Data 621 Homework 1: Code Appendix
Jeff Nieman, Scott Karr, James Topor, Armenoush Aslanian-Persico
Part 1. Data Exploration
library(alr3)
library(car)
library(corrplot)
library(fBasics)
library(knitr)
library(MASS)library(psych)
library(car)
library(corrplot)Load and explore original data
mb_train <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/moneyball-training-data.csv")
describe(mb_train)## vars n mean sd median trimmed mad min
## INDEX 1 2276 1268.46 736.35 1270.5 1268.57 952.57 1
## TARGET_WINS 2 2276 80.79 15.75 82.0 81.31 14.83 0
## TEAM_BATTING_H 3 2276 1469.27 144.59 1454.0 1459.04 114.16 891
## TEAM_BATTING_2B 4 2276 241.25 46.80 238.0 240.40 47.44 69
## TEAM_BATTING_3B 5 2276 55.25 27.94 47.0 52.18 23.72 0
## TEAM_BATTING_HR 6 2276 99.61 60.55 102.0 97.39 78.58 0
## TEAM_BATTING_BB 7 2276 501.56 122.67 512.0 512.18 94.89 0
## TEAM_BATTING_SO 8 2174 735.61 248.53 750.0 742.31 284.66 0
## TEAM_BASERUN_SB 9 2145 124.76 87.79 101.0 110.81 60.79 0
## TEAM_BASERUN_CS 10 1504 52.80 22.96 49.0 50.36 17.79 0
## TEAM_BATTING_HBP 11 191 59.36 12.97 58.0 58.86 11.86 29
## TEAM_PITCHING_H 12 2276 1779.21 1406.84 1518.0 1555.90 174.95 1137
## TEAM_PITCHING_HR 13 2276 105.70 61.30 107.0 103.16 74.13 0
## TEAM_PITCHING_BB 14 2276 553.01 166.36 536.5 542.62 98.59 0
## TEAM_PITCHING_SO 15 2174 817.73 553.09 813.5 796.93 257.23 0
## TEAM_FIELDING_E 16 2276 246.48 227.77 159.0 193.44 62.27 65
## TEAM_FIELDING_DP 17 1990 146.39 26.23 149.0 147.58 23.72 52
## max range skew kurtosis se
## INDEX 2535 2534 0.00 -1.22 15.43
## TARGET_WINS 146 146 -0.40 1.03 0.33
## TEAM_BATTING_H 2554 1663 1.57 7.28 3.03
## TEAM_BATTING_2B 458 389 0.22 0.01 0.98
## TEAM_BATTING_3B 223 223 1.11 1.50 0.59
## TEAM_BATTING_HR 264 264 0.19 -0.96 1.27
## TEAM_BATTING_BB 878 878 -1.03 2.18 2.57
## TEAM_BATTING_SO 1399 1399 -0.30 -0.32 5.33
## TEAM_BASERUN_SB 697 697 1.97 5.49 1.90
## TEAM_BASERUN_CS 201 201 1.98 7.62 0.59
## TEAM_BATTING_HBP 95 66 0.32 -0.11 0.94
## TEAM_PITCHING_H 30132 28995 10.33 141.84 29.49
## TEAM_PITCHING_HR 343 343 0.29 -0.60 1.28
## TEAM_PITCHING_BB 3645 3645 6.74 96.97 3.49
## TEAM_PITCHING_SO 19278 19278 22.17 671.19 11.86
## TEAM_FIELDING_E 1898 1833 2.99 10.97 4.77
## TEAM_FIELDING_DP 228 176 -0.39 0.18 0.59boxplot(mb_train, xlab="Boxplot Predictor Comparitive") 
Look for correlations among values
## INDEX TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B
## INDEX 1.00000000 -0.04895047 -0.09493748 -0.01841285
## TARGET_WINS -0.04895047 1.00000000 0.46994665 0.31298400
## TEAM_BATTING_H -0.09493748 0.46994665 1.00000000 0.56177286
## TEAM_BATTING_2B -0.01841285 0.31298400 0.56177286 1.00000000
## TEAM_BATTING_3B -0.04639454 -0.12434586 0.21391883 0.04203441
## TEAM_BATTING_HR -0.09532668 0.42241683 0.39627593 0.25099045
## TEAM_BATTING_BB 0.04702541 0.46868793 0.19735234 0.19749256
## TEAM_BATTING_SO 0.04132959 -0.22889273 -0.34174328 -0.06415123
## TEAM_BASERUN_SB -0.03159666 0.01483639 0.07167495 -0.18768279
## TEAM_BASERUN_CS -0.07692325 -0.17875598 -0.09377545 -0.20413884
## TEAM_BATTING_HBP 0.07719303 0.07350424 -0.02911218 0.04608475
## TEAM_PITCHING_H -0.08865725 0.47123431 0.99919269 0.56045355
## TEAM_PITCHING_HR -0.09361594 0.42246683 0.39495630 0.24999875
## TEAM_PITCHING_BB 0.04958287 0.46839882 0.19529071 0.19592157
## TEAM_PITCHING_SO 0.04466127 -0.22936481 -0.34445001 -0.06616615
## TEAM_FIELDING_E -0.02004841 -0.38668800 -0.25381638 -0.19427027
## TEAM_FIELDING_DP 0.13168916 -0.19586601 0.01776946 -0.02488808
## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## INDEX -0.04639454 -0.09532668 0.04702541
## TARGET_WINS -0.12434586 0.42241683 0.46868793
## TEAM_BATTING_H 0.21391883 0.39627593 0.19735234
## TEAM_BATTING_2B 0.04203441 0.25099045 0.19749256
## TEAM_BATTING_3B 1.00000000 -0.21879927 -0.20584392
## TEAM_BATTING_HR -0.21879927 1.00000000 0.45638161
## TEAM_BATTING_BB -0.20584392 0.45638161 1.00000000
## TEAM_BATTING_SO -0.19291841 0.21045444 0.21833871
## TEAM_BASERUN_SB 0.16946086 -0.19021893 -0.08806123
## TEAM_BASERUN_CS 0.23213978 -0.27579838 -0.20878051
## TEAM_BATTING_HBP -0.17424715 0.10618116 0.04746007
## TEAM_PITCHING_H 0.21250322 0.39549390 0.19848687
## TEAM_PITCHING_HR -0.21973263 0.99993259 0.45659283
## TEAM_PITCHING_BB -0.20675383 0.45542468 0.99988140
## TEAM_PITCHING_SO -0.19386654 0.20829574 0.21793253
## TEAM_FIELDING_E -0.06513145 0.01567397 -0.07847126
## TEAM_FIELDING_DP 0.13314758 -0.06182222 -0.07929078
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS
## INDEX 0.04132959 -0.03159666 -0.076923249
## TARGET_WINS -0.22889273 0.01483639 -0.178755979
## TEAM_BATTING_H -0.34174328 0.07167495 -0.093775445
## TEAM_BATTING_2B -0.06415123 -0.18768279 -0.204138837
## TEAM_BATTING_3B -0.19291841 0.16946086 0.232139777
## TEAM_BATTING_HR 0.21045444 -0.19021893 -0.275798375
## TEAM_BATTING_BB 0.21833871 -0.08806123 -0.208780510
## TEAM_BATTING_SO 1.00000000 -0.07475974 -0.056130355
## TEAM_BASERUN_SB -0.07475974 1.00000000 0.624737808
## TEAM_BASERUN_CS -0.05613035 0.62473781 1.000000000
## TEAM_BATTING_HBP 0.22094219 -0.06400498 -0.070513896
## TEAM_PITCHING_H -0.34145321 0.07395373 -0.092977893
## TEAM_PITCHING_HR 0.21111617 -0.18948057 -0.275471495
## TEAM_PITCHING_BB 0.21895783 -0.08741902 -0.208470154
## TEAM_PITCHING_SO 0.99976835 -0.07351325 -0.055308336
## TEAM_FIELDING_E 0.30814540 0.04292341 0.207701189
## TEAM_FIELDING_DP -0.12319072 -0.13023054 -0.006764233
## TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## INDEX 0.07719303 -0.08865725 -0.09361594
## TARGET_WINS 0.07350424 0.47123431 0.42246683
## TEAM_BATTING_H -0.02911218 0.99919269 0.39495630
## TEAM_BATTING_2B 0.04608475 0.56045355 0.24999875
## TEAM_BATTING_3B -0.17424715 0.21250322 -0.21973263
## TEAM_BATTING_HR 0.10618116 0.39549390 0.99993259
## TEAM_BATTING_BB 0.04746007 0.19848687 0.45659283
## TEAM_BATTING_SO 0.22094219 -0.34145321 0.21111617
## TEAM_BASERUN_SB -0.06400498 0.07395373 -0.18948057
## TEAM_BASERUN_CS -0.07051390 -0.09297789 -0.27547150
## TEAM_BATTING_HBP 1.00000000 -0.02769699 0.10675878
## TEAM_PITCHING_H -0.02769699 1.00000000 0.39463199
## TEAM_PITCHING_HR 0.10675878 0.39463199 1.00000000
## TEAM_PITCHING_BB 0.04785137 0.19703302 0.45580983
## TEAM_PITCHING_SO 0.22157375 -0.34330646 0.20920115
## TEAM_FIELDING_E 0.04178971 -0.25073028 0.01689330
## TEAM_FIELDING_DP -0.07120824 0.01416807 -0.06292475
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E
## INDEX 0.04958287 0.04466127 -0.02004841
## TARGET_WINS 0.46839882 -0.22936481 -0.38668800
## TEAM_BATTING_H 0.19529071 -0.34445001 -0.25381638
## TEAM_BATTING_2B 0.19592157 -0.06616615 -0.19427027
## TEAM_BATTING_3B -0.20675383 -0.19386654 -0.06513145
## TEAM_BATTING_HR 0.45542468 0.20829574 0.01567397
## TEAM_BATTING_BB 0.99988140 0.21793253 -0.07847126
## TEAM_BATTING_SO 0.21895783 0.99976835 0.30814540
## TEAM_BASERUN_SB -0.08741902 -0.07351325 0.04292341
## TEAM_BASERUN_CS -0.20847015 -0.05530834 0.20770119
## TEAM_BATTING_HBP 0.04785137 0.22157375 0.04178971
## TEAM_PITCHING_H 0.19703302 -0.34330646 -0.25073028
## TEAM_PITCHING_HR 0.45580983 0.20920115 0.01689330
## TEAM_PITCHING_BB 1.00000000 0.21887700 -0.07692315
## TEAM_PITCHING_SO 0.21887700 1.00000000 0.31008407
## TEAM_FIELDING_E -0.07692315 0.31008407 1.00000000
## TEAM_FIELDING_DP -0.08040645 -0.12492321 0.04020581
## TEAM_FIELDING_DP
## INDEX 0.131689160
## TARGET_WINS -0.195866006
## TEAM_BATTING_H 0.017769456
## TEAM_BATTING_2B -0.024888081
## TEAM_BATTING_3B 0.133147578
## TEAM_BATTING_HR -0.061822219
## TEAM_BATTING_BB -0.079290775
## TEAM_BATTING_SO -0.123190715
## TEAM_BASERUN_SB -0.130230537
## TEAM_BASERUN_CS -0.006764233
## TEAM_BATTING_HBP -0.071208241
## TEAM_PITCHING_H 0.014168073
## TEAM_PITCHING_HR -0.062924751
## TEAM_PITCHING_BB -0.080406452
## TEAM_PITCHING_SO -0.124923213
## TEAM_FIELDING_E 0.040205814
## TEAM_FIELDING_DP 1.000000000Part 2. Data Preparation
New Variable Creation
Creating a new column for batting singles and eliminating hits for batting
mb_e <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/moneyball-training-data.csv")
#eliminate index column
mb_e1 <- mb_e[,-1]
#add singles column for hitting
mb_e1$TEAM_BATTING_1B <- as.numeric(mb_e1$TEAM_BATTING_H-mb_e1$TEAM_BATTING_2B-mb_e1$TEAM_BATTING_3B-mb_e1$TEAM_BATTING_HR)
mb_e1 <- mb_e1[,-2]
mb_e1 <- as.data.frame(mb_e1)Building a regression model and filling in NA’s for SB.
Note: This approach is suggested in LMAR p. 201. “A more sophisticated alternative to mean imputation is to use regression methods to predict the missing values of the covariates.”
SB <- lm(data=mb_e1, TEAM_BASERUN_SB~.)
summary(SB)
#eliminate CS as there are no blank SB's with a value for CS + eliminate pitching, wins and fielding variables
SB1 <- lm(data=mb_e1, TEAM_BASERUN_SB~TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB)
summary(SB1)
#eliminate singles
SB2 <- lm(data=mb_e1, TEAM_BASERUN_SB~TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB)
summary(SB2)
#fill in NA for SB
mb_e2 <- mb_e1
mb_e2$TEAM_BASERUN_SB[is.na(mb_e2$TEAM_BASERUN_SB)]<-round(79.36805-0.19419*mb_e2$TEAM_BATTING_2B+1.41686*mb_e2$TEAM_BATTING_3B-0.24513*mb_e2$TEAM_BATTING_HR+0.08060*mb_e2$TEAM_BATTING_BB)Building a linear regression model and filling in NA’s for CS
CS <- lm(data=mb_e2, TEAM_BASERUN_CS~.)
summary(CS)
#eliminate wins, pitching and fielding
CS1 <- lm(data=mb_e2, TEAM_BASERUN_CS~TEAM_BASERUN_SB +TEAM_BATTING_1B +TEAM_BATTING_2B + TEAM_BATTING_3B +TEAM_BATTING_BB + TEAM_BATTING_HR)
summary(CS1)
#eliminate walks
CS2 <- lm(data=mb_e2, TEAM_BASERUN_CS~TEAM_BASERUN_SB +TEAM_BATTING_2B + TEAM_BATTING_3B +TEAM_BATTING_1B + TEAM_BATTING_HR)
summary(CS2)
#fill in NA for CS
mb_e3 <- mb_e2
mb_e3$TEAM_BASERUN_CS[is.na(mb_e3$TEAM_BASERUN_CS)]<-round(49.356793+0.322543*mb_e3$TEAM_BASERUN_SB-0.044486*mb_e3$TEAM_BATTING_2B+0.281124*mb_e3$TEAM_BATTING_3B-0.10797*mb_e3$TEAM_BATTING_HR-0.014034*mb_e3$TEAM_BATTING_1B)Building a regression model and filling in NA’s for batting SO’s
BSO <- lm(data=mb_e3, TEAM_BATTING_SO~.)
summary(BSO)
#eliminate fielding and wins and baserunning and HBP and pitching SO's as it contains similar blanks
BSO1 <- lm(data=mb_e3, TEAM_BATTING_SO~TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_PITCHING_H + TEAM_PITCHING_BB + TEAM_PITCHING_HR)
summary(BSO1)
#eliminate pitching HR's
BSO2 <- lm(data=mb_e3, TEAM_BATTING_SO~TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_BB + TEAM_PITCHING_H + TEAM_PITCHING_BB + TEAM_BATTING_HR)
summary(BSO2)
#fill in NA for batting SO
mb_e4 <- mb_e3
mb_e4$TEAM_BATTING_SO[is.na(mb_e4$TEAM_BATTING_SO)]<-round(1605-0.8434*mb_e4$TEAM_BATTING_1B+0.2832*mb_e4$TEAM_BATTING_2B-1.348*mb_e4$TEAM_BATTING_3B-0.3493*mb_e4$TEAM_BATTING_BB-0.02903*mb_e4$TEAM_PITCHING_H+0.1657*mb_e4$TEAM_PITCHING_BB+1.703*mb_e$TEAM_BATTING_HR)Building a regression model and filling in NA’s for pitching SO’s
PSO <- lm(data=mb_e4, TEAM_PITCHING_SO~.)
summary(PSO)
#eliminate wins, fielding, baserunning and HBP
PSO1 <- lm(data=mb_e4, TEAM_PITCHING_SO~TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_PITCHING_H + TEAM_BATTING_SO + TEAM_PITCHING_BB + TEAM_PITCHING_HR)
summary(PSO1)
#eliminate batting 3B's
PSO2 <- lm(data=mb_e4, TEAM_PITCHING_SO~TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_PITCHING_H + TEAM_BATTING_SO + TEAM_PITCHING_BB + TEAM_PITCHING_HR)
summary(PSO2)
#replace NA with values for pitching SO
mb_e5 <- mb_e4
mb_e5$TEAM_PITCHING_SO[is.na(mb_e5$TEAM_PITCHING_SO)]<-round(4422.87422-0.46455*mb_e5$TEAM_BATTING_1B + 0.72823*mb_e5$TEAM_BATTING_2B +8.06941*mb_e5$TEAM_BATTING_HR -3.45005*mb_e5$TEAM_BATTING_BB-0.01815*mb_e5$TEAM_PITCHING_H+1.20501*mb_e5$TEAM_BATTING_SO+3.03598*mb_e5$TEAM_PITCHING_BB-8.40807*mb_e$TEAM_PITCHING_HR)Building a linear regression and filling in NA’s for DP
#build a regression model for DP's
DP <- lm(data=mb_e5, TEAM_FIELDING_DP~.)
