.32 0.311 0.315 0.302 0.318 0.315 0.324 0.33 0.335 ...
$ SLG : num 0.418 0.389 0.417 0.415 0.378 0.422 0.411 0.381 0.436 0.422 ...
$ BA : num 0.259 0.247 0.247 0.26 0.24 0.255 0.251 0.251 0.274 0.268 ...
$ Playoffs : int 0 1 1 0 0 0 1 0 0 1 ...
$ RankSeason : int NA 4 5 NA NA NA 2 NA NA 6 ...
$ RankPlayoffs: int NA 5 4 NA NA NA 4 NA NA 2 ...
$ G : int 162 162 162 162 162 162 162 162 162 162 ...
$ OOBP : num 0.317 0.306 0.315 0.331 0.335 0.319 0.305 0.336 0.357 0.314 ...
$ OSLG : num 0.415 0.378 0.403 0.428 0.424 0.405 0.39 0.43 0.47 0.402 ...summary(baseball) Team League Year RS RA W OBP SLG BA Playoffs
Length :1232 Length :1232 Min. :1962 Min. : 463.0 Min. : 472.0 Min. : 40.0 Min. :0.2770 Min. :0.3010 Min. :0.2140 Min. :0.0000
N.unique : 39 N.unique : 2 1st Qu.:1977 1st Qu.: 652.0 1st Qu.: 649.8 1st Qu.: 73.0 1st Qu.:0.3170 1st Qu.:0.3750 1st Qu.:0.2510 1st Qu.:0.0000
N.blank : 0 N.blank : 0 Median :1989 Median : 711.0 Median : 709.0 Median : 81.0 Median :0.3260 Median :0.3960 Median :0.2600 Median :0.0000
Min.nchar: 3 Min.nchar: 2 Mean :1989 Mean : 715.1 Mean : 715.1 Mean : 80.9 Mean :0.3263 Mean :0.3973 Mean :0.2593 Mean :0.1981
Max.nchar: 3 Max.nchar: 2 3rd Qu.:2002 3rd Qu.: 775.0 3rd Qu.: 774.2 3rd Qu.: 89.0 3rd Qu.:0.3370 3rd Qu.:0.4210 3rd Qu.:0.2680 3rd Qu.:0.0000
Max. :2012 Max. :1009.0 Max. :1103.0 Max. :116.0 Max. :0.3730 Max. :0.4910 Max. :0.2940 Max. :1.0000
RankSeason RankPlayoffs G OOBP OSLG
Min. :1.000 Min. :1.000 Min. :158.0 Min. :0.2940 Min. :0.3460
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:162.0 1st Qu.:0.3210 1st Qu.:0.4010
Median :3.000 Median :3.000 Median :162.0 Median :0.3310 Median :0.4190
Mean :3.123 Mean :2.717 Mean :161.9 Mean :0.3323 Mean :0.4197
3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:162.0 3rd Qu.:0.3430 3rd Qu.:0.4380
Max. :8.000 Max. :5.000 Max. :165.0 Max. :0.3840 Max. :0.4990
NAs :988 NAs :988 NAs :812 NAs :812 #Keep only playoff teams
baseball <- subset(baseball, Playoffs == 1)
nrow(baseball)[1] 244#number of playoff teams each year
PlayoffTable <- table(baseball$Year)
PlayoffTable
1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1973 1974 1975 1976 1977 1978 1979 1980 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1996 1997 1998 1999 2000
2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 8 8 8 8
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
8 8 8 8 8 8 8 8 8 8 8 10 #NumCompetitors variable
baseball$NumCompetitors <- PlayoffTable[as.character(baseball$Year)]table(baseball$NumCompetitors)
2 4 8 10
14 92 128 10 #WorldSeries variable
baseball$WorldSeries <- as.numeric(baseball$RankPlayoffs == 1)
table(baseball$WorldSeries)
0 1
197 47 variables <- c(
"Year",
"RS",
"RA",
"W",
"OBP",
"SLG",
"BA",
"RankSeason",
"OOBP",
"OSLG",
"NumCompetitors",
"League"
)
for(v in variables){
formula <- as.formula(
paste("WorldSeries ~", v)
)
model <- glm(formula,
data = baseball,
family = "binomial")
cat("\n=====================\n")
cat("Predictor:", v, "\n")
print(summary(model))
}
=====================
Predictor: Year
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 72.23602 22.64409 3.19 0.00142 **
Year -0.03700 0.01138 -3.25 0.00115 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 228.35 on 242 degrees of freedom
AIC: 232.35
Number of Fisher Scoring iterations: 4
=====================
Predictor: RS
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.661226 1.636494 0.404 0.686
RS -0.002681 0.002098 -1.278 0.201
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 237.45 on 242 degrees of freedom
AIC: 241.45