summary(DP)
#eliminate wins, hitting, HBP
DP1 <- lm(data=mb_e5, TEAM_FIELDING_DP~ TEAM_BASERUN_SB+TEAM_BASERUN_CS+TEAM_PITCHING_H+TEAM_PITCHING_HR+TEAM_PITCHING_BB+TEAM_PITCHING_SO+TEAM_FIELDING_E)
summary(DP1)
#eliminate pitching hits allowed
DP2 <- lm(data=mb_e5, TEAM_FIELDING_DP~ TEAM_BASERUN_SB+TEAM_BASERUN_CS+TEAM_PITCHING_HR+TEAM_PITCHING_BB+TEAM_PITCHING_SO+TEAM_FIELDING_E)
summary(DP2)
#eliminate CS as it makes no sense
DP3 <- lm(data=mb_e5, TEAM_FIELDING_DP~ TEAM_BASERUN_SB+TEAM_PITCHING_HR+TEAM_PITCHING_BB+TEAM_PITCHING_SO+TEAM_FIELDING_E)
summary(DP3)
#replace NA with values for DP
mb_e6 <- mb_e5
mb_e6$TEAM_FIELDING_DP[is.na(mb_e6$TEAM_FIELDING_DP)]<- round(158.8-0.1235*mb_e6$TEAM_BASERUN_SB +0.03320*mb_e6$TEAM_PITCHING_HR+0.02815*mb_e6$TEAM_PITCHING_BB - 0.006109*mb_e6$TEAM_PITCHING_SO - 0.06573*mb_e6$TEAM_FIELDING_E)
summary(mb_e6)
#only NA's left are HBPData Imputation
# read EVALUATION data set
eval_data <- read.csv("https://raw.githubusercontent.com/jtopor/CUNY-MSDA-621/master/HW-1/moneyball-evaluation-data.csv")
# read training data set
mb_e <- read.csv("https://raw.githubusercontent.com/jtopor/CUNY-MSDA-621/master/HW-1/moneyball-training-data.csv")
#eliminate index column
# mb_e1 <- mb_e[,-1]
mb_e1 <- mb_e
#####Creating a new column for batting singles and eliminating hits for batting
#add singles column for hitting
mb_e1$TEAM_BATTING_1B <- as.numeric(mb_e1$TEAM_BATTING_H-mb_e1$TEAM_BATTING_2B-mb_e1$TEAM_BATTING_3B-mb_e1$TEAM_BATTING_HR)
mb_e1 <- mb_e1[,-3]
mb_e1 <- as.data.frame(mb_e1)
eval_data$TEAM_BATTING_1B <- as.numeric(eval_data$TEAM_BATTING_H - eval_data$TEAM_BATTING_2B - eval_data$TEAM_BATTING_3B - eval_data$TEAM_BATTING_HR)
# HITS is in second column in eval data
eval_data <- eval_data[,-2]
# ADD A DUMMY COLUMN TO EVAL DATA FOR TARGET WINS
eval_data$TARGET_WINS <- 0Eliminate HBP, CS, and pitching HR’s.
mb <- mb_e1[,-c(9,10,12)]
# summary(mb)
eval_data <- eval_data[,-c(8,9,11)]
# summary(eval_data)Build model for batting SO using Gelman approach
#take out double plays + pitching SO + SB as data set is incomplete + Wins as they are not present in the evaluation data
BSO.1 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB -TARGET_WINS)
summary(BSO.1)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -367.76 -82.46 -3.12 76.44 401.62
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1978.17499 44.47257 44.481 < 2e-16 ***
## TEAM_BATTING_2B -0.17459 0.17430 -1.002 0.316646
## TEAM_BATTING_3B -2.29879 0.24381 -9.429 < 2e-16 ***
## TEAM_BATTING_HR 0.88912 0.18212 4.882 1.14e-06 ***
## TEAM_BATTING_BB 0.98359 0.43292 2.272 0.023203 *
## TEAM_PITCHING_H 0.36442 0.15123 2.410 0.016066 *
## TEAM_PITCHING_BB -1.17748 0.41011 -2.871 0.004137 **
## TEAM_FIELDING_E -0.29146 0.07594 -3.838 0.000128 ***
## TEAM_BATTING_1B -1.45473 0.16446 -8.845 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.1 on 1826 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7248, Adjusted R-squared: 0.7236
## F-statistic: 601.1 on 8 and 1826 DF, p-value: < 2.2e-16#eliminate doubles
BSO.2 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B)
summary(BSO.2)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -366.77 -82.05 -2.74 76.89 399.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1975.11400 44.36750 44.517 < 2e-16 ***
## TEAM_BATTING_3B -2.17815 0.21199 -10.275 < 2e-16 ***
## TEAM_BATTING_HR 1.02471 0.12183 8.411 < 2e-16 ***
## TEAM_BATTING_BB 0.59635 0.19483 3.061 0.002240 **
## TEAM_PITCHING_H 0.22723 0.06414 3.543 0.000406 ***
## TEAM_PITCHING_BB -0.81040 0.18409 -4.402 1.13e-05 ***
## TEAM_FIELDING_E -0.26762 0.07212 -3.711 0.000213 ***
## TEAM_BATTING_1B -1.31541 0.08777 -14.988 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.1 on 1827 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7246, Adjusted R-squared: 0.7236
## F-statistic: 686.8 on 7 and 1827 DF, p-value: < 2.2e-16vif(BSO.2)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_PITCHING_H
## 2.984944 6.215565 39.110249 17.594555
## TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_BATTING_1B
## 45.384546 2.448073 8.602393# vif says remove TEAM_PITCHING_BB
BSO.3 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B - TEAM_PITCHING_BB)
summary(BSO.3)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -385.33 -80.03 -1.99 77.48 399.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1980.01367 44.57596 44.419 < 2e-16 ***
## TEAM_BATTING_3B -1.79602 0.19437 -9.240 < 2e-16 ***
## TEAM_BATTING_HR 1.42972 0.08027 17.812 < 2e-16 ***
## TEAM_BATTING_BB -0.24810 0.03431 -7.230 7.06e-13 ***
## TEAM_PITCHING_H -0.03911 0.02139 -1.828 0.0677 .
## TEAM_FIELDING_E -0.29047 0.07229 -4.018 6.11e-05 ***
## TEAM_BATTING_1B -0.99171 0.04816 -20.591 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.6 on 1828 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7217, Adjusted R-squared: 0.7208
## F-statistic: 790.1 on 6 and 1828 DF, p-value: < 2.2e-16# pvals say remove PITCHING_H
BSO.4 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B - TEAM_PITCHING_BB - TEAM_PITCHING_H)
summary(BSO.4)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_PITCHING_BB - TEAM_PITCHING_H, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -384.09 -79.88 -1.51 77.07 393.44
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1986.07279 44.48099 44.650 < 2e-16 ***
## TEAM_BATTING_3B -1.86025 0.19129 -9.725 < 2e-16 ***
## TEAM_BATTING_HR 1.37824 0.07521 18.325 < 2e-16 ***
## TEAM_BATTING_BB -0.25047 0.03431 -7.300 4.28e-13 ***
## TEAM_FIELDING_E -0.29947 0.07217 -4.149 3.49e-05 ***
## TEAM_BATTING_1B -1.04331 0.03905 -26.719 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.7 on 1829 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7212, Adjusted R-squared: 0.7204
## F-statistic: 946.2 on 5 and 1829 DF, p-value: < 2.2e-16vif(BSO.4)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_FIELDING_E
## 2.403283 2.342414 1.199339 2.424099
## TEAM_BATTING_1B
## 1.683596##All p-values are low with a 686.8 F-statistic and adjusted R squared of 0.7236
#take a look
par(mfrow=c(2,2))
plot(BSO.2)
# ---------------------------------------
# function definition for impute function
impute <- function (a, a.impute){
ifelse (is.na(a), a.impute,a)
}
# ---------------------------------------
#prediction function
pred.BSO <- round(predict(BSO.4, mb))
BSO.imp <- impute(mb$TEAM_BATTING_SO, pred.BSO)
# impute the evaluation data
pred_eval.BSO <- round(predict(BSO.4, eval_data))
eval.BSO.imp <- impute(eval_data$TEAM_BATTING_SO, pred_eval.BSO)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb$TEAM_BATTING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 548.0 750.0 735.6 930.0 1399.0 102summary(BSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 543.8 730.0 727.6 925.0 1399.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb$TEAM_BATTING_SO, breaks = 200)
hist(BSO.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data$TEAM_BATTING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 545.0 686.0 709.3 912.0 1268.0 18summary(eval.BSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 532.5 677.0 699.8 904.5 1268.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data$TEAM_BATTING_SO, breaks = 30)
hist(eval.BSO.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb1 <- mb
mb1$TEAM_BATTING_SO <- BSO.imp
eval_data.1 <- eval_data
eval_data.1$TEAM_BATTING_SO <- eval.BSO.imp
Build model for Pitching SO
#take out double plays + SB as data set is incomplete and wins as they are not present in evaluation data
PSO.1 <- lm(data=mb1, TEAM_PITCHING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_BASERUN_SB - TARGET_WINS)
summary(PSO.1)##
## Call:
## lm(formula = TEAM_PITCHING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_BASERUN_SB - TARGET_WINS, data = mb1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -130.988 -3.674 1.299 4.675 147.753
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.693339 8.122849 0.085 0.932
## TEAM_BATTING_2B -0.291561 0.022062 -13.216 < 2e-16 ***
## TEAM_BATTING_3B -0.268622 0.031593 -8.503 < 2e-16 ***
## TEAM_BATTING_HR -0.269698 0.023194 -11.628 < 2e-16 ***
## TEAM_BATTING_BB -0.883985 0.054857 -16.114 < 2e-16 ***
## TEAM_BATTING_SO 1.044883 0.002961 352.860 < 2e-16 ***
## TEAM_PITCHING_H 0.270090 0.019167 14.092 < 2e-16 ***
## TEAM_PITCHING_BB 0.850575 0.052011 16.354 < 2e-16 ***
## TEAM_FIELDING_E -0.057521 0.009648 -5.962 2.99e-09 ***
## TEAM_BATTING_1B -0.280665 0.021251 -13.207 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.43 on 1825 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.9958, Adjusted R-squared: 0.9958
## F-statistic: 4.809e+04 on 9 and 1825 DF, p-value: < 2.2e-16vif(PSO.1)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 7.903547 4.140572 14.070952 193.640509
## TEAM_BATTING_SO TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_FIELDING_E
## 3.633459 98.139615 226.271134 2.736403
## TEAM_BATTING_1B
## 31.499003# vif says remove TEAM_PITCHING_BB
PSO.2 <- lm(data=mb1, TEAM_PITCHING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_BASERUN_SB - TARGET_WINS - TEAM_PITCHING_BB)
summary(PSO.2)##
## Call:
## lm(formula = TEAM_PITCHING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_BASERUN_SB - TARGET_WINS - TEAM_PITCHING_BB, data = mb1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -126.748 -4.347 1.094 5.334 149.232
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.722036 8.665285 1.353 0.1763
## TEAM_BATTING_2B -0.613714 0.010633 -57.719 <2e-16 ***
## TEAM_BATTING_3B -0.578732 0.027050 -21.395 <2e-16 ***
## TEAM_BATTING_HR -0.601828 0.011993 -50.181 <2e-16 ***
## TEAM_BATTING_BB 0.010252 0.004704 2.180 0.0294 *
## TEAM_BATTING_SO 1.041636 0.003163 329.346 <2e-16 ***
## TEAM_PITCHING_H 0.580032 0.003060 189.545 <2e-16 ***
## TEAM_FIELDING_E -0.097555 0.009990 -9.765 <2e-16 ***
## TEAM_BATTING_1B -0.610139 0.007239 -84.289 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.45 on 1826 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.9952, Adjusted R-squared: 0.9952
## F-statistic: 4.719e+04 on 8 and 1826 DF, p-value: < 2.2e-16vif(PSO.2)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 1.602077 2.648887 3.282938 1.242359
## TEAM_BATTING_SO TEAM_PITCHING_H TEAM_FIELDING_E TEAM_BATTING_1B
## 3.617130 2.183095 2.560245 3.189218#all low P value and F statistic of 4719 with adj R squared of 0.9952
#take a look
par(mfrow=c(2,2))
plot(PSO.2)
#place back in the data base with imputed data for SO's
pred.PSO <- round(predict(PSO.2, mb1))
PSO.imp <- impute(mb1$TEAM_PITCHING_SO, pred.PSO)
# impute the evaluation data
pred_eval.PSO <- round(predict(PSO.2, eval_data.1))
eval.PSO.imp <- impute(eval_data.1$TEAM_PITCHING_SO, pred_eval.PSO)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb1$TEAM_PITCHING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 615.0 813.5 817.7 968.0 19280.0 102summary(PSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 606.0 797.0 807.4 957.0 19280.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb1$TEAM_PITCHING_SO, breaks = 200)
hist(PSO.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.1$TEAM_PITCHING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 613.0 745.0 799.7 938.0 9963.0 18summary(eval.PSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 596.0 728.0 785.4 927.5 9963.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.1$TEAM_PITCHING_SO, breaks = 30)
hist(eval.PSO.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb2 <- mb1
mb2$TEAM_PITCHING_SO <- PSO.imp
eval_data.2 <- eval_data.1
eval_data.2$TEAM_PITCHING_SO <- eval.PSO.imp
Build model for SB
#Take out DP as incomplete data and target wins
SB.1 <- lm(data=mb2, TEAM_BASERUN_SB~. -INDEX -TEAM_FIELDING_DP - TARGET_WINS)
summary(SB.1)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -115.054 -32.496 -5.714 28.546 206.666
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -181.56290 25.61997 -7.087 1.92e-12 ***
## TEAM_BATTING_2B -0.21829 0.07305 -2.988 0.002841 **
## TEAM_BATTING_3B 0.31700 0.10053 3.153 0.001640 **
## TEAM_BATTING_HR -0.61700 0.07599 -8.119 8.27e-16 ***
## TEAM_BATTING_BB 0.12841 0.18355 0.700 0.484255
## TEAM_BATTING_SO 0.43941 0.07872 5.582 2.71e-08 ***
## TEAM_PITCHING_H 0.20258 0.06368 3.181 0.001489 **
## TEAM_PITCHING_BB -0.08197 0.17430 -0.470 0.638206
## TEAM_PITCHING_SO -0.25116 0.07480 -3.358 0.000801 ***
## TEAM_FIELDING_E 0.32079 0.02796 11.473 < 2e-16 ***
## TEAM_BATTING_1B -0.12224 0.07046 -1.735 0.082937 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.26 on 1926 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3552, Adjusted R-squared: 0.3518
## F-statistic: 106.1 on 10 and 1926 DF, p-value: < 2.2e-16#eliminate pitching BB's
SB.2 <- lm(data=mb2, TEAM_BASERUN_SB~. -INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS)
summary(SB.2)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -115.234 -32.317 -5.706 28.512 206.540
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -182.64502 25.51127 -7.159 1.15e-12 ***
## TEAM_BATTING_2B -0.19473 0.05316 -3.663 0.000256 ***
## TEAM_BATTING_3B 0.34027 0.08749 3.889 0.000104 ***
## TEAM_BATTING_HR -0.59236 0.05503 -10.765 < 2e-16 ***
## TEAM_BATTING_BB 0.04234 0.01376 3.076 0.002127 **
## TEAM_BATTING_SO 0.45256 0.07357 6.151 9.32e-10 ***
## TEAM_PITCHING_H 0.17992 0.04164 4.321 1.63e-05 ***
## TEAM_PITCHING_SO -0.26348 0.07004 -3.762 0.000174 ***
## TEAM_FIELDING_E 0.32263 0.02768 11.655 < 2e-16 ***
## TEAM_BATTING_1B -0.09787 0.04774 -2.050 0.040499 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.25 on 1927 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3551, Adjusted R-squared: 0.3521
## F-statistic: 117.9 on 9 and 1927 DF, p-value: < 2.2e-16#eliminate singles
SB.3 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB -TEAM_BATTING_1B - TARGET_WINS)
summary(SB.3)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TEAM_BATTING_1B - TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -113.836 -32.731 -5.467 28.523 205.971
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -201.72737 23.77215 -8.486 < 2e-16 ***
## TEAM_BATTING_2B -0.11845 0.03799 -3.118 0.00185 **
## TEAM_BATTING_3B 0.40962 0.08075 5.073 4.30e-07 ***
## TEAM_BATTING_HR -0.51178 0.03855 -13.277 < 2e-16 ***
## TEAM_BATTING_BB 0.04187 0.01377 3.040 0.00240 **
## TEAM_BATTING_SO 0.32253 0.03731 8.645 < 2e-16 ***
## TEAM_PITCHING_H 0.10155 0.01650 6.154 9.17e-10 ***
## TEAM_PITCHING_SO -0.13495 0.03125 -4.318 1.66e-05 ***
## TEAM_FIELDING_E 0.33595 0.02693 12.475 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.29 on 1928 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3537, Adjusted R-squared: 0.351
## F-statistic: 131.9 on 8 and 1928 DF, p-value: < 2.2e-16#simplify the model by taking out pitching
SB.4 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB -TEAM_BATTING_1B - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H)
summary(SB.4)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TEAM_BATTING_1B - TARGET_WINS - TEAM_PITCHING_SO -
## TEAM_PITCHING_H, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -117.914 -33.217 -5.623 29.822 199.657
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -83.147587 14.021226 -5.930 3.58e-09 ***
## TEAM_BATTING_2B 0.041592 0.028337 1.468 0.1423
## TEAM_BATTING_3B 0.572336 0.077093 7.424 1.70e-13 ***
## TEAM_BATTING_HR -0.405437 0.034672 -11.694 < 2e-16 ***
## TEAM_BATTING_BB 0.035111 0.013862 2.533 0.0114 *
## TEAM_BATTING_SO 0.151522 0.008054 18.814 < 2e-16 ***
## TEAM_FIELDING_E 0.360947 0.026930 13.403 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.77 on 1930 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3395, Adjusted R-squared: 0.3374
## F-statistic: 165.3 on 6 and 1930 DF, p-value: < 2.2e-16#add singles back in
SB.5 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H)
summary(SB.5)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H,
## data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.276 -33.011 -5.119 28.546 203.041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.872e+02 2.563e+01 -7.305 4.05e-13 ***
## TEAM_BATTING_2B -1.075e-03 2.952e-02 -0.036 0.97096
## TEAM_BATTING_3B 5.195e-01 7.742e-02 6.710 2.55e-11 ***
## TEAM_BATTING_HR -4.080e-01 3.448e-02 -11.834 < 2e-16 ***
## TEAM_BATTING_BB 3.995e-02 1.382e-02 2.891 0.00388 **
## TEAM_BATTING_SO 1.762e-01 9.496e-03 18.558 < 2e-16 ***
## TEAM_FIELDING_E 3.577e-01 2.678e-02 13.356 < 2e-16 ***
## TEAM_BATTING_1B 9.198e-02 1.901e-02 4.839 1.41e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.5 on 1929 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3474, Adjusted R-squared: 0.345
## F-statistic: 146.7 on 7 and 1929 DF, p-value: < 2.2e-16#eliminate doubles
SB.6 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H - TEAM_BATTING_2B)
summary(SB.6)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H -
## TEAM_BATTING_2B, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.233 -32.996 -5.134 28.584 203.038
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.872e+02 2.561e+01 -7.309 3.91e-13 ***
## TEAM_BATTING_3B 5.190e-01 7.610e-02 6.820 1.21e-11 ***
## TEAM_BATTING_HR -4.084e-01 3.261e-02 -12.522 < 2e-16 ***
## TEAM_BATTING_BB 3.991e-02 1.376e-02 2.900 0.00377 **
## TEAM_BATTING_SO 1.762e-01 9.475e-03 18.596 < 2e-16 ***
## TEAM_FIELDING_E 3.579e-01 2.624e-02 13.642 < 2e-16 ***
## TEAM_BATTING_1B 9.177e-02 1.813e-02 5.060 4.58e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.49 on 1930 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3474, Adjusted R-squared: 0.3454
## F-statistic: 171.2 on 6 and 1930 DF, p-value: < 2.2e-16#eliminate walks
SB.7 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H - TEAM_BATTING_2B - TEAM_BATTING_BB)
summary(SB.7)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H -
## TEAM_BATTING_2B - TEAM_BATTING_BB, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.972 -32.412 -5.034 29.206 206.559
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.609e+02 2.400e+01 -6.705 2.63e-11 ***
## TEAM_BATTING_3B 5.197e-01 7.624e-02 6.816 1.25e-11 ***
## TEAM_BATTING_HR -3.807e-01 3.124e-02 -12.185 < 2e-16 ***
## TEAM_BATTING_SO 1.715e-01 9.351e-03 18.336 < 2e-16 ***
## TEAM_FIELDING_E 3.453e-01 2.592e-02 13.320 < 2e-16 ***
## TEAM_BATTING_1B 8.923e-02 1.815e-02 4.917 9.54e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.58 on 1931 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3446, Adjusted R-squared: 0.3429
## F-statistic: 203 on 5 and 1931 DF, p-value: < 2.2e-16#all low P value and F statistic of 202.9 with adj R squared of 0.3427
#take a look
par(mfrow=c(2,2))
plot(SB.7)
#place back in the data base with imputed data for SB's
pred.SB <- round(predict(SB.7, mb2))
SB.imp <- impute(mb2$TEAM_BASERUN_SB, pred.SB)
# impute the evaluation data
pred_eval.SB <- round(predict(SB.7, eval_data.2))
eval.SB.imp <- impute(eval_data.2$TEAM_BASERUN_SB, pred_eval.SB)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb2$TEAM_BASERUN_SB)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 66.0 101.0 124.8 156.0 697.0 131summary(SB.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 67.0 106.0 137.8 172.0 697.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb2$TEAM_BASERUN_SB, breaks = 200)
hist(SB.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.2$TEAM_BASERUN_SB)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 59.0 92.0 123.7 151.8 580.0 13summary(eval.SB.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 60.5 96.0 134.9 164.5 580.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.2$TEAM_BASERUN_SB, breaks = 30)
hist(eval.SB.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb3 <- mb2
mb3$TEAM_BASERUN_SB <- SB.imp
eval_data.3 <- eval_data.2
eval_data.3$TEAM_BASERUN_SB <- eval.SB.imp
Build model to replace DP
#remove target wins
DP.1 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS)
summary(DP.1)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.685 -13.815 -0.923 13.056 64.642
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 119.570410 11.008885 10.861 < 2e-16 ***
## TEAM_BATTING_2B 0.015947 0.013100 1.217 0.22360
## TEAM_BATTING_3B -0.095545 0.031158 -3.066 0.00220 **
## TEAM_BATTING_HR 0.062465 0.016446 3.798 0.00015 ***
## TEAM_BATTING_BB 0.195238 0.027750 7.036 2.72e-12 ***
## TEAM_BATTING_SO -0.107809 0.015781 -6.831 1.12e-11 ***
## TEAM_BASERUN_SB -0.126130 0.009838 -12.820 < 2e-16 ***
## TEAM_PITCHING_H 0.009159 0.004069 2.251 0.02448 *
## TEAM_PITCHING_BB -0.153349 0.025468 -6.021 2.06e-09 ***
## TEAM_PITCHING_SO 0.090351 0.014318 6.310 3.43e-10 ***
## TEAM_FIELDING_E -0.068602 0.009653 -7.107 1.65e-12 ***
## TEAM_BATTING_1B 0.024316 0.010083 2.412 0.01598 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.05 on 1978 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4185, Adjusted R-squared: 0.4153
## F-statistic: 129.4 on 11 and 1978 DF, p-value: < 2.2e-16#remove batting 2B's
DP.2 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS - TEAM_BATTING_2B)
summary(DP.2)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.620 -14.051 -1.043 12.979 64.061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 120.547069 10.980952 10.978 < 2e-16 ***
## TEAM_BATTING_3B -0.087844 0.030513 -2.879 0.00403 **
## TEAM_BATTING_HR 0.065419 0.016268 4.021 6.00e-05 ***
## TEAM_BATTING_BB 0.200115 0.027463 7.287 4.56e-13 ***
## TEAM_BATTING_SO -0.107359 0.015779 -6.804 1.34e-11 ***
## TEAM_BASERUN_SB -0.126208 0.009839 -12.827 < 2e-16 ***
## TEAM_PITCHING_H 0.010913 0.003806 2.868 0.00418 **
## TEAM_PITCHING_BB -0.157287 0.025265 -6.226 5.84e-10 ***
## TEAM_PITCHING_SO 0.090027 0.014318 6.288 3.95e-10 ***
## TEAM_FIELDING_E -0.072227 0.009183 -7.865 6.01e-15 ***
## TEAM_BATTING_1B 0.024008 0.010081 2.381 0.01734 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.06 on 1979 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4181, Adjusted R-squared: 0.4152
## F-statistic: 142.2 on 10 and 1979 DF, p-value: < 2.2e-16# results show that EVERYTHING ELSE is statistically signficant, so:
# run vif to check for collinearity
vif(DP.2)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## 2.378033 4.489647 40.081217 61.937276
## TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_PITCHING_SO
## 2.207539 10.533005 33.459414 51.795257
## TEAM_FIELDING_E TEAM_BATTING_1B
## 6.392623 4.748132# results show TEAM_BATTING_SO should be removed
# remove TEAM_BATTING_SO
DP.3 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO)
summary(DP.3)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -70.858 -14.365 -0.308 13.180 68.663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.364168 10.931590 9.821 < 2e-16 ***
## TEAM_BATTING_3B -0.075566 0.030806 -2.453 0.01425 *
## TEAM_BATTING_HR 0.049820 0.016289 3.059 0.00225 **
## TEAM_BATTING_BB 0.059620 0.018312 3.256 0.00115 **
## TEAM_BASERUN_SB -0.135254 0.009860 -13.717 < 2e-16 ***
## TEAM_PITCHING_H 0.016359 0.003763 4.348 1.45e-05 ***
## TEAM_PITCHING_BB -0.022297 0.015820 -1.409 0.15887
## TEAM_PITCHING_SO -0.003527 0.004037 -0.874 0.38244
## TEAM_FIELDING_E -0.057520 0.009027 -6.372 2.31e-10 ***
## TEAM_BATTING_1B 0.020596 0.010183 2.023 0.04326 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.28 on 1980 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4045, Adjusted R-squared: 0.4018
## F-statistic: 149.4 on 9 and 1980 DF, p-value: < 2.2e-16# p-value says remove TEAM_PITCHING_SO;
# remove TEAM_PITCHING_SO
DP.4 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TEAM_BATTING_2B -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO)
summary(DP.4)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TEAM_BATTING_2B -
## TARGET_WINS - TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.801 -14.399 -0.536 13.355 68.091
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 100.469748 7.563815 13.283 < 2e-16 ***
## TEAM_BATTING_3B -0.067701 0.029459 -2.298 0.021658 *
## TEAM_BATTING_HR 0.045067 0.015352 2.936 0.003368 **
## TEAM_BATTING_BB 0.063875 0.017651 3.619 0.000303 ***
## TEAM_BASERUN_SB -0.138490 0.009137 -15.157 < 2e-16 ***
## TEAM_PITCHING_H 0.015675 0.003680 4.259 2.15e-05 ***
## TEAM_PITCHING_BB -0.025444 0.015403 -1.652 0.098711 .
## TEAM_FIELDING_E -0.055612 0.008758 -6.350 2.66e-10 ***
## TEAM_BATTING_1B 0.025138 0.008755 2.871 0.004134 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.28 on 1981 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4043, Adjusted R-squared: 0.4018
## F-statistic: 168 on 8 and 1981 DF, p-value: < 2.2e-16vif(DP.4)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.167319 3.909442 16.189150 1.861261
## TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_BATTING_1B
## 9.630593 12.159984 5.684878 3.501740# P values and vif both indicate remove TEAM_PITCHING_BB
# remove TEAM_PITCHING_BB
DP.5 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(DP.5)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.547 -14.352 -0.402 13.240 66.253
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 98.606000 7.482458 13.178 < 2e-16 ***
## TEAM_BATTING_3B -0.071477 0.029383 -2.433 0.0151 *
## TEAM_BATTING_HR 0.057086 0.013524 4.221 2.54e-05 ***
## TEAM_BATTING_BB 0.036352 0.005830 6.235 5.51e-10 ***
## TEAM_BASERUN_SB -0.138165 0.009139 -15.118 < 2e-16 ***
## TEAM_PITCHING_H 0.011078 0.002409 4.598 4.53e-06 ***
## TEAM_FIELDING_E -0.051135 0.008332 -6.137 1.01e-09 ***
## TEAM_BATTING_1B 0.032220 0.007637 4.219 2.57e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.29 on 1982 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4034, Adjusted R-squared: 0.4013
## F-statistic: 191.5 on 7 and 1982 DF, p-value: < 2.2e-16vif(DP.5)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.154275 3.031272 1.764845 1.860396
## TEAM_PITCHING_H TEAM_FIELDING_E TEAM_BATTING_1B
## 4.123897 5.140583 2.662224# vif says remove TEAM_FIELDING_E; p-values all < .05 so remove TEAM_FIELDING_E
DP.6 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E)
summary(DP.6)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.558 -14.399 -0.152 13.362 64.018
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 86.427823 7.280960 11.870 < 2e-16 ***
## TEAM_BATTING_3B -0.093997 0.029422 -3.195 0.00142 **
## TEAM_BATTING_HR 0.091627 0.012411 7.383 2.27e-13 ***
## TEAM_BATTING_BB 0.045730 0.005678 8.053 1.38e-15 ***
## TEAM_BASERUN_SB -0.155983 0.008745 -17.836 < 2e-16 ***
## TEAM_PITCHING_H 0.001250 0.001817 0.688 0.49148
## TEAM_BATTING_1B 0.044340 0.007446 5.955 3.07e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.48 on 1983 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.3921, Adjusted R-squared: 0.3903
## F-statistic: 213.2 on 6 and 1983 DF, p-value: < 2.2e-16vif(DP.6)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.120678 2.506351 1.643620 1.672663
## TEAM_PITCHING_H TEAM_BATTING_1B
## 2.301907 2.484225# now no collinearity but p-values say remove TEAM_PITCHING_H
DP.7 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E - TEAM_PITCHING_H)
summary(DP.7)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E -
## TEAM_PITCHING_H, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.58 -14.41 -0.19 13.38 63.83
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 85.333602 7.104233 12.012 < 2e-16 ***
## TEAM_BATTING_3B -0.094593 0.029405 -3.217 0.00132 **
## TEAM_BATTING_HR 0.094530 0.011670 8.100 9.47e-16 ***
## TEAM_BATTING_BB 0.044401 0.005339 8.316 < 2e-16 ***
## TEAM_BASERUN_SB -0.153554 0.008000 -19.194 < 2e-16 ***
## TEAM_BATTING_1B 0.047370 0.006003 7.892 4.88e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.48 on 1984 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.3919, Adjusted R-squared: 0.3904
## F-statistic: 255.8 on 5 and 1984 DF, p-value: < 2.2e-16vif(DP.7)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.118844 2.216648 1.453424 1.400175
## TEAM_BATTING_1B
## 1.615010# no collinearity, all p-values < .05 so stop
#all low P value and F statistic of 255.8 with adj R squared of 0.3904
#take a look
par(mfrow=c(2,2))
plot(DP.7)
#place back in the data base with imputed data for SB's
# NOTE: Changed DP.4 to DP.7 here
pred.DP <- round(predict(DP.7, mb3))
DP.imp <- impute(mb3$TEAM_FIELDING_DP, pred.DP)
# impute the evaluation data
pred_eval.DP <- round(predict(DP.7, eval_data.3))
eval.DP.imp <- impute(eval_data.3$TEAM_FIELDING_DP, pred_eval.DP)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb3$TEAM_FIELDING_DP)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 52.0 131.0 149.0 146.4 164.0 228.0 286summary(DP.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 48.0 124.0 145.0 141.5 162.0 228.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb3$TEAM_FIELDING_DP, breaks = 200)
hist(DP.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.3$TEAM_FIELDING_DP)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 69.0 131.0 148.0 146.1 164.0 204.0 31summary(eval.DP.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 52.0 123.5 146.0 141.3 160.5 204.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.3$TEAM_FIELDING_DP, breaks = 30)
hist(eval.DP.imp, breaks = 30)
###################################################
# update data frames with imputed values
mb4 <- mb3
mb4$TEAM_FIELDING_DP <- DP.imp
eval_data.4 <- eval_data.3
eval_data.4$TEAM_FIELDING_DP <- eval.DP.imp
Eliminate unhistorical outliers - DO THIS FOR THE EVAL DATA AS WELL
# check rowcount before removal of outliers
nrow(mb4)## [1] 2276nrow(eval_data.4)## [1] 259############## TEAM PITCHING_SO ############################
#most pitching SO's is 1450. So delete all records with more than 1450 pitching SO's
mb5 <- mb4
# fixed error in this line: dataframe in 'which' call was mb1 so changed to mb5
mb5 <- mb5[which(mb5$TEAM_PITCHING_SO < 1450),]
eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_PITCHING_SO < 1450),]
# check rowcount
nrow(mb5)## [1] 2251nrow(eval_data.4)## [1] 257############ TEAM_PITCHING_H ##############################
#most ever hits by a team is 1730. So delete all pitching hits >3000 to be conservative with the median
mb6 <- mb5
mb6 <- mb6[which(mb6$TEAM_PITCHING_H < 3001),]
eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_PITCHING_H < 3001),]
# check rowcount
nrow(mb6)## [1] 2174nrow(eval_data.4)## [1] 249############ TEAM_FIELDING_E ##############################
#most ever errors by a team is 639 by 1883 Philadelphia. Prorating to 162 games gives a value of 1046.
mb7 <- mb6
mb7 <- mb7[which(mb7$TEAM_FIELDING_E < 1047),]
eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_FIELDING_E < 1047),]
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# check rowcount: result is 2172 => removed total of 104 rows
nrow(mb7)## [1] 2172nrow(eval_data.4)## [1] 248dim(mb)-dim(mb7)## [1] 104 0#we removed 104 rows total due to outliers in TRAINING data set.