Number of Fisher Scoring iterations: 4
=====================
Predictor: RA
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.888174 1.483831 1.272 0.2032
RA -0.005053 0.002273 -2.223 0.0262 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 233.88 on 242 degrees of freedom
AIC: 237.88
Number of Fisher Scoring iterations: 4
=====================
Predictor: W
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.85568 2.87620 -2.384 0.0171 *
W 0.05671 0.02988 1.898 0.0577 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 235.51 on 242 degrees of freedom
AIC: 239.51
Number of Fisher Scoring iterations: 4
=====================
Predictor: OBP
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.741 3.989 0.687 0.492
OBP -12.402 11.865 -1.045 0.296
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 238.02 on 242 degrees of freedom
AIC: 242.02
Number of Fisher Scoring iterations: 4
=====================
Predictor: SLG
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.200 2.358 1.357 0.1748
SLG -11.130 5.689 -1.956 0.0504 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 235.23 on 242 degrees of freedom
AIC: 239.23
Number of Fisher Scoring iterations: 4
=====================
Predictor: BA
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.6392 3.8988 -0.164 0.870
BA -2.9765 14.6123 -0.204 0.839
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 239.08 on 242 degrees of freedom
AIC: 243.08
Number of Fisher Scoring iterations: 4
=====================
Predictor: RankSeason
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.8256 0.3268 -2.527 0.0115 *
RankSeason -0.2069 0.1027 -2.016 0.0438 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 234.75 on 242 degrees of freedom
AIC: 238.75
Number of Fisher Scoring iterations: 4
=====================
Predictor: OOBP
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.9306 8.3728 -0.111 0.912
OOBP -3.2233 26.0587 -0.124 0.902
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 84.926 on 113 degrees of freedom
Residual deviance: 84.910 on 112 degrees of freedom
(130 observations deleted due to missingness)
AIC: 88.91
Number of Fisher Scoring iterations: 4
=====================
Predictor: OSLG
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.08725 6.07285 -0.014 0.989
OSLG -4.65992 15.06881 -0.309 0.757
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 84.926 on 113 degrees of freedom
Residual deviance: 84.830 on 112 degrees of freedom
(130 observations deleted due to missingness)
AIC: 88.83
Number of Fisher Scoring iterations: 4
=====================
Predictor: NumCompetitors
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.03868 0.43750 0.088 0.929559
NumCompetitors -0.25220 0.07422 -3.398 0.000678 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 226.96 on 242 degrees of freedom
AIC: 230.96
Number of Fisher Scoring iterations: 4
=====================
Predictor: League
Call:
glm(formula = formula, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.3558 0.2243 -6.045 1.5e-09 ***
LeagueNL -0.1583 0.3252 -0.487 0.626
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 238.88 on 242 degrees of freedom
AIC: 242.88
Number of Fisher Scoring iterations: 4#Build the multivariate model
LogModel <- glm(
WorldSeries ~ Year + RA + RankSeason + NumCompetitors,
data = baseball,
family = "binomial"
)
summary(LogModel)
Call:
glm(formula = WorldSeries ~ Year + RA + RankSeason + NumCompetitors,
family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 12.5874376 53.6474210 0.235 0.814
Year -0.0061425 0.0274665 -0.224 0.823