# we removed 11 rows from the EVALUATION data set
# now renumber rows of dataframe so that there are no gaps in row numbers
rownames(mb7) <- 1:nrow(mb7)
rownames(eval_data.4) <- 1:nrow(eval_data.4)
# drop INDEX column from training set
# mb7 <- mb7[,-1]
# now drop dummy column from evaluation data
# eval_data.4 <- eval_data.4[,-14]
# create CSV files containing updated data sets
#SMK commented out for now-doesn't work on a mac
#write.csv(mb7, file = "C:/SQLData/621-HW1-Clean-Data.csv", row.names = FALSE, col.names = TRUE)
#write.csv(eval_data.4, file = "C:/SQLData/621-HW1-Clean-EvalData-.csv", row.names = FALSE, col.names = TRUE)Part 3. Build Models
Model 1: General Model Using Backward Selection
library(car)
mb_clean <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/621-HW1-Clean-Data.csv") Build Models
Model using all remaining variables as a starting point
Yields r^2= 0.3347, Adj r^2 = 0.3322, F = 136
# keep the clean data set pure
mb <- mb_clean
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.179 -7.684 0.193 7.338 63.241
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.966514 5.630361 8.697 < 2e-16 ***
## TEAM_BATTING_2B -0.042963 0.009058 -4.743 2.24e-06 ***
## TEAM_BATTING_3B 0.119709 0.017111 6.996 3.50e-12 ***
## TEAM_BATTING_HR 0.076628 0.010255 7.473 1.14e-13 ***
## TEAM_BATTING_BB 0.179272 0.016504 10.863 < 2e-16 ***
## TEAM_BATTING_SO -0.047387 0.011793 -4.018 6.06e-05 ***
## TEAM_BASERUN_SB 0.067351 0.004963 13.570 < 2e-16 ***
## TEAM_PITCHING_H 0.038622 0.004966 7.778 1.13e-14 ***
## TEAM_PITCHING_BB -0.139535 0.014311 -9.750 < 2e-16 ***
## TEAM_PITCHING_SO 0.029867 0.011011 2.712 0.00673 **
## TEAM_FIELDING_E -0.076068 0.003894 -19.535 < 2e-16 ***
## TEAM_FIELDING_DP -0.118907 0.013074 -9.095 < 2e-16 ***
## TEAM_BATTING_1B -0.011641 0.006975 -1.669 0.09526 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.62 on 2159 degrees of freedom
## Multiple R-squared: 0.3658, Adjusted R-squared: 0.3623
## F-statistic: 103.8 on 12 and 2159 DF, p-value: < 2.2e-16# p-value indicates remove TEAM_BATTING_1B
# --------------------
# remove TEAM_BATTING_1B
model.2 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.306 -7.736 0.089 7.278 61.942
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 43.726614 4.675707 9.352 < 2e-16 ***
## TEAM_BATTING_2B -0.037030 0.008334 -4.443 9.32e-06 ***
## TEAM_BATTING_3B 0.123030 0.017002 7.236 6.37e-13 ***
## TEAM_BATTING_HR 0.084581 0.009084 9.311 < 2e-16 ***
## TEAM_BATTING_BB 0.175496 0.016355 10.731 < 2e-16 ***
## TEAM_BATTING_SO -0.057558 0.010100 -5.699 1.37e-08 ***
## TEAM_BASERUN_SB 0.066640 0.004947 13.471 < 2e-16 ***
## TEAM_PITCHING_H 0.032020 0.003003 10.663 < 2e-16 ***
## TEAM_PITCHING_BB -0.136552 0.014205 -9.613 < 2e-16 ***
## TEAM_PITCHING_SO 0.040806 0.008851 4.610 4.26e-06 ***
## TEAM_FIELDING_E -0.074297 0.003748 -19.823 < 2e-16 ***
## TEAM_FIELDING_DP -0.120293 0.013053 -9.216 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.62 on 2160 degrees of freedom
## Multiple R-squared: 0.365, Adjusted R-squared: 0.3618
## F-statistic: 112.9 on 11 and 2160 DF, p-value: < 2.2e-16# p-values are OK so check collinearity
vif(model.2)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.319929 3.359689 4.643042 43.103947
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 83.755735 3.378362 9.471591 37.110476
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 62.742239 4.973211 2.082577# vif says remove TEAM_BATTING_SO or PITCHING_SO, so remove PITCHING_SO per other models
# -------------------
#eliminate TEAM_PITCHING_SO
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.949 -7.717 0.285 7.601 63.510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.652404 4.565554 8.466 < 2e-16 ***
## TEAM_BATTING_2B -0.042295 0.008294 -5.099 3.71e-07 ***
## TEAM_BATTING_3B 0.107468 0.016741 6.419 1.68e-10 ***
## TEAM_BATTING_HR 0.077621 0.009000 8.625 < 2e-16 ***
## TEAM_BATTING_BB 0.123390 0.011876 10.390 < 2e-16 ***
## TEAM_BATTING_SO -0.012083 0.002182 -5.538 3.43e-08 ***
## TEAM_BASERUN_SB 0.061650 0.004850 12.713 < 2e-16 ***
## TEAM_PITCHING_H 0.036828 0.002829 13.017 < 2e-16 ***
## TEAM_PITCHING_BB -0.090392 0.010123 -8.929 < 2e-16 ***
## TEAM_FIELDING_E -0.071010 0.003697 -19.208 < 2e-16 ***
## TEAM_FIELDING_DP -0.119234 0.013112 -9.093 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.67 on 2161 degrees of freedom
## Multiple R-squared: 0.3588, Adjusted R-squared: 0.3558
## F-statistic: 120.9 on 10 and 2161 DF, p-value: < 2.2e-16vif(model.3)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.276374 3.227243 4.514804 22.517049
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 3.871698 3.216671 8.329160 18.672715
## TEAM_FIELDING_E TEAM_FIELDING_DP
## 4.793258 2.081932# vif says remove TEAM_BATTING_BB or PITCHINNG_BB so go with PITCHING_BB
# -------------------
#eliminate TEAM_PITCHING_BB
model.4 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.780 -8.035 0.320 7.776 69.832
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 62.579012 3.763135 16.629 < 2e-16 ***
## TEAM_BATTING_2B -0.008694 0.007525 -1.155 0.248
## TEAM_BATTING_3B 0.134601 0.016760 8.031 1.57e-15 ***
## TEAM_BATTING_HR 0.103304 0.008681 11.899 < 2e-16 ***
## TEAM_BATTING_BB 0.020938 0.003117 6.716 2.37e-11 ***
## TEAM_BATTING_SO -0.016911 0.002152 -7.859 6.07e-15 ***
## TEAM_BASERUN_SB 0.063121 0.004934 12.793 < 2e-16 ***
## TEAM_PITCHING_H 0.016891 0.001769 9.549 < 2e-16 ***
## TEAM_FIELDING_E -0.069910 0.003761 -18.586 < 2e-16 ***
## TEAM_FIELDING_DP -0.108598 0.013294 -8.169 5.22e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.89 on 2162 degrees of freedom
## Multiple R-squared: 0.3351, Adjusted R-squared: 0.3323
## F-statistic: 121.1 on 9 and 2162 DF, p-value: < 2.2e-16# --------------------
# eliminate TEAM_BATTING_2B
model.5 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_BATTING_2B)
summary(model.5)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB - TEAM_BATTING_2B, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.412 -8.089 0.329 7.776 68.696
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 62.392894 3.759976 16.594 < 2e-16 ***
## TEAM_BATTING_3B 0.132616 0.016673 7.954 2.89e-15 ***
## TEAM_BATTING_HR 0.101500 0.008541 11.884 < 2e-16 ***
## TEAM_BATTING_BB 0.020574 0.003102 6.633 4.14e-11 ***
## TEAM_BATTING_SO -0.017105 0.002145 -7.973 2.49e-15 ***
## TEAM_BASERUN_SB 0.063188 0.004934 12.806 < 2e-16 ***
## TEAM_PITCHING_H 0.015911 0.001553 10.248 < 2e-16 ***
## TEAM_FIELDING_E -0.068573 0.003579 -19.158 < 2e-16 ***
## TEAM_FIELDING_DP -0.108871 0.013293 -8.190 4.40e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.89 on 2163 degrees of freedom
## Multiple R-squared: 0.3347, Adjusted R-squared: 0.3322
## F-statistic: 136 on 8 and 2163 DF, p-value: < 2.2e-16# p-values < .05 so check for collinearity
vif(model.5)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## 3.088083 3.922549 1.481720 3.611668
## TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E TEAM_FIELDING_DP
## 3.212525 2.419816 4.334892 2.064098# no colinearity so STOP HEREDIAGNOSTICS
Plots are linear except for errors
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.5, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Lack of constant variability in Resid vs. Fitted. Normal QQ shows a bit of skew in upper right end but not drastic; Residuals appear to be within 2 std devs. Outliers at 1920, 1737, 393, 1515
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.5)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for several variables: 3B, HR, SB, Pitch_H, Fielding_E, BATT_BB, BATT_SO, FIELDING_DP
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.5)
par(mfrow=c(2,2))
plot(mb$TEAM_BATTING_3B, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_HR, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_PITCHING_H, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship whose slope might be skewed by outliers in upper right of plot
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.5$fitted.values
# nrow(fit1)
par(mfrow = c(1,1))
plot(fit1, mb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb$TARGET_WINS),lty=2)
Now cleanup data objects that are no longer required
rm(model, model.2, model.3, model.4)REMOVE OUTLIERS AND REFIT
Per Cooks Distance, remove items 1920, 1737, 393, 1515
############ FIRST SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem <- mb_clean[-c(1920, 1737, 393, 1515),]
# renumber rows
rownames(mb_rem) <- 1:nrow(mb_rem)Now refit first model from above: all variables
Yields r^2= 0.3504, Adj r^2 = 0.348, F = 145.6
# keep the clean data set pure
mb <- mb_rem
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.312 -7.606 0.169 7.370 45.974
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.702659 5.533457 9.524 < 2e-16 ***
## TEAM_BATTING_2B -0.048364 0.008899 -5.435 6.10e-08 ***
## TEAM_BATTING_3B 0.131471 0.016835 7.809 8.91e-15 ***
## TEAM_BATTING_HR 0.077797 0.010045 7.745 1.46e-14 ***
## TEAM_BATTING_BB 0.184502 0.016217 11.377 < 2e-16 ***
## TEAM_BATTING_SO -0.049773 0.011616 -4.285 1.91e-05 ***
## TEAM_BASERUN_SB 0.069365 0.004863 14.265 < 2e-16 ***
## TEAM_PITCHING_H 0.039055 0.004879 8.005 1.94e-15 ***
## TEAM_PITCHING_BB -0.144207 0.014074 -10.246 < 2e-16 ***
## TEAM_PITCHING_SO 0.031063 0.010855 2.862 0.00425 **
## TEAM_FIELDING_E -0.081383 0.003851 -21.135 < 2e-16 ***
## TEAM_FIELDING_DP -0.119896 0.012795 -9.370 < 2e-16 ***
## TEAM_BATTING_1B -0.013777 0.006856 -2.010 0.04460 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.37 on 2155 degrees of freedom
## Multiple R-squared: 0.3839, Adjusted R-squared: 0.3805
## F-statistic: 111.9 on 12 and 2155 DF, p-value: < 2.2e-16vif(model)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.753180 3.434748 5.922306 44.068099
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 115.662896 3.377840 25.603370 37.973500
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 98.479804 5.337711 2.083157 8.252408# vif indicates remove TEAM_PITCHING_SO
# --------------------
# remove TEAM_PITCHING_SO
model.2 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.494 -7.559 0.328 7.446 45.527
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.515612 5.454519 10.178 < 2e-16 ***
## TEAM_BATTING_2B -0.056967 0.008389 -6.790 1.44e-11 ***
## TEAM_BATTING_3B 0.120478 0.016419 7.338 3.06e-13 ***
## TEAM_BATTING_HR 0.066476 0.009248 7.188 9.02e-13 ***
## TEAM_BATTING_BB 0.162650 0.014330 11.350 < 2e-16 ***
## TEAM_BATTING_SO -0.017208 0.002335 -7.368 2.45e-13 ***
## TEAM_BASERUN_SB 0.067604 0.004831 13.992 < 2e-16 ***
## TEAM_PITCHING_H 0.048059 0.003735 12.866 < 2e-16 ***
## TEAM_PITCHING_BB -0.124471 0.012289 -10.129 < 2e-16 ***
## TEAM_FIELDING_E -0.081495 0.003857 -21.130 < 2e-16 ***
## TEAM_FIELDING_DP -0.117961 0.012798 -9.217 < 2e-16 ***
## TEAM_BATTING_1B -0.025520 0.005501 -4.639 3.71e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.39 on 2156 degrees of freedom
## Multiple R-squared: 0.3816, Adjusted R-squared: 0.3784
## F-statistic: 120.9 on 11 and 2156 DF, p-value: < 2.2e-16# p-values are OK so check collinearity
vif(model.2)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.438954 3.255919 5.003748 34.297363
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 4.659832 3.323768 14.956756 28.854387
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 5.337159 2.077336 5.295547# vif says remove TEAM_PITCHING_BB
# -------------------
#eliminate TEAM_PITCHING_BB
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.824 -7.989 0.294 7.673 42.263
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.243821 5.574685 10.448 < 2e-16 ***
## TEAM_BATTING_2B -0.014168 0.007416 -1.910 0.0562 .
## TEAM_BATTING_3B 0.142709 0.016650 8.571 < 2e-16 ***
## TEAM_BATTING_HR 0.106734 0.008545 12.491 < 2e-16 ***
## TEAM_BATTING_BB 0.020695 0.003061 6.762 1.75e-11 ***
## TEAM_BATTING_SO -0.015795 0.002386 -6.621 4.49e-11 ***
## TEAM_BASERUN_SB 0.063058 0.004923 12.810 < 2e-16 ***
## TEAM_PITCHING_H 0.015173 0.001890 8.028 1.61e-15 ***
## TEAM_FIELDING_E -0.072930 0.003851 -18.940 < 2e-16 ***
## TEAM_FIELDING_DP -0.111549 0.013080 -8.528 < 2e-16 ***
## TEAM_BATTING_1B 0.007382 0.004543 1.625 0.1043
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.65 on 2157 degrees of freedom
## Multiple R-squared: 0.3522, Adjusted R-squared: 0.3492
## F-statistic: 117.3 on 10 and 2157 DF, p-value: < 2.2e-16# p-values say remove TEAM_BATTING_1B
# -------------------
#eliminate TEAM_BATTING_1B
model.4 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_1B - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.166 -7.970 0.318 7.689 41.838
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 65.022700 3.699490 17.576 < 2e-16 ***
## TEAM_BATTING_2B -0.013481 0.007407 -1.820 0.0689 .
## TEAM_BATTING_3B 0.146314 0.016508 8.863 < 2e-16 ***
## TEAM_BATTING_HR 0.105677 0.008524 12.398 < 2e-16 ***
## TEAM_BATTING_BB 0.020919 0.003059 6.839 1.03e-11 ***
## TEAM_BATTING_SO -0.017600 0.002112 -8.334 < 2e-16 ***
## TEAM_BASERUN_SB 0.064519 0.004842 13.326 < 2e-16 ***
## TEAM_PITCHING_H 0.016390 0.001736 9.443 < 2e-16 ***
## TEAM_FIELDING_E -0.074524 0.003725 -20.007 < 2e-16 ***
## TEAM_FIELDING_DP -0.109715 0.013037 -8.416 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.66 on 2158 degrees of freedom
## Multiple R-squared: 0.3514, Adjusted R-squared: 0.3487
## F-statistic: 129.9 on 9 and 2158 DF, p-value: < 2.2e-16vif(model.4)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 1.814319 3.140953 4.055967 1.491080
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E
## 3.636171 3.185297 3.081945 4.750943
## TEAM_FIELDING_DP
## 2.056837# pvals say remove TEAM_BATTING_2B
model.5 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_BATTING_2B - TEAM_BATTING_1B - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.5)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_BATTING_2B - TEAM_BATTING_1B -
## TEAM_PITCHING_SO - TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.605 -8.030 0.317 7.757 42.164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.703618 3.697313 17.500 < 2e-16 ***
## TEAM_BATTING_3B 0.143076 0.016420 8.713 < 2e-16 ***
## TEAM_BATTING_HR 0.102858 0.008386 12.265 < 2e-16 ***
## TEAM_BATTING_BB 0.020349 0.003044 6.684 2.94e-11 ***
## TEAM_BATTING_SO -0.017890 0.002107 -8.491 < 2e-16 ***
## TEAM_BASERUN_SB 0.064609 0.004844 13.338 < 2e-16 ***
## TEAM_PITCHING_H 0.014888 0.001528 9.745 < 2e-16 ***
## TEAM_FIELDING_E -0.072407 0.003541 -20.450 < 2e-16 ***
## TEAM_FIELDING_DP -0.110117 0.013042 -8.443 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.66 on 2159 degrees of freedom
## Multiple R-squared: 0.3504, Adjusted R-squared: 0.348
## F-statistic: 145.6 on 8 and 2159 DF, p-value: < 2.2e-16vif(model.5)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## 3.104460 3.922081 1.475492 3.615480
## TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E TEAM_FIELDING_DP
## 3.184962 2.384787 4.287809 2.056247# vif and pvals OK so stopSUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Lack of constant variability in Resid vs. Fitted. Normal QQ shows a bit of skew in upper right end but not drastic; Residuals appear to be within 2 std devs. Might not be a good model.
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.4)
Plots show outliers so remove them and re-fit
Per Cooks Distance, remove items 1931, 391, 820, 1933, 835, 2124
############ FIRST SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem2 <- mb[-c(1931, 391, 820, 1933, 835, 2124),]
# renumber rows
rownames(mb_rem2) <- 1:nrow(mb_rem2)Model using all remaining variables as a starting point
Yields r^2= 0.3598, Adj r^2 = 0.3572, F = 134.4
# keep the clean data set pure
mb <- mb_rem2
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX )
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.835 -7.607 0.200 7.360 45.489
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 53.581847 5.491812 9.757 < 2e-16 ***
## TEAM_BATTING_2B -0.051601 0.008852 -5.829 6.40e-09 ***
## TEAM_BATTING_3B 0.131444 0.016694 7.874 5.42e-15 ***
## TEAM_BATTING_HR 0.080041 0.009950 8.044 1.42e-15 ***
## TEAM_BATTING_BB 0.171434 0.016181 10.595 < 2e-16 ***
## TEAM_BATTING_SO -0.042020 0.011568 -3.633 0.000287 ***
## TEAM_BASERUN_SB 0.068541 0.004809 14.252 < 2e-16 ***
## TEAM_PITCHING_H 0.039065 0.004831 8.086 1.02e-15 ***
## TEAM_PITCHING_BB -0.132140 0.014071 -9.391 < 2e-16 ***
## TEAM_PITCHING_SO 0.023143 0.010823 2.138 0.032608 *
## TEAM_FIELDING_E -0.080763 0.003829 -21.093 < 2e-16 ***
## TEAM_FIELDING_DP -0.118407 0.012650 -9.360 < 2e-16 ***
## TEAM_BATTING_1B -0.013730 0.006805 -2.018 0.043761 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.24 on 2149 degrees of freedom
## Multiple R-squared: 0.3885, Adjusted R-squared: 0.3851
## F-statistic: 113.8 on 12 and 2149 DF, p-value: < 2.2e-16# p-values all < .05 so check collinearity
vif(model)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.747597 3.421239 5.926475 44.308309
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 116.779721 3.345094 25.197359 38.414216
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 99.525121 5.265275 2.072666 8.259655# vif says remove TEAM_PITCHING_SO
# -------------------
#eliminate TEAM_PITCHING_SO
model.2 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.771 -7.636 0.258 7.342 45.148
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.723220 5.404214 10.311 < 2e-16 ***
## TEAM_BATTING_2B -0.057976 0.008342 -6.950 4.82e-12 ***
## TEAM_BATTING_3B 0.123500 0.016289 7.582 5.04e-14 ***
## TEAM_BATTING_HR 0.071757 0.009173 7.823 8.03e-15 ***
## TEAM_BATTING_BB 0.154860 0.014216 10.893 < 2e-16 ***
## TEAM_BATTING_SO -0.017783 0.002312 -7.691 2.20e-14 ***
## TEAM_BASERUN_SB 0.067235 0.004774 14.083 < 2e-16 ***
## TEAM_PITCHING_H 0.045685 0.003712 12.308 < 2e-16 ***
## TEAM_PITCHING_BB -0.117136 0.012207 -9.596 < 2e-16 ***
## TEAM_FIELDING_E -0.080871 0.003832 -21.106 < 2e-16 ***
## TEAM_FIELDING_DP -0.116948 0.012642 -9.251 < 2e-16 ***
## TEAM_BATTING_1B -0.022420 0.005463 -4.104 4.22e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.25 on 2150 degrees of freedom
## Multiple R-squared: 0.3872, Adjusted R-squared: 0.384
## F-statistic: 123.5 on 11 and 2150 DF, p-value: < 2.2e-16# p-values OK so check collinearity
vif(model.2)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.435898 3.251820 5.028029 34.141690
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 4.657608 3.291089 14.849242 28.862800
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 5.264363 2.066635 5.314335# vif says remove TEAM_PITCHING_BB
# -------------------
#eliminate TEAM_BATTING_BB
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.474 -7.928 0.289 7.545 42.297
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.415319 5.509998 10.602 < 2e-16 ***
## TEAM_BATTING_2B -0.018310 0.007397 -2.475 0.0134 *
## TEAM_BATTING_3B 0.145166 0.016470 8.814 < 2e-16 ***
## TEAM_BATTING_HR 0.109983 0.008436 13.038 < 2e-16 ***
## TEAM_BATTING_BB 0.021452 0.003028 7.084 1.89e-12 ***
## TEAM_BATTING_SO -0.016549 0.002357 -7.021 2.93e-12 ***
## TEAM_BASERUN_SB 0.063016 0.004854 12.984 < 2e-16 ***
## TEAM_PITCHING_H 0.014679 0.001865 7.872 5.48e-15 ***
## TEAM_FIELDING_E -0.073003 0.003821 -19.104 < 2e-16 ***
## TEAM_FIELDING_DP -0.110856 0.012890 -8.600 < 2e-16 ***
## TEAM_BATTING_1B 0.008578 0.004498 1.907 0.0567 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.48 on 2151 degrees of freedom
## Multiple R-squared: 0.3609, Adjusted R-squared: 0.358
## F-statistic: 121.5 on 10 and 2151 DF, p-value: < 2.2e-16# p-values says remove TEAM_BATTING_1B
# -------------------
#eliminate TEAM_BATTING_1B
model.4 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_BATTING_1B)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB -
## TEAM_BATTING_1B, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.519 -8.001 0.336 7.614 41.812
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 66.261095 3.667019 18.069 < 2e-16 ***
## TEAM_BATTING_2B -0.017347 0.007384 -2.349 0.0189 *
## TEAM_BATTING_3B 0.149391 0.016330 9.148 < 2e-16 ***
## TEAM_BATTING_HR 0.108695 0.008414 12.919 < 2e-16 ***
## TEAM_BATTING_BB 0.021727 0.003027 7.178 9.67e-13 ***
## TEAM_BATTING_SO -0.018634 0.002089 -8.920 < 2e-16 ***
## TEAM_BASERUN_SB 0.064701 0.004775 13.549 < 2e-16 ***
## TEAM_PITCHING_H 0.016082 0.001715 9.379 < 2e-16 ***
## TEAM_FIELDING_E -0.074833 0.003701 -20.219 < 2e-16 ***
## TEAM_FIELDING_DP -0.108762 0.012851 -8.463 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.49 on 2152 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3572
## F-statistic: 134.4 on 9 and 2152 DF, p-value: < 2.2e-16# p-values OK so check collinearity
vif(model.4)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 1.829117 3.131630 4.053547 1.482965
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E
## 3.643091 3.155029 3.036321 4.706195
## TEAM_FIELDING_DP
## 2.046463# vif OK so STOP
# get MSE of residuals
anova(model.4)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_2B 1 23852 23852 180.7371 < 2.2e-16 ***
## TEAM_BATTING_3B 1 12881 12881 97.6052 < 2.2e-16 ***
## TEAM_BATTING_HR 1 30779 30779 233.2296 < 2.2e-16 ***
## TEAM_BATTING_BB 1 15162 15162 114.8928 < 2.2e-16 ***
## TEAM_BATTING_SO 1 5965 5965 45.2032 2.268e-11 ***
## TEAM_BASERUN_SB 1 12795 12795 96.9513 < 2.2e-16 ***
## TEAM_PITCHING_H 1 63 63 0.4781 0.4894
## TEAM_FIELDING_E 1 48693 48693 368.9741 < 2.2e-16 ***
## TEAM_FIELDING_DP 1 9452 9452 71.6227 < 2.2e-16 ***
## Residuals 2152 283999 132
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Diagnostics
Plots are linear except for errors
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.4, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Lack of constant variability in Resid vs. Fitted. Normal QQ shows a bit of skew in upper right end but not drastic; Residuals appear to be within 2 std devs.
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.4)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for several variables: 3B, HR, SB, Pitch_H, Fielding_E, PITCH_BB, PITCH_SO, FIELDING_DP
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.4)
par(mfrow=c(2,2))
plot(mb$TEAM_BATTING_2B, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_3B, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_HR, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_PITCHING_H, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship whose slope might be skewed by outliers in upper right of plot
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.4$fitted.values
# nrow(fit1)
par(mfrow = c(1,1))
plot(fit1, mb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb$TARGET_WINS),lty=2)
Now try same model but with FIELD_E transformed by Box-Cox recommended power transform
# TEAM_FIELDING_E: Box-cox yields -1 => 1/y
mb$TEAM_FIELDING_E <- 1/mb$TEAM_FIELDING_EYields r^2= 0.3168, Adj r^2 = 0.3143, F = 124.8
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.440 -7.481 0.083 7.789 41.052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.414e+01 5.587e+00 4.321 1.62e-05 ***
## TEAM_BATTING_2B -2.377e-02 8.948e-03 -2.656 0.00797 **
## TEAM_BATTING_3B 1.520e-01 1.771e-02 8.585 < 2e-16 ***
## TEAM_BATTING_HR 8.730e-02 1.038e-02 8.414 < 2e-16 ***
## TEAM_BATTING_BB 1.226e-01 1.663e-02 7.372 2.38e-13 ***
## TEAM_BATTING_SO -4.739e-02 1.204e-02 -3.936 8.55e-05 ***
## TEAM_BASERUN_SB 3.330e-02 4.524e-03 7.360 2.60e-13 ***
## TEAM_PITCHING_H 1.082e-02 4.739e-03 2.284 0.02250 *
## TEAM_PITCHING_BB -8.508e-02 1.440e-02 -5.907 4.05e-09 ***
## TEAM_PITCHING_SO 2.482e-02 1.126e-02 2.205 0.02754 *
## TEAM_FIELDING_E 3.247e+03 2.057e+02 15.781 < 2e-16 ***
## TEAM_FIELDING_DP -1.143e-01 1.318e-02 -8.673 < 2e-16 ***
## TEAM_BATTING_1B 1.841e-02 6.831e-03 2.696 0.00708 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.69 on 2149 degrees of freedom
## Multiple R-squared: 0.3385, Adjusted R-squared: 0.3348
## F-statistic: 91.65 on 12 and 2149 DF, p-value: < 2.2e-16# p-values all < .05 so check collinearity
vif(model)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.595850 3.558823 5.957395 43.240147
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 116.965149 2.736438 22.414047 37.210796
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 99.513424 4.243335 2.081098 7.692617# vif says remove TEAM_PITCHING_SO
# -------------------
#eliminate TEAM_PITCHING_SO
model.2 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.855 -7.541 0.243 7.891 39.291
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.640e+01 5.498e+00 4.802 1.68e-06 ***
## TEAM_BATTING_2B -3.055e-02 8.410e-03 -3.633 0.000287 ***
## TEAM_BATTING_3B 1.435e-01 1.730e-02 8.296 < 2e-16 ***
## TEAM_BATTING_HR 7.844e-02 9.574e-03 8.193 4.34e-16 ***
## TEAM_BATTING_BB 1.047e-01 1.453e-02 7.205 8.01e-13 ***
## TEAM_BATTING_SO -2.140e-02 2.459e-03 -8.701 < 2e-16 ***
## TEAM_BASERUN_SB 3.184e-02 4.480e-03 7.108 1.59e-12 ***
## TEAM_PITCHING_H 1.788e-02 3.498e-03 5.112 3.48e-07 ***
## TEAM_PITCHING_BB -6.891e-02 1.241e-02 -5.553 3.16e-08 ***
## TEAM_FIELDING_E 3.250e+03 2.059e+02 15.784 < 2e-16 ***
## TEAM_FIELDING_DP -1.128e-01 1.317e-02 -8.558 < 2e-16 ***
## TEAM_BATTING_1B 9.141e-03 5.388e-03 1.697 0.089933 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.7 on 2150 degrees of freedom
## Multiple R-squared: 0.337, Adjusted R-squared: 0.3336
## F-statistic: 99.36 on 11 and 2150 DF, p-value: < 2.2e-16# p-values says remove TEAM_BATTING_1B
# -------------------
#eliminate TEAM_BATTING_1B
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.322 -7.571 0.210 7.727 39.339
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.140e+01 4.642e+00 6.765 1.71e-11 ***
## TEAM_BATTING_2B -3.284e-02 8.305e-03 -3.954 7.94e-05 ***
## TEAM_BATTING_3B 1.435e-01 1.731e-02 8.290 < 2e-16 ***
## TEAM_BATTING_HR 7.398e-02 9.211e-03 8.032 1.56e-15 ***
## TEAM_BATTING_BB 1.187e-01 1.199e-02 9.902 < 2e-16 ***
## TEAM_BATTING_SO -2.305e-02 2.258e-03 -10.212 < 2e-16 ***
## TEAM_BASERUN_SB 3.240e-02 4.469e-03 7.250 5.79e-13 ***
## TEAM_PITCHING_H 2.159e-02 2.733e-03 7.900 4.42e-15 ***
## TEAM_PITCHING_BB -8.082e-02 1.024e-02 -7.893 4.67e-15 ***
## TEAM_FIELDING_E 3.274e+03 2.055e+02 15.931 < 2e-16 ***
## TEAM_FIELDING_DP -1.111e-01 1.315e-02 -8.453 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.7 on 2151 degrees of freedom
## Multiple R-squared: 0.3361, Adjusted R-squared: 0.3331
## F-statistic: 108.9 on 10 and 2151 DF, p-value: < 2.2e-16vif(model.3)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 2.230211 3.389546 4.682396 22.413215
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB
## 4.100904 2.663642 7.432730 18.756439
## TEAM_FIELDING_E TEAM_FIELDING_DP
## 4.223007 2.063646# p-values says remove TEAM_PITCHING_BB
# -------------------
#eliminate TEAM_BATTING_BB
model.4 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.522 -7.843 0.386 7.968 39.441
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.286e+01 3.815e+00 13.856 < 2e-16 ***
## TEAM_BATTING_2B -3.694e-03 7.545e-03 -0.490 0.6245
## TEAM_BATTING_3B 1.696e-01 1.723e-02 9.847 < 2e-16 ***
## TEAM_BATTING_HR 9.684e-02 8.867e-03 10.921 < 2e-16 ***
## TEAM_BATTING_BB 2.722e-02 3.103e-03 8.771 < 2e-16 ***
## TEAM_BATTING_SO -2.741e-02 2.220e-03 -12.349 < 2e-16 ***
## TEAM_BASERUN_SB 3.418e-02 4.527e-03 7.550 6.38e-14 ***
## TEAM_PITCHING_H 3.888e-03 1.584e-03 2.455 0.0142 *
## TEAM_FIELDING_E 3.282e+03 2.084e+02 15.744 < 2e-16 ***
## TEAM_FIELDING_DP -1.022e-01 1.328e-02 -7.693 2.17e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.87 on 2152 degrees of freedom
## Multiple R-squared: 0.3169, Adjusted R-squared: 0.3141
## F-statistic: 110.9 on 9 and 2152 DF, p-value: < 2.2e-16# p-values say remove doubles
model.5 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B - TEAM_PITCHING_BB - TEAM_BATTING_2B)
summary(model.5)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B -
## TEAM_PITCHING_BB - TEAM_BATTING_2B, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.512 -7.826 0.349 8.005 39.581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.288e+01 3.815e+00 13.862 < 2e-16 ***
## TEAM_BATTING_3B 1.685e-01 1.707e-02 9.873 < 2e-16 ***
## TEAM_BATTING_HR 9.616e-02 8.757e-03 10.981 < 2e-16 ***
## TEAM_BATTING_BB 2.701e-02 3.075e-03 8.785 < 2e-16 ***
## TEAM_BATTING_SO -2.741e-02 2.219e-03 -12.350 < 2e-16 ***
## TEAM_BASERUN_SB 3.443e-02 4.496e-03 7.658 2.84e-14 ***
## TEAM_PITCHING_H 3.568e-03 1.442e-03 2.474 0.0134 *
## TEAM_FIELDING_E 3.252e+03 1.997e+02 16.288 < 2e-16 ***
## TEAM_FIELDING_DP -1.023e-01 1.328e-02 -7.708 1.94e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.86 on 2153 degrees of freedom
## Multiple R-squared: 0.3168, Adjusted R-squared: 0.3143
## F-statistic: 124.8 on 8 and 2153 DF, p-value: < 2.2e-16vif(model.5)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## 3.206158 4.116662 1.434886 3.855309
## TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E TEAM_FIELDING_DP
## 2.622091 2.014360 3.877112 2.047278# vif OK so STOP
# turn off scientific formatting of results
options(scipen=999)
model.5##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_BATTING_1B -
## TEAM_PITCHING_BB - TEAM_BATTING_2B, data = mb)
##
## Coefficients:
## (Intercept) TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 52.876911 0.168490 0.096164 0.027014
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_FIELDING_E
## -0.027410 0.034431 0.003568 3252.309198
## TEAM_FIELDING_DP
## -0.102330anova(model.5)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_3B 1 7851 7851 55.7747 0.00000000000011740 ***
## TEAM_BATTING_HR 1 55626 55626 395.1504 < 0.00000000000000022 ***
## TEAM_BATTING_BB 1 16652 16652 118.2947 < 0.00000000000000022 ***
## TEAM_BATTING_SO 1 6913 6913 49.1095 0.00000000000322538 ***
## TEAM_BASERUN_SB 1 12274 12274 87.1878 < 0.00000000000000022 ***
## TEAM_PITCHING_H 1 118 118 0.8379 0.3601
## TEAM_FIELDING_E 1 32763 32763 232.7428 < 0.00000000000000022 ***
## TEAM_FIELDING_DP 1 8364 8364 59.4139 0.00000000000001937 ***
## Residuals 2153 303080 141
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Diagnostics
Plots are all linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.5, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Some lack of constant variability in Resid vs. Fitted. Normal QQ shows a bit of skew in lower left end but not drastic; Residuals not all within 2 std devs.
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.5)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for several variables: 3B, HR, BB, SO, SB, Pitch_H, Fielding_E
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.5)
par(mfrow=c(2,2))
plot(mb$TEAM_BATTING_3B, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_HR, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_PITCHING_H, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship whose slope might be slightly skewed by outliers in upper right of plot
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.5$fitted.values
# nrow(fit1)
par(mfrow = c(1,1))
plot(fit1, mb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb$TARGET_WINS),lty=2)
# clean up objects in memory
rm(list = ls())Model 2: Total Bases
library(car)
mb_clean <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/621-HW1-Clean-Data.csv") Build a model with Total Bases added and all of the other hitting vars removed
First, create the new variable and discard its components
mb_t <- mb_clean
mb_t$TOTAL_BASES <- mb_clean$TEAM_BATTING_1B + (2 * mb_clean$TEAM_BATTING_2B) +
(3 * mb_clean$TEAM_BATTING_3B) + (4 * mb_clean$TEAM_BATTING_HR)
# plot histogram to check shape of distribution
par(mfrow = c(1,1))
hist(mb_t$TOTAL_BASES, breaks = 200)
# now drop 1B, 2B, 3B, HR
mb_tb <- mb_t[,c(1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 15)]
###################################################################
# check correlation with WINS and run simple linear model
cor(mb_tb$TARGET_WINS, mb_tb$TOTAL_BASES) ## [1] 0.3817283mtest <- lm(data=mb_tb, TARGET_WINS ~ TOTAL_BASES)
summary(mtest) ##
## Call:
## lm(formula = TARGET_WINS ~ TOTAL_BASES, data = mb_tb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.515 -9.242 0.330 9.134 49.895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.309929 2.498670 13.33 <0.0000000000000002 ***
## TOTAL_BASES 0.022526 0.001171 19.24 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.45 on 2170 degrees of freedom
## Multiple R-squared: 0.1457, Adjusted R-squared: 0.1453
## F-statistic: 370.1 on 1 and 2170 DF, p-value: < 0.00000000000000022# shows .381 correlation and Adj R^2 of 0.1453
plot(mb_tb$TARGET_WINS ~ mb_tb$TOTAL_BASES)
abline(lm(mb_tb$TARGET_WINS ~ mb_tb$TOTAL_BASES), lty=2)
# plot doesn't show unusual relationship
######################################################################Yields r^2= 0.3175, Adj. R^2 = 0.3153, F = 143.8
# fit model
model <- lm(data=mb_tb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb_tb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.709 -8.023 -0.060 7.601 53.946
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.488500 4.028435 9.802 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.150859 0.016604 9.085 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.068106 0.011085 -6.144 0.00000000095530289 ***
## TEAM_BASERUN_SB 0.066840 0.004931 13.554 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.017824 0.003839 4.643 0.00000363574932803 ***
## TEAM_PITCHING_BB -0.113929 0.014384 -7.921 0.00000000000000375 ***
## TEAM_PITCHING_SO 0.051088 0.009671 5.283 0.00000014005177514 ***
## TEAM_FIELDING_E -0.063746 0.003731 -17.084 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.122049 0.013247 -9.213 < 0.0000000000000002 ***
## TOTAL_BASES 0.014634 0.002346 6.239 0.00000000052927091 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.87 on 2162 degrees of freedom
## Multiple R-squared: 0.3368, Adjusted R-squared: 0.3341
## F-statistic: 122 on 9 and 2162 DF, p-value: < 0.00000000000000022# All p-values < .05 so check collinearity
vif(model)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 42.583711 96.685910 3.217711 14.833674
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 36.467493 71.783178 4.724229 2.055734
## TOTAL_BASES
## 5.151420# vif indicates remove TEAM_BATTING_SO or TEAM_PITCHING_SO. CHoose PITCHING_SO as in other models
# ----------------------
# remove TEAM_PITCHING_SO
model.2 <- lm(data=mb_tb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb_tb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.524 -7.899 0.111 7.765 53.216
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.957133 3.857791 8.543 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.099826 0.013589 7.346 0.000000000000287 ***
## TEAM_BATTING_SO -0.010106 0.001537 -6.576 0.000000000060537 ***
## TEAM_BASERUN_SB 0.060228 0.004799 12.549 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.027950 0.003347 8.352 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.067548 0.011464 -5.892 0.000000004411900 ***
## TEAM_FIELDING_E -0.061895 0.003738 -16.559 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.118816 0.013315 -8.923 < 0.0000000000000002 ***
## TOTAL_BASES 0.009245 0.002125 4.350 0.000014249957148 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.94 on 2163 degrees of freedom
## Multiple R-squared: 0.3283, Adjusted R-squared: 0.3258
## F-statistic: 132.1 on 8 and 2163 DF, p-value: < 0.00000000000000022# All p-values < .05 so check collinearity
vif(model.2)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 28.169559 1.835552 3.010433 11.135442
## TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 22.880704 4.682562 2.051346 4.177202# vif indicates remove TEAM_PITCHING_BB
# ----------------------
# remove TEAM_PITCHING_BB
model.3 <- lm(data=mb_tb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB,
## data = mb_tb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.761 -8.220 0.160 7.833 58.011
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.087126 3.287882 13.713 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.021880 0.003130 6.990 0.00000000000365 ***
## TEAM_BATTING_SO -0.013037 0.001465 -8.897 < 0.0000000000000002 ***
## TEAM_BASERUN_SB 0.060536 0.004836 12.517 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.011527 0.001867 6.175 0.00000000078674 ***
## TEAM_FIELDING_E -0.059620 0.003747 -15.912 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.114299 0.013396 -8.532 < 0.0000000000000002 ***
## TOTAL_BASES 0.017639 0.001590 11.097 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.04 on 2164 degrees of freedom
## Multiple R-squared: 0.3175, Adjusted R-squared: 0.3153
## F-statistic: 143.8 on 7 and 2164 DF, p-value: < 0.00000000000000022# All p-values < .05 so check collinearity
vif(model.3)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 1.471732 1.643149 3.010077 3.411334
## TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 4.632607 2.044547 2.300575# no further collinearity issues so STOP
# check 95% confidence intervals for coefficients
confint(model.3)## 2.5 % 97.5 %
## (Intercept) 38.639390134 51.53486272
## TEAM_BATTING_BB 0.015741199 0.02801786
## TEAM_BATTING_SO -0.015910936 -0.01016372
## TEAM_BASERUN_SB 0.051051063 0.07002015
## TEAM_PITCHING_H 0.007866465 0.01518776
## TEAM_FIELDING_E -0.066967986 -0.05227251
## TEAM_FIELDING_DP -0.140569909 -0.08802864
## TOTAL_BASES 0.014522018 0.02075646Diagnostics
Plots for Fielding_E shows skew. Others are pretty linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.3, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots look good except for outliers. Lack of Constant variability in Resid vs. Fitted at very large values of Yhat; normal distribution of residuals except for outliers, most residuals within 2 std dev and well within Cook’s distance
#Figure 5.6 on page 129 MARR text
par(mfrow=c(2,2))
plot(model.3)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for BASERUN_SB, PITCHING_H, PITCHING_SO, FIELDING_E, FIELDING_DP
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.3)
par(mfrow=c(2,2))
plot(mb_tb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TEAM_PITCHING_H, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb_tb$TOTAL_BASES, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Might be some skew due to outliers
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.3$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb_tb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb_tb$TARGET_WINS),lty=2)
REMOVE OUTLIERS AND REFIT
Per Cooks Distance, remove items 1920, 1737, 393, 1515
############ FIRST SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem <- mb_tb[-c(1920, 1737, 393, 1515),]
# renumber rows
rownames(mb_rem) <- 1:nrow(mb_rem)Now refit first model from above: all variables
Yields r^2= 0.3287, Adj r^2 = 0.3265, F = 151.1
# keep the clean data set pure
mb <- mb_rem
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.516 -8.071 0.049 7.522 47.810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.441249 3.987025 10.645 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.154335 0.016410 9.405 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.072357 0.010950 -6.608 0.000000000048869495 ***
## TEAM_BASERUN_SB 0.069009 0.004860 14.199 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.016802 0.003788 4.435 0.000009658905673535 ***
## TEAM_PITCHING_BB -0.117154 0.014229 -8.234 0.000000000000000311 ***
## TEAM_PITCHING_SO 0.053942 0.009551 5.648 0.000000018371250928 ***
## TEAM_FIELDING_E -0.067499 0.003699 -18.248 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.123715 0.013030 -9.495 < 0.0000000000000002 ***
## TOTAL_BASES 0.014732 0.002311 6.375 0.000000000222616213 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.67 on 2158 degrees of freedom
## Multiple R-squared: 0.3493, Adjusted R-squared: 0.3466
## F-statistic: 128.7 on 9 and 2158 DF, p-value: < 0.00000000000000022# pvals all < .05 so check collinearity
vif(model)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 42.781793 97.442002 3.199402 14.634840
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 36.800848 72.280509 4.670280 2.048269
## TOTAL_BASES
## 5.161481# vif indicates remove TEAM_BATTING_SO and PITCHING_SO. CHoose PITCHING_SO again
# --------------------
# remove TEAM_PITCHING_SO
model.2 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.867 -7.942 0.093 7.845 44.545
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 35.499141 3.819886 9.293 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.100306 0.013428 7.470 0.000000000000116 ***