RA -0.0008238 0.0027391 -0.301 0.764
RankSeason -0.0685046 0.1203459 -0.569 0.569
NumCompetitors -0.1794264 0.1815933 -0.988 0.323
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 226.37 on 239 degrees of freedom
AIC: 236.37
Number of Fisher Scoring iterations: 4#Correlation matrix
cor(
baseball[c("Year",
"RA",
"RankSeason",
"NumCompetitors")]
) Year RA RankSeason NumCompetitors
Year 1.0000000 0.4762422 0.3852191 0.9139548
RA 0.4762422 1.0000000 0.3991413 0.5136769
RankSeason 0.3852191 0.3991413 1.0000000 0.4247393
NumCompetitors 0.9139548 0.5136769 0.4247393 1.0000000#Two-variable models
model13 <- glm(WorldSeries ~ Year + RA,
data=baseball,
family="binomial")
model14 <- glm(WorldSeries ~ Year + RankSeason,
data=baseball,
family="binomial")
model15 <- glm(WorldSeries ~ Year + NumCompetitors,
data=baseball,
family="binomial")
model16 <- glm(WorldSeries ~ RA + RankSeason,
data=baseball,
family="binomial")
model17 <- glm(WorldSeries ~ RA + NumCompetitors,
data=baseball,
family="binomial")
model18 <- glm(WorldSeries ~ RankSeason + NumCompetitors,
data=baseball,
family="binomial")summary(model13)
Call:
glm(formula = WorldSeries ~ Year + RA, family = "binomial", data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 63.610741 25.654830 2.479 0.0132 *
Year -0.032084 0.013323 -2.408 0.0160 *
RA -0.001766 0.002585 -0.683 0.4945
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 227.88 on 241 degrees of freedom
AIC: 233.88
Number of Fisher Scoring iterations: 4summary(model14)
Call:
glm(formula = WorldSeries ~ Year + RankSeason, family = "binomial",
data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 63.64855 24.37063 2.612 0.00901 **
Year -0.03254 0.01231 -2.643 0.00822 **
RankSeason -0.10064 0.11352 -0.887 0.37534
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 227.55 on 241 degrees of freedom
AIC: 233.55
Number of Fisher Scoring iterations: 4summary(model15)
Call:
glm(formula = WorldSeries ~ Year + NumCompetitors, family = "binomial",
data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 13.350467 53.481896 0.250 0.803
Year -0.006802 0.027328 -0.249 0.803
NumCompetitors -0.212610 0.175520 -1.211 0.226
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 226.90 on 241 degrees of freedom
AIC: 232.9
Number of Fisher Scoring iterations: 4summary(model16)
Call:
glm(formula = WorldSeries ~ RA + RankSeason, family = "binomial",
data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.487461 1.506143 0.988 0.323
RA -0.003815 0.002441 -1.563 0.118
RankSeason -0.140824 0.110908 -1.270 0.204
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 232.22 on 241 degrees of freedom
AIC: 238.22
Number of Fisher Scoring iterations: 4summary(model17)
Call:
glm(formula = WorldSeries ~ RA + NumCompetitors, family = "binomial",
data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.716895 1.528736 0.469 0.63911
RA -0.001233 0.002661 -0.463 0.64313
NumCompetitors -0.229385 0.088399 -2.595 0.00946 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 226.74 on 241 degrees of freedom
AIC: 232.74
Number of Fisher Scoring iterations: 4summary(model18)
Call:
glm(formula = WorldSeries ~ RankSeason + NumCompetitors, family = "binomial",
data = baseball)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.12277 0.45737 0.268 0.78837
RankSeason -0.07697 0.11711 -0.657 0.51102
NumCompetitors -0.22784 0.08201 -2.778 0.00546 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 239.12 on 243 degrees of freedom
Residual deviance: 226.52 on 241 degrees of freedom
AIC: 232.52
Number of Fisher Scoring iterations: 4