## TEAM_BATTING_SO -0.011103 0.001519 -7.308 0.000000000000379 ***
## TEAM_BASERUN_SB 0.061945 0.004730 13.097 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.027469 0.003307 8.305 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.068029 0.011341 -5.998 0.000000002329868 ***
## TEAM_FIELDING_E -0.065403 0.003707 -17.645 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.120236 0.013108 -9.173 < 0.0000000000000002 ***
## TOTAL_BASES 0.009060 0.002096 4.323 0.000016126085257 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.76 on 2159 degrees of freedom
## Multiple R-squared: 0.3397, Adjusted R-squared: 0.3373
## F-statistic: 138.8 on 8 and 2159 DF, p-value: < 0.00000000000000022# p-values are OK so check collinearity
vif(model.2)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 28.243542 1.849306 2.987512 10.997742
## TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 23.050031 4.623291 2.043691 4.186652# vif says remove TEAM_BATTING_BB
# -------------------
#eliminate TEAM_BATTING_BB or PITCHING_BB so choose PITCHING_BB
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_SO)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_SO,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.456 -8.196 0.174 7.785 43.234
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 47.746708 3.254440 14.671 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.021878 0.003085 7.092 0.00000000000178 ***
## TEAM_BATTING_SO -0.014068 0.001448 -9.715 < 0.0000000000000002 ***
## TEAM_BASERUN_SB 0.062245 0.004768 13.055 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.010923 0.001840 5.937 0.00000000336791 ***
## TEAM_FIELDING_E -0.063123 0.003717 -16.983 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.115737 0.013192 -8.773 < 0.0000000000000002 ***
## TOTAL_BASES 0.017495 0.001567 11.166 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.85 on 2160 degrees of freedom
## Multiple R-squared: 0.3287, Adjusted R-squared: 0.3265
## F-statistic: 151.1 on 7 and 2160 DF, p-value: < 0.00000000000000022# p-values OK so check collinearity
vif(model.3)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 1.466753 1.653485 2.987180 3.348759
## TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 4.574645 2.036999 2.302144# vif and pvals OK so STOP HERE
# check 95% confidence intervals for coefficients
confint(model.3)## 2.5 % 97.5 %
## (Intercept) 41.364546361 54.12886979
## TEAM_BATTING_BB 0.015828537 0.02792739
## TEAM_BATTING_SO -0.016907860 -0.01122823
## TEAM_BASERUN_SB 0.052894909 0.07159443
## TEAM_PITCHING_H 0.007315473 0.01453144
## TEAM_FIELDING_E -0.070411557 -0.05583395
## TEAM_FIELDING_DP -0.141607287 -0.08986612
## TOTAL_BASES 0.014422320 0.02056738Diagnostics
Plots for Fielding_E shows skew. Others are pretty linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.3, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Lack of constant variability in Resid vs. Fitted. Normal QQ shows a bit of skew in upper right end but not drastic; Some residuals appear to be outside 2 std devs. Might not be a good model. Outliers at 1528, 1922, 820, 1933, 1733, 835
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.3)
Plots show outliers so remove them and re-fit
Per Cooks Distance, remove 1528, 1922, 820, 1933, 1733, 835
############ SECOND SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem2 <- mb[-c(1528, 1922, 820, 1933, 1733, 835),]
# renumber rows
rownames(mb_rem2) <- 1:nrow(mb_rem2)Model using all remaining variables as a starting point
Yields r^2= 0.33655, Adj r^2 = 0.3343, F = 156
# keep the clean data set pure
mb <- mb_rem2
# use p-value elimination
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.179 -8.045 0.044 7.493 44.739
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 43.011185 3.992399 10.773 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.147363 0.016384 8.994 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.068624 0.010941 -6.272 0.0000000004293871 ***
## TEAM_BASERUN_SB 0.069068 0.004809 14.363 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.016311 0.003801 4.291 0.0000185345938702 ***
## TEAM_PITCHING_BB -0.110736 0.014225 -7.784 0.0000000000000108 ***
## TEAM_PITCHING_SO 0.049930 0.009554 5.226 0.0000001900846778 ***
## TEAM_FIELDING_E -0.067668 0.003665 -18.461 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.123738 0.012888 -9.601 < 0.0000000000000002 ***
## TOTAL_BASES 0.015058 0.002300 6.546 0.0000000000734869 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.54 on 2152 degrees of freedom
## Multiple R-squared: 0.3547, Adjusted R-squared: 0.352
## F-statistic: 131.4 on 9 and 2152 DF, p-value: < 0.00000000000000022# p-values all < .05 so check collinearity
vif(model)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 43.067052 98.922118 3.175291 14.605057
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 37.353473 73.550826 4.602276 2.044406
## TOTAL_BASES
## 5.191730# vif says remove TEAM_BATTING_SO
# -------------------
#eliminate TEAM_BATTING_SO or PITCHING_SO so choose PITCHING_SO again
model.2 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.995 -7.977 0.065 7.750 42.855
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.541180 3.818699 9.569 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.097250 0.013365 7.276 0.00000000000047808 ***
## TEAM_BATTING_SO -0.011989 0.001512 -7.928 0.00000000000000353 ***
## TEAM_BASERUN_SB 0.062616 0.004676 13.391 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.026191 0.003317 7.895 0.00000000000000459 ***
## TEAM_PITCHING_BB -0.065120 0.011301 -5.762 0.00000000948828590 ***
## TEAM_FIELDING_E -0.065835 0.003671 -17.935 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.120626 0.012953 -9.313 < 0.0000000000000002 ***
## TOTAL_BASES 0.009848 0.002086 4.722 0.00000248533829969 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.61 on 2153 degrees of freedom
## Multiple R-squared: 0.3465, Adjusted R-squared: 0.3441
## F-statistic: 142.7 on 8 and 2153 DF, p-value: < 0.00000000000000022# p-values OK so check collinearity
vif(model.2)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 28.313487 1.866693 2.965972 10.991773
## TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 23.288881 4.560154 2.040042 4.216460# vif says remove TEAM_BATTING_BB or PITCHING_BB so choose PITCHING_BB again
# -------------------
#eliminate TEAM_PITCHING_BB
model.3 <- lm(data=mb, TARGET_WINS ~. - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_SO - TEAM_PITCHING_BB,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.210 -8.207 0.091 7.683 41.423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.485759 3.231012 15.006 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.022237 0.003050 7.291 0.000000000000431 ***
## TEAM_BATTING_SO -0.014906 0.001436 -10.384 < 0.0000000000000002 ***
## TEAM_BASERUN_SB 0.062907 0.004711 13.355 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.010197 0.001831 5.571 0.000000028565450 ***
## TEAM_FIELDING_E -0.063675 0.003679 -17.308 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.116577 0.013030 -8.947 < 0.0000000000000002 ***
## TOTAL_BASES 0.017963 0.001550 11.591 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.7 on 2154 degrees of freedom
## Multiple R-squared: 0.3365, Adjusted R-squared: 0.3343
## F-statistic: 156 on 7 and 2154 DF, p-value: < 0.00000000000000022vif(model.3)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## 1.452828 1.657492 2.965626 3.297456
## TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 4.512577 2.034037 2.293841# p-values and VIF OK so STOP
anova(model.3)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_BB 1 30649 30649 223.999 < 0.00000000000000022 ***
## TEAM_BATTING_SO 1 7298 7298 53.341 0.000000000000392795 ***
## TEAM_BASERUN_SB 1 9655 9655 70.563 < 0.00000000000000022 ***
## TEAM_PITCHING_H 1 12282 12282 89.763 < 0.00000000000000022 ***
## TEAM_FIELDING_E 1 62709 62709 458.310 < 0.00000000000000022 ***
## TEAM_FIELDING_DP 1 8464 8464 61.863 0.000000000000005775 ***
## TOTAL_BASES 1 18384 18384 134.357 < 0.00000000000000022 ***
## Residuals 2154 294726 137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# check 95% confidence intervals for coefficients
confint(model.3)## 2.5 % 97.5 %
## (Intercept) 42.149531058 54.82198731
## TEAM_BATTING_BB 0.016256026 0.02821876
## TEAM_BATTING_SO -0.017720942 -0.01209071
## TEAM_BASERUN_SB 0.053669147 0.07214436
## TEAM_PITCHING_H 0.006607378 0.01378706
## TEAM_FIELDING_E -0.070888990 -0.05646022
## TEAM_FIELDING_DP -0.142128959 -0.09102440
## TOTAL_BASES 0.014924337 0.02100264Diagnostics
Plots for Fielding_E shows skew. Others are pretty linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.3, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Lack of constant variability in Resid vs. Fitted but only for extreme outliers. Normal QQ looks very good; Some Residuals appear to be outside 2 std devs
# plot summary residual plots
par(mfrow=c(2,2))
plot(model.3)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for BASERUN_SB, PITCHING_H, PITCHING_SO, FIELDING_E, FIELDING_DP
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.3)
par(mfrow=c(2,2))
plot(mb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_PITCHING_H, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb$TOTAL_BASES, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Might be some skew due to outliers
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.3$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb$TARGET_WINS),lty=2)
# ——————————————————————————————- # ——————————————————————————————-
Now try same model but with FIELD_E transformed according to Box-Cox
# TEAM_FIELDING_E: Box-Cox yields power xform of -1 => 1/y
mb$TEAM_FIELDING_E <- 1/mb$TEAM_FIELDING_ENow refit first model from above: all variables
Model using all remaining variables as a starting point
Yields r^2= 0.3048, Adj r^2 = 0.3029, F = 157.5
# fit model
model <- lm(data=mb, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.449 -7.663 0.017 7.875 44.521
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.940450 4.062200 8.355 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.109123 0.016792 6.499 0.000000000100466 ***
## TEAM_BATTING_SO -0.053628 0.011230 -4.775 0.000001914819121 ***
## TEAM_BASERUN_SB 0.040792 0.004460 9.146 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.004967 0.003821 1.300 0.19381
## TEAM_PITCHING_BB -0.074106 0.014533 -5.099 0.000000370699407 ***
## TEAM_PITCHING_SO 0.027384 0.009820 2.789 0.00534 **
## TEAM_FIELDING_E 2695.772954 195.354383 13.799 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.117721 0.013328 -8.833 < 0.0000000000000002 ***
## TOTAL_BASES 0.017392 0.002373 7.328 0.000000000000329 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.91 on 2152 degrees of freedom
## Multiple R-squared: 0.3133, Adjusted R-squared: 0.3104
## F-statistic: 109.1 on 9 and 2152 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_H
# ----------------------
# remove TEAM_PITCHING_H
model.2 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.790 -7.818 0.083 7.925 45.364
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 37.568737 2.951626 12.728 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.103043 0.016130 6.388 0.00000000020485 ***
## TEAM_BATTING_SO -0.062243 0.009067 -6.865 0.00000000000868 ***
## TEAM_BASERUN_SB 0.042673 0.004219 10.113 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.069557 0.014107 -4.931 0.00000088225033 ***
## TEAM_PITCHING_SO 0.034309 0.008250 4.159 0.00003328511411 ***
## TEAM_FIELDING_E 2664.401602 193.888720 13.742 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.116848 0.013313 -8.777 < 0.0000000000000002 ***
## TOTAL_BASES 0.020029 0.001231 16.267 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.91 on 2153 degrees of freedom
## Multiple R-squared: 0.3128, Adjusted R-squared: 0.3102
## F-statistic: 122.5 on 8 and 2153 DF, p-value: < 0.00000000000000022vif(model.2)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_BB
## 39.211674 63.814882 2.296332 34.506646
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 51.516155 3.631039 2.049298 1.397321# vif says remove TEAM_BATTING_SO or PITCHING_SO so discard PITCHING_SO again
# ----------------------
# remove TEAM_PITCHING_SO
model.3 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.511 -7.762 0.113 8.049 44.351
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.139798 2.938399 13.320 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.042183 0.006807 6.197 0.000000000688 ***
## TEAM_BATTING_SO -0.025194 0.001690 -14.906 < 0.0000000000000002 ***
## TEAM_BASERUN_SB 0.041624 0.004228 9.845 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.016370 0.005975 -2.740 0.0062 **
## TEAM_FIELDING_E 2640.049236 194.531863 13.571 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.113486 0.013339 -8.508 < 0.0000000000000002 ***
## TOTAL_BASES 0.019976 0.001236 16.164 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.95 on 2154 degrees of freedom
## Multiple R-squared: 0.3072, Adjusted R-squared: 0.305
## F-statistic: 136.5 on 7 and 2154 DF, p-value: < 0.00000000000000022vif(model.3)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_BB
## 6.931405 2.200940 2.288133 6.142926
## TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 3.627727 2.041739 1.397168# vif say remove TEAM_BATTING_BB or PITCHING_BB - go with PITCHING_BB again
# ----------------------
# remove TEAM_PITCHING_BB
model.4 <- lm(data=mb, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.763 -7.899 0.209 8.121 43.323
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.164119 2.942818 13.308 <0.0000000000000002 ***
## TEAM_BATTING_BB 0.025404 0.002976 8.535 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.024551 0.001676 -14.645 <0.0000000000000002 ***
## TEAM_BASERUN_SB 0.038058 0.004028 9.447 <0.0000000000000002 ***
## TEAM_FIELDING_E 2714.549336 192.912713 14.071 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.114953 0.013348 -8.612 <0.0000000000000002 ***
## TOTAL_BASES 0.019678 0.001233 15.961 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.97 on 2155 degrees of freedom
## Multiple R-squared: 0.3048, Adjusted R-squared: 0.3029
## F-statistic: 157.5 on 6 and 2155 DF, p-value: < 0.00000000000000022# pvals all < .05 so check collinearity
vif(model.4)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_FIELDING_E
## 1.321097 2.158564 2.071297 3.556849
## TEAM_FIELDING_DP TOTAL_BASES
## 2.038449 1.386329options(scipen=999)
model.4##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb)
##
## Coefficients:
## (Intercept) TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## 39.16412 0.02540 -0.02455 0.03806
## TEAM_FIELDING_E TEAM_FIELDING_DP TOTAL_BASES
## 2714.54934 -0.11495 0.01968anova(model.4)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_BB 1 30649 30649 213.905 < 0.00000000000000022 ***
## TEAM_BATTING_SO 1 7298 7298 50.937 0.0000000000012976902 ***
## TEAM_BASERUN_SB 1 9655 9655 67.383 0.0000000000000003804 ***
## TEAM_FIELDING_E 1 46368 46368 323.609 < 0.00000000000000022 ***
## TEAM_FIELDING_DP 1 4920 4920 34.334 0.0000000053558270759 ***
## TOTAL_BASES 1 36500 36500 254.739 < 0.00000000000000022 ***
## Residuals 2155 308778 143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# no collinearity so STOP
# check 95% confidence intervals for coefficients
confint(model.4)## 2.5 % 97.5 %
## (Intercept) 33.39305950 44.93517803
## TEAM_BATTING_BB 0.01956697 0.03124054
## TEAM_BATTING_SO -0.02783859 -0.02126358
## TEAM_BASERUN_SB 0.03015808 0.04595838
## TEAM_FIELDING_E 2336.23488507 3092.86378594
## TEAM_FIELDING_DP -0.14112951 -0.08877633
## TOTAL_BASES 0.01725985 0.02209542Diagnostics
Plots show all variables are linear to response
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.4, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Some lack of Constant variability in Resid vs. Fitted at both ends; normal distribution of residuals; many residuals outside of 2 std devs PROBABLY NOT A GOOD MODEL
#Figure 5.6 on page 129 MARR text
par(mfrow=c(2,2))
plot(model.4)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for PITCHING_SO, FIELDING_E
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.4)
par(mfrow=c(2,2))
plot(mb$TEAM_BATTING_BB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_BASERUN_SB, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb$TOTAL_BASES, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship with no pattern or skew
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.4$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb$TARGET_WINS),lty=2)
# clean up objects in memory
rm(list = ls())Model 3: Total Bases PLUS
library(car)
# read clean data set from Github
mb_clean <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/621-HW1-Clean-Data.csv") Build a model with Total Bases + SB + BB added and all of the other hitting vars removed
# create new variable and drop its components
mb_t <- mb_clean
mb_t$TB_PLUS <- mb_clean$TEAM_BATTING_1B + (2 * mb_clean$TEAM_BATTING_2B) +
(3 * mb_clean$TEAM_BATTING_3B) + (4 * mb_clean$TEAM_BATTING_HR) +
mb_clean$TEAM_BATTING_BB + mb_clean$TEAM_BASERUN_SB
par(mfrow = c(1,1))
hist(mb_t$TB_PLUS, breaks = 200)
# now drop 1B, 2B, 3B, HR, BB, SB
mb_tbp <- mb_t[,c(1, 2, 7, 9, 10, 11, 12, 13, 15)]
###################################################################
# check correlation with WINS and run simple linear model
cor(mb_tbp$TARGET_WINS, mb_tbp$TB_PLUS) ## [1] 0.4478658mtest <- lm(data=mb_tbp, TARGET_WINS ~ TB_PLUS)
summary(mtest) ##
## Call:
## lm(formula = TARGET_WINS ~ TB_PLUS, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.805 -9.087 0.294 8.845 47.414
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.7055981 2.6867939 6.962 0.00000000000443 ***
## TB_PLUS 0.0225394 0.0009659 23.334 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.01 on 2170 degrees of freedom
## Multiple R-squared: 0.2006, Adjusted R-squared: 0.2002
## F-statistic: 544.5 on 1 and 2170 DF, p-value: < 0.00000000000000022# shows .448 correlation and Adj R^2 of 0.2002 => better than TOTAL_BASES
plot(mb_tbp$TARGET_WINS ~ mb_tbp$TB_PLUS)
abline(lm(mb_tbp$TARGET_WINS ~ mb_tbp$TB_PLUS), lty=2)
# plot doesn't show unusual relationship
######################################################################Yields r^2= 0.2845, Adj. R^2 = 0.2832, F = 215.4
# fit model
model <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.983 -8.050 0.222 8.210 55.388
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51.167966 3.948869 12.958 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.036400 0.010160 -3.583 0.000347 ***
## TEAM_PITCHING_H 0.001971 0.003587 0.549 0.582772
## TEAM_PITCHING_BB -0.006469 0.003749 -1.726 0.084516 .
## TEAM_PITCHING_SO 0.020377 0.008595 2.371 0.017836 *
## TEAM_FIELDING_E -0.042058 0.003130 -13.437 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.157922 0.012357 -12.780 < 0.0000000000000002 ***
## TB_PLUS 0.026357 0.002152 12.247 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.22 on 2164 degrees of freedom
## Multiple R-squared: 0.2965, Adjusted R-squared: 0.2942
## F-statistic: 130.3 on 7 and 2164 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_H
# ----------------------
# remove TEAM_PITCHING_H
model.2 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.105 -8.066 0.209 8.169 55.518
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.382736 3.271336 16.013 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.041392 0.004546 -9.106 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.007564 0.003175 -2.383 0.0173 *
## TEAM_PITCHING_SO 0.024536 0.004070 6.028 0.00000000195 ***
## TEAM_FIELDING_E -0.041729 0.003072 -13.584 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.157238 0.012293 -12.791 < 0.0000000000000002 ***
## TB_PLUS 0.027353 0.001161 23.559 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.22 on 2165 degrees of freedom
## Multiple R-squared: 0.2964, Adjusted R-squared: 0.2945
## F-statistic: 152 on 6 and 2165 DF, p-value: < 0.00000000000000022# All p-values < .05 so check collinearity
vif(model.2)## TEAM_BATTING_SO TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E
## 15.346530 1.676592 12.003206 3.021956
## TEAM_FIELDING_DP TB_PLUS
## 1.670760 1.637689# vif indicates remove TEAM_BATTING_SO or TEAM_PITCHING_SO, so try removing PITCHING_SO
# remove TEAM_PITCHING_SO
model.3 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO,
## data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.713 -8.090 0.168 8.157 58.048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 49.697441 3.267190 15.211 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.015274 0.001386 -11.022 <0.0000000000000002 ***
## TEAM_PITCHING_BB -0.001905 0.003057 -0.623 0.533
## TEAM_FIELDING_E -0.030940 0.002517 -12.293 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.150607 0.012343 -12.202 <0.0000000000000002 ***
## TB_PLUS 0.026000 0.001148 22.641 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.32 on 2166 degrees of freedom
## Multiple R-squared: 0.2846, Adjusted R-squared: 0.283
## F-statistic: 172.3 on 5 and 2166 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_BB
# ----------------------
# remove TEAM_PITCHING_BB
model.4 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.491 -8.058 0.195 8.127 58.467
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 49.7754486 3.2643296 15.25 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.0151681 0.0013752 -11.03 <0.0000000000000002 ***
## TEAM_FIELDING_E -0.0309293 0.0025164 -12.29 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.1512808 0.0122935 -12.31 <0.0000000000000002 ***
## TB_PLUS 0.0255985 0.0009504 26.93 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.32 on 2167 degrees of freedom
## Multiple R-squared: 0.2845, Adjusted R-squared: 0.2832
## F-statistic: 215.4 on 4 and 2167 DF, p-value: < 0.00000000000000022# pvals all < .05 so check collinearity
vif(model.4)## TEAM_BATTING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TB_PLUS
## 1.382409 1.995902 1.644666 1.080068# no collinearity so STOPDiagnostics
Plots for Fielding_E shows skew. Others are pretty linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.4, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: outliers at 2012, 1820, 859. Lack of Constant variability in Resid vs. Fitted at very large values of Yhat; normal distribution of residuals except for outliers, most residuals within 2 std dev and well within Cook’s distance
#Figure 5.6 on page 129 MARR text
par(mfrow=c(2,2))
plot(model.4)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for PITCHING_SO, FIELDING_E, FIELDING_DP, TB_PLUS
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.4)
par(mfrow=c(2,2))
plot(mb_tbp$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TB_PLUS, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship with no pattern or skew
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.4$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb_tbp$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb_tbp$TARGET_WINS),lty=2)
REMOVE OUTLIERS AND REFIT
Per Cooks Distance, remove items 836, 821, 1920, 1737, 1515
############ FIRST SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem <- mb_tbp[-c(836, 821, 1920, 1737, 1515),]
# save first data set
mb_tbp_orig <- mb_tbp
# renumber rows
rownames(mb_rem) <- 1:nrow(mb_rem)Now refit first model from above: all variables
Yields r^2= 0.2944, Adj r^2 = 0.2931, F = 225.5
# keep the clean data set pure
mb_tbp <- mb_rem
# fit model
model <- lm(data=mb_tbp, TARGET_WINS ~ .- INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.431 -8.016 0.145 8.107 46.678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.3616387 3.9168318 13.879 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.0391427 0.0100487 -3.895 0.000101 ***
## TEAM_PITCHING_H 0.0004962 0.0035469 0.140 0.888754
## TEAM_PITCHING_BB -0.0063810 0.0037061 -1.722 0.085255 .
## TEAM_PITCHING_SO 0.0216633 0.0084996 2.549 0.010880 *
## TEAM_FIELDING_E -0.0441685 0.0031036 -14.232 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.1600617 0.0121816 -13.140 < 0.0000000000000002 ***
## TB_PLUS 0.0266454 0.0021256 12.536 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.03 on 2159 degrees of freedom
## Multiple R-squared: 0.3048, Adjusted R-squared: 0.3025
## F-statistic: 135.2 on 7 and 2159 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_H
# ----------------------
# remove TEAM_PITCHING_H
model.2 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.427 -7.980 0.143 8.125 46.678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.670270 3.235709 16.896 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.040401 0.004482 -9.014 < 0.0000000000000002 ***
## TEAM_PITCHING_BB -0.006657 0.003139 -2.121 0.034 *
## TEAM_PITCHING_SO 0.022711 0.004019 5.651 0.0000000181 ***
## TEAM_FIELDING_E -0.044089 0.003051 -14.451 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.159894 0.012120 -13.193 < 0.0000000000000002 ***
## TB_PLUS 0.026896 0.001146 23.459 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.03 on 2160 degrees of freedom
## Multiple R-squared: 0.3048, Adjusted R-squared: 0.3028
## F-statistic: 157.8 on 6 and 2160 DF, p-value: < 0.00000000000000022# All p-values < .05 so check collinearity
vif(model.2)## TEAM_BATTING_SO TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E
## 15.343276 1.680924 12.009587 2.981041
## TEAM_FIELDING_DP TB_PLUS
## 1.666368 1.641975# vif indicates remove TEAM_BATTING_SO or TEAM_PITCHING_SO, so remove PITCHING_SO again
# ----------------------
# remove TEAM_PITCHING_SO
model.3 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO,
## data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.795 -8.018 0.197 8.113 46.888
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.267886 3.230538 16.179 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.016264 0.001368 -11.886 <0.0000000000000002 ***
## TEAM_PITCHING_BB -0.001378 0.003018 -0.457 0.648
## TEAM_FIELDING_E -0.034211 0.002518 -13.585 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.153843 0.012159 -12.653 <0.0000000000000002 ***
## TB_PLUS 0.025628 0.001132 22.633 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.12 on 2161 degrees of freedom
## Multiple R-squared: 0.2945, Adjusted R-squared: 0.2928
## F-statistic: 180.4 on 5 and 2161 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_BB
# ----------------------
# remove TEAM_PITCHING_BB
model.4 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_H - TEAM_PITCHING_SO -
## TEAM_PITCHING_BB, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.678 -7.990 0.207 8.069 46.752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.3303439 3.2270486 16.22 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.0161904 0.0013585 -11.92 <0.0000000000000002 ***
## TEAM_FIELDING_E -0.0342138 0.0025179 -13.59 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.1543417 0.0121072 -12.75 <0.0000000000000002 ***
## TB_PLUS 0.0253371 0.0009362 27.06 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.12 on 2162 degrees of freedom
## Multiple R-squared: 0.2944, Adjusted R-squared: 0.2931
## F-statistic: 225.5 on 4 and 2162 DF, p-value: < 0.00000000000000022# pvals all < .05 so check collinearity
vif(model.4)## TEAM_BATTING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TB_PLUS
## 1.390169 2.002462 1.640012 1.079847anova(model)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_SO 1 2189 2189 15.114 0.0001043 ***
## TEAM_PITCHING_H 1 13926 13926 96.157 < 0.00000000000000022 ***
## TEAM_PITCHING_BB 1 21937 21937 151.472 < 0.00000000000000022 ***
## TEAM_PITCHING_SO 1 36638 36638 252.979 < 0.00000000000000022 ***
## TEAM_FIELDING_E 1 14063 14063 97.103 < 0.00000000000000022 ***
## TEAM_FIELDING_DP 1 25556 25556 176.456 < 0.00000000000000022 ***
## TB_PLUS 1 22758 22758 157.139 < 0.00000000000000022 ***
## Residuals 2159 312681 145
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# no collinearity so STOPDiagnostics
Plots for Fielding_E shows skew. Others are pretty linear
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.4, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Some lack of Constant variability in Resid vs. Fitted at very large values of Yhat; normal distribution of residuals; most residuals within 2 std dev and well within Cook’s distance
#Figure 5.6 on page 129 MARR text
par(mfrow=c(2,2))
plot(model.4)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for PITCHING_SO, FIELDING_E, FIELDING_DP, TB_PLUS
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.4)
par(mfrow=c(2,2))
plot(mb_tbp$TEAM_BATTING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TB_PLUS, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship with no pattern or skew
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.4$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb_tbp$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb_tbp$TARGET_WINS),lty=2)
Now try same model but with FIELD_E transformed using Box-Cox
# TEAM_FIELDING_E: Box-cox says -1 power transform => 1/y
mb_tbp$TEAM_FIELDING_E <- 1/mb_tbp$TEAM_FIELDING_ENow refit first model from above: Start with all variables
Yields r^2= 0.2932, Adj r^2 = 0.2919, F = 224.3
# fit model
model <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX)
summary(model)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.857 -7.906 0.310 8.238 43.204
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 44.224515 3.776056 11.712 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.033405 0.010094 -3.310 0.00095 ***
## TEAM_PITCHING_H -0.003282 0.003541 -0.927 0.35409
## TEAM_PITCHING_BB -0.002060 0.003735 -0.552 0.58128
## TEAM_PITCHING_SO 0.008654 0.008520 1.016 0.30983
## TEAM_FIELDING_E 2367.159014 184.199571 12.851 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.138889 0.011786 -11.784 < 0.0000000000000002 ***
## TB_PLUS 0.023995 0.002172 11.049 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.13 on 2159 degrees of freedom
## Multiple R-squared: 0.2936, Adjusted R-squared: 0.2913
## F-statistic: 128.2 on 7 and 2159 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_BB
# ----------------------
# remove TEAM_PITCHING_BB
model.2 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB)
summary(model.2)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.992 -7.888 0.292 8.267 43.111
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 43.622192 3.614144 12.070 < 0.0000000000000002 ***
## TEAM_BATTING_SO -0.030130 0.008160 -3.692 0.000228 ***
## TEAM_PITCHING_H -0.002208 0.002957 -0.747 0.455333
## TEAM_PITCHING_SO 0.005899 0.006900 0.855 0.392714
## TEAM_FIELDING_E 2371.413436 184.008382 12.888 < 0.0000000000000002 ***
## TEAM_FIELDING_DP -0.139854 0.011654 -12.001 < 0.0000000000000002 ***
## TB_PLUS 0.023137 0.001515 15.268 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.13 on 2160 degrees of freedom
## Multiple R-squared: 0.2935, Adjusted R-squared: 0.2915
## F-statistic: 149.5 on 6 and 2160 DF, p-value: < 0.00000000000000022# p-values say remove TEAM_PITCHING_H
# ----------------------
# remove TEAM_PITCHING_H
model.3 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H)
summary(model.3)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H,
## data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.307 -7.918 0.345 8.182 42.508
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.0041157 2.8921302 14.524 < 0.0000000000000002
## TEAM_BATTING_SO -0.0247576 0.0038507 -6.429 0.000000000157
## TEAM_PITCHING_SO 0.0013897 0.0033380 0.416 0.677
## TEAM_FIELDING_E 2387.2244422 182.7672567 13.062 < 0.0000000000000002
## TEAM_FIELDING_DP -0.1396085 0.0116479 -11.986 < 0.0000000000000002
## TB_PLUS 0.0222592 0.0009561 23.280 < 0.0000000000000002
##
## (Intercept) ***
## TEAM_BATTING_SO ***
## TEAM_PITCHING_SO
## TEAM_FIELDING_E ***
## TEAM_FIELDING_DP ***
## TB_PLUS ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.13 on 2161 degrees of freedom
## Multiple R-squared: 0.2933, Adjusted R-squared: 0.2917
## F-statistic: 179.4 on 5 and 2161 DF, p-value: < 0.00000000000000022# p-vals say remove TEAM_PITCHING_SO
# ----------------------
# remove TEAM_PITCHING_SO
model.4 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H - TEAM_PITCHING_SO)
summary(model.4)##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H -
## TEAM_PITCHING_SO, data = mb_tbp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.310 -7.909 0.320 8.191 42.644
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.1597649 2.8673139 14.70 <0.0000000000000002 ***
## TEAM_BATTING_SO -0.0233150 0.0016789 -13.89 <0.0000000000000002 ***
## TEAM_FIELDING_E 2366.8259932 176.0432309 13.45 <0.0000000000000002 ***
## TEAM_FIELDING_DP -0.1400776 0.0115910 -12.09 <0.0000000000000002 ***
## TB_PLUS 0.0222811 0.0009545 23.34 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.13 on 2162 degrees of freedom
## Multiple R-squared: 0.2932, Adjusted R-squared: 0.2919
## F-statistic: 224.3 on 4 and 2162 DF, p-value: < 0.00000000000000022# pvals all < .05 so check collinearity
vif(model.4)## TEAM_BATTING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TB_PLUS
## 2.119682 2.906955 1.500660 1.120613# no collinearity so STOP
options(scipen=999)
model.4##
## Call:
## lm(formula = TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H -
## TEAM_PITCHING_SO, data = mb_tbp)
##
## Coefficients:
## (Intercept) TEAM_BATTING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 42.15976 -0.02331 2366.82599 -0.14008
## TB_PLUS
## 0.02228anova(model.4)## Analysis of Variance Table
##
## Response: TARGET_WINS
## Df Sum Sq Mean Sq F value Pr(>F)
## TEAM_BATTING_SO 1 2189 2189 14.888 0.0001174 ***
## TEAM_FIELDING_E 1 34681 34681 235.888 < 0.00000000000000022 ***
## TEAM_FIELDING_DP 1 14903 14903 101.365 < 0.00000000000000022 ***
## TB_PLUS 1 80112 80112 544.895 < 0.00000000000000022 ***
## Residuals 2162 317863 147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Diagnostics
Plots show all variables are linear to response
# CREATE ADDED VARIABLE PLOTS TO ASSESS predictor vs response
avPlots(model.4, id.n = 2)
SUMMARY MODEL DIAGNOSTIC PLOTS
Plots: Some lack of Constant variability in Resid vs. Fitted at very large values of Yhat; normal distribution of residuals; most residuals within 2 std dev and well within Cook’s distance
#Figure 5.6 on page 129 MARR text
par(mfrow=c(2,2))
plot(model.4)
PLOT STANDARDIZED RESIDUALS AGAINST EACH PREDICTOR
Results show lack of constant variability for PITCHING_SO, FIELDING_E, FIELDING_DP, TB_PLUS
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
StanRes1 <- rstandard(model.4)
par(mfrow=c(2,2))
plot(mb_tbp$TEAM_PITCHING_SO, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_E, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TEAM_FIELDING_DP, StanRes1, ylab="Standardized Residuals")
plot(mb_tbp$TB_PLUS, StanRes1, ylab="Standardized Residuals")
PLOT Y AGAINST FITTED VALUES
Plot shows a linear relationship with no pattern or skew
# get rows have no NA's from data frame
# NoNA <- mb_mods[!rowSums(is.na(mb_mods[1:13])), ]
fit1 <- model.4$fitted.values
par(mfrow = c(1,1))
plot(fit1, mb_tbp$TARGET_WINS,xlab="Fitted Values")
abline(lsfit(fit1, mb_tbp$TARGET_WINS),lty=2)
# clean up objects in memory
rm(list = ls())Model 4: Sabermetrics Model
library(car)# read EVALUATION data set
eval_data <- read.csv("https://raw.githubusercontent.com/jtopor/CUNY-MSDA-621/master/HW-1/moneyball-evaluation-data.csv")
# read training data set
mb_e <- read.csv("https://raw.githubusercontent.com/jtopor/CUNY-MSDA-621/master/HW-1/moneyball-training-data.csv")
#eliminate index column
# mb_e1 <- mb_e[,-1]
mb_e1 <- mb_e
#####Creating a new column for batting singles and eliminating hits for batting
#add singles column for hitting
mb_e1$TEAM_BATTING_1B <- as.numeric(mb_e1$TEAM_BATTING_H-mb_e1$TEAM_BATTING_2B-mb_e1$TEAM_BATTING_3B-mb_e1$TEAM_BATTING_HR)
mb_e1 <- mb_e1[,-3]
mb_e1 <- as.data.frame(mb_e1)
eval_data$TEAM_BATTING_1B <- as.numeric(eval_data$TEAM_BATTING_H - eval_data$TEAM_BATTING_2B - eval_data$TEAM_BATTING_3B - eval_data$TEAM_BATTING_HR)
# HITS is in second column in eval data
eval_data <- eval_data[,-2]
# ADD A DUMMY COLUMN TO EVAL DATA FOR TARGET WINS
eval_data$TARGET_WINS <- 0Eliminate HBP, CS, and pitching HR’s.
mb <- mb_e1[,-c(9,10,12)]
# summary(mb)
eval_data <- eval_data[,-c(8,9,11)]
# summary(eval_data)Build model for batting SO using Gelman approach
#take out double plays + pitching SO + SB as data set is incomplete + Wins as they are not present in the evaluation data
BSO.1 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB -TARGET_WINS)
summary(BSO.1)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -367.76 -82.46 -3.12 76.44 401.62
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1978.17499 44.47257 44.481 < 0.0000000000000002 ***
## TEAM_BATTING_2B -0.17459 0.17430 -1.002 0.316646
## TEAM_BATTING_3B -2.29879 0.24381 -9.429 < 0.0000000000000002 ***
## TEAM_BATTING_HR 0.88912 0.18212 4.882 0.00000114 ***
## TEAM_BATTING_BB 0.98359 0.43292 2.272 0.023203 *
## TEAM_PITCHING_H 0.36442 0.15123 2.410 0.016066 *
## TEAM_PITCHING_BB -1.17748 0.41011 -2.871 0.004137 **
## TEAM_FIELDING_E -0.29146 0.07594 -3.838 0.000128 ***
## TEAM_BATTING_1B -1.45473 0.16446 -8.845 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.1 on 1826 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7248, Adjusted R-squared: 0.7236
## F-statistic: 601.1 on 8 and 1826 DF, p-value: < 0.00000000000000022#eliminate doubles
BSO.2 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B)
summary(BSO.2)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B,
## data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -366.77 -82.05 -2.74 76.89 399.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1975.11400 44.36750 44.517 < 0.0000000000000002 ***
## TEAM_BATTING_3B -2.17815 0.21199 -10.275 < 0.0000000000000002 ***
## TEAM_BATTING_HR 1.02471 0.12183 8.411 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.59635 0.19483 3.061 0.002240 **
## TEAM_PITCHING_H 0.22723 0.06414 3.543 0.000406 ***
## TEAM_PITCHING_BB -0.81040 0.18409 -4.402 0.0000113 ***
## TEAM_FIELDING_E -0.26762 0.07212 -3.711 0.000213 ***
## TEAM_BATTING_1B -1.31541 0.08777 -14.988 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.1 on 1827 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7246, Adjusted R-squared: 0.7236
## F-statistic: 686.8 on 7 and 1827 DF, p-value: < 0.00000000000000022vif(BSO.2)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_PITCHING_H
## 2.984944 6.215565 39.110249 17.594555
## TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_BATTING_1B
## 45.384546 2.448073 8.602393# vif says remove TEAM_PITCHING_BB
BSO.3 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B - TEAM_PITCHING_BB)
summary(BSO.3)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_PITCHING_BB, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -385.33 -80.03 -1.99 77.48 399.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1980.01367 44.57596 44.419 < 0.0000000000000002 ***
## TEAM_BATTING_3B -1.79602 0.19437 -9.240 < 0.0000000000000002 ***
## TEAM_BATTING_HR 1.42972 0.08027 17.812 < 0.0000000000000002 ***
## TEAM_BATTING_BB -0.24810 0.03431 -7.230 0.000000000000706 ***
## TEAM_PITCHING_H -0.03911 0.02139 -1.828 0.0677 .
## TEAM_FIELDING_E -0.29047 0.07229 -4.018 0.000061107070801 ***
## TEAM_BATTING_1B -0.99171 0.04816 -20.591 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.6 on 1828 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7217, Adjusted R-squared: 0.7208
## F-statistic: 790.1 on 6 and 1828 DF, p-value: < 0.00000000000000022# pvals say remove PITCHING_H
BSO.4 <- lm(data=mb, TEAM_BATTING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_SO -TEAM_BASERUN_SB - TARGET_WINS -TEAM_BATTING_2B - TEAM_PITCHING_BB - TEAM_PITCHING_H)
summary(BSO.4)##
## Call:
## lm(formula = TEAM_BATTING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_SO - TEAM_BASERUN_SB - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_PITCHING_BB - TEAM_PITCHING_H, data = mb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -384.09 -79.88 -1.51 77.07 393.44
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1986.07279 44.48099 44.650 < 0.0000000000000002 ***
## TEAM_BATTING_3B -1.86025 0.19129 -9.725 < 0.0000000000000002 ***
## TEAM_BATTING_HR 1.37824 0.07521 18.325 < 0.0000000000000002 ***
## TEAM_BATTING_BB -0.25047 0.03431 -7.300 0.000000000000428 ***
## TEAM_FIELDING_E -0.29947 0.07217 -4.149 0.000034869615225 ***
## TEAM_BATTING_1B -1.04331 0.03905 -26.719 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 114.7 on 1829 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.7212, Adjusted R-squared: 0.7204
## F-statistic: 946.2 on 5 and 1829 DF, p-value: < 0.00000000000000022vif(BSO.4)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_FIELDING_E
## 2.403283 2.342414 1.199339 2.424099
## TEAM_BATTING_1B
## 1.683596##All p-values are low with a 686.8 F-statistic and adjusted R squared of 0.7236
#take a look
par(mfrow=c(2,2))
plot(BSO.2)
# ---------------------------------------
# function definition for impute function
impute <- function (a, a.impute){
ifelse (is.na(a), a.impute,a)
}
# ---------------------------------------
#prediction function
pred.BSO <- round(predict(BSO.4, mb))
BSO.imp <- impute(mb$TEAM_BATTING_SO, pred.BSO)
# impute the evaluation data
pred_eval.BSO <- round(predict(BSO.4, eval_data))
eval.BSO.imp <- impute(eval_data$TEAM_BATTING_SO, pred_eval.BSO)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb$TEAM_BATTING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 548.0 750.0 735.6 930.0 1399.0 102summary(BSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 543.8 730.0 727.6 925.0 1399.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb$TEAM_BATTING_SO, breaks = 200)
hist(BSO.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data$TEAM_BATTING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 545.0 686.0 709.3 912.0 1268.0 18summary(eval.BSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 532.5 677.0 699.8 904.5 1268.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data$TEAM_BATTING_SO, breaks = 30)
hist(eval.BSO.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb1 <- mb
mb1$TEAM_BATTING_SO <- BSO.imp
eval_data.1 <- eval_data
eval_data.1$TEAM_BATTING_SO <- eval.BSO.imp
Build model for Pitching SO
#take out double plays + SB as data set is incomplete and wins as they are not present in evaluation data
PSO.1 <- lm(data=mb1, TEAM_PITCHING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_BASERUN_SB - TARGET_WINS)
summary(PSO.1)##
## Call:
## lm(formula = TEAM_PITCHING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_BASERUN_SB - TARGET_WINS, data = mb1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -130.988 -3.674 1.299 4.675 147.753
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.693339 8.122849 0.085 0.932
## TEAM_BATTING_2B -0.291561 0.022062 -13.216 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.268622 0.031593 -8.503 < 0.0000000000000002 ***
## TEAM_BATTING_HR -0.269698 0.023194 -11.628 < 0.0000000000000002 ***
## TEAM_BATTING_BB -0.883985 0.054857 -16.114 < 0.0000000000000002 ***
## TEAM_BATTING_SO 1.044883 0.002961 352.860 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.270090 0.019167 14.092 < 0.0000000000000002 ***
## TEAM_PITCHING_BB 0.850575 0.052011 16.354 < 0.0000000000000002 ***
## TEAM_FIELDING_E -0.057521 0.009648 -5.962 0.00000000299 ***
## TEAM_BATTING_1B -0.280665 0.021251 -13.207 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.43 on 1825 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.9958, Adjusted R-squared: 0.9958
## F-statistic: 4.809e+04 on 9 and 1825 DF, p-value: < 0.00000000000000022vif(PSO.1)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 7.903547 4.140572 14.070952 193.640509
## TEAM_BATTING_SO TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_FIELDING_E
## 3.633459 98.139615 226.271134 2.736403
## TEAM_BATTING_1B
## 31.499003# vif says remove TEAM_PITCHING_BB
PSO.2 <- lm(data=mb1, TEAM_PITCHING_SO~. - INDEX -TEAM_FIELDING_DP -TEAM_BASERUN_SB - TARGET_WINS - TEAM_PITCHING_BB)
summary(PSO.2)##
## Call:
## lm(formula = TEAM_PITCHING_SO ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_BASERUN_SB - TARGET_WINS - TEAM_PITCHING_BB, data = mb1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -126.748 -4.347 1.094 5.334 149.232
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.722036 8.665285 1.353 0.1763
## TEAM_BATTING_2B -0.613714 0.010633 -57.719 <0.0000000000000002 ***
## TEAM_BATTING_3B -0.578732 0.027050 -21.395 <0.0000000000000002 ***
## TEAM_BATTING_HR -0.601828 0.011993 -50.181 <0.0000000000000002 ***
## TEAM_BATTING_BB 0.010252 0.004704 2.180 0.0294 *
## TEAM_BATTING_SO 1.041636 0.003163 329.346 <0.0000000000000002 ***
## TEAM_PITCHING_H 0.580032 0.003060 189.545 <0.0000000000000002 ***
## TEAM_FIELDING_E -0.097555 0.009990 -9.765 <0.0000000000000002 ***
## TEAM_BATTING_1B -0.610139 0.007239 -84.289 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.45 on 1826 degrees of freedom
## (441 observations deleted due to missingness)
## Multiple R-squared: 0.9952, Adjusted R-squared: 0.9952
## F-statistic: 4.719e+04 on 8 and 1826 DF, p-value: < 0.00000000000000022vif(PSO.2)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 1.602077 2.648887 3.282938 1.242359
## TEAM_BATTING_SO TEAM_PITCHING_H TEAM_FIELDING_E TEAM_BATTING_1B
## 3.617130 2.183095 2.560245 3.189218#all low P value and F statistic of 4719 with adj R squared of 0.9952
#take a look
par(mfrow=c(2,2))
plot(PSO.2)
#place back in the data base with imputed data for SO's
pred.PSO <- round(predict(PSO.2, mb1))
PSO.imp <- impute(mb1$TEAM_PITCHING_SO, pred.PSO)
# impute the evaluation data
pred_eval.PSO <- round(predict(PSO.2, eval_data.1))
eval.PSO.imp <- impute(eval_data.1$TEAM_PITCHING_SO, pred_eval.PSO)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb1$TEAM_PITCHING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 615.0 813.5 817.7 968.0 19280.0 102summary(PSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 606.0 797.0 807.4 957.0 19280.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb1$TEAM_PITCHING_SO, breaks = 200)
hist(PSO.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.1$TEAM_PITCHING_SO)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 613.0 745.0 799.7 938.0 9963.0 18summary(eval.PSO.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 596.0 728.0 785.4 927.5 9963.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.1$TEAM_PITCHING_SO, breaks = 30)
hist(eval.PSO.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb2 <- mb1
mb2$TEAM_PITCHING_SO <- PSO.imp
eval_data.2 <- eval_data.1
eval_data.2$TEAM_PITCHING_SO <- eval.PSO.imp
Build model for SB
#Take out DP as incomplete data and target wins
SB.1 <- lm(data=mb2, TEAM_BASERUN_SB~. -INDEX -TEAM_FIELDING_DP - TARGET_WINS)
summary(SB.1)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -115.054 -32.496 -5.714 28.546 206.666
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -181.56290 25.61997 -7.087 0.000000000001918208 ***
## TEAM_BATTING_2B -0.21829 0.07305 -2.988 0.002841 **
## TEAM_BATTING_3B 0.31700 0.10053 3.153 0.001640 **
## TEAM_BATTING_HR -0.61700 0.07599 -8.119 0.000000000000000827 ***
## TEAM_BATTING_BB 0.12841 0.18355 0.700 0.484255
## TEAM_BATTING_SO 0.43941 0.07872 5.582 0.000000027139177568 ***
## TEAM_PITCHING_H 0.20258 0.06368 3.181 0.001489 **
## TEAM_PITCHING_BB -0.08197 0.17430 -0.470 0.638206
## TEAM_PITCHING_SO -0.25116 0.07480 -3.358 0.000801 ***
## TEAM_FIELDING_E 0.32079 0.02796 11.473 < 0.0000000000000002 ***
## TEAM_BATTING_1B -0.12224 0.07046 -1.735 0.082937 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.26 on 1926 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3552, Adjusted R-squared: 0.3518
## F-statistic: 106.1 on 10 and 1926 DF, p-value: < 0.00000000000000022#eliminate pitching BB's
SB.2 <- lm(data=mb2, TEAM_BASERUN_SB~. -INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS)
summary(SB.2)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -115.234 -32.317 -5.706 28.512 206.540
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -182.64502 25.51127 -7.159 0.00000000000115 ***
## TEAM_BATTING_2B -0.19473 0.05316 -3.663 0.000256 ***
## TEAM_BATTING_3B 0.34027 0.08749 3.889 0.000104 ***
## TEAM_BATTING_HR -0.59236 0.05503 -10.765 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.04234 0.01376 3.076 0.002127 **
## TEAM_BATTING_SO 0.45256 0.07357 6.151 0.00000000093186 ***
## TEAM_PITCHING_H 0.17992 0.04164 4.321 0.00001629409305 ***
## TEAM_PITCHING_SO -0.26348 0.07004 -3.762 0.000174 ***
## TEAM_FIELDING_E 0.32263 0.02768 11.655 < 0.0000000000000002 ***
## TEAM_BATTING_1B -0.09787 0.04774 -2.050 0.040499 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.25 on 1927 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3551, Adjusted R-squared: 0.3521
## F-statistic: 117.9 on 9 and 1927 DF, p-value: < 0.00000000000000022#eliminate singles
SB.3 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB -TEAM_BATTING_1B - TARGET_WINS)
summary(SB.3)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TEAM_BATTING_1B - TARGET_WINS, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -113.836 -32.731 -5.467 28.523 205.971
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -201.72737 23.77215 -8.486 < 0.0000000000000002 ***
## TEAM_BATTING_2B -0.11845 0.03799 -3.118 0.00185 **
## TEAM_BATTING_3B 0.40962 0.08075 5.073 0.000000429809 ***
## TEAM_BATTING_HR -0.51178 0.03855 -13.277 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.04187 0.01377 3.040 0.00240 **
## TEAM_BATTING_SO 0.32253 0.03731 8.645 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.10155 0.01650 6.154 0.000000000917 ***
## TEAM_PITCHING_SO -0.13495 0.03125 -4.318 0.000016553542 ***
## TEAM_FIELDING_E 0.33595 0.02693 12.475 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.29 on 1928 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3537, Adjusted R-squared: 0.351
## F-statistic: 131.9 on 8 and 1928 DF, p-value: < 0.00000000000000022#simplify the model by taking out pitching
SB.4 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB -TEAM_BATTING_1B - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H)
summary(SB.4)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TEAM_BATTING_1B - TARGET_WINS - TEAM_PITCHING_SO -
## TEAM_PITCHING_H, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -117.914 -33.217 -5.623 29.822 199.657
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -83.147587 14.021226 -5.930 0.00000000357797 ***
## TEAM_BATTING_2B 0.041592 0.028337 1.468 0.1423
## TEAM_BATTING_3B 0.572336 0.077093 7.424 0.00000000000017 ***
## TEAM_BATTING_HR -0.405437 0.034672 -11.694 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.035111 0.013862 2.533 0.0114 *
## TEAM_BATTING_SO 0.151522 0.008054 18.814 < 0.0000000000000002 ***
## TEAM_FIELDING_E 0.360947 0.026930 13.403 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.77 on 1930 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3395, Adjusted R-squared: 0.3374
## F-statistic: 165.3 on 6 and 1930 DF, p-value: < 0.00000000000000022#add singles back in
SB.5 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H)
summary(SB.5)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H,
## data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.276 -33.011 -5.119 28.546 203.041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -187.229045 25.631485 -7.305 0.000000000000405 ***
## TEAM_BATTING_2B -0.001075 0.029522 -0.036 0.97096
## TEAM_BATTING_3B 0.519499 0.077423 6.710 0.000000000025523 ***
## TEAM_BATTING_HR -0.407981 0.034476 -11.834 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.039950 0.013818 2.891 0.00388 **
## TEAM_BATTING_SO 0.176220 0.009496 18.558 < 0.0000000000000002 ***
## TEAM_FIELDING_E 0.357712 0.026783 13.356 < 0.0000000000000002 ***
## TEAM_BATTING_1B 0.091975 0.019007 4.839 0.000001408714177 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.5 on 1929 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3474, Adjusted R-squared: 0.345
## F-statistic: 146.7 on 7 and 1929 DF, p-value: < 0.00000000000000022#eliminate doubles
SB.6 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H - TEAM_BATTING_2B)
summary(SB.6)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H -
## TEAM_BATTING_2B, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.233 -32.996 -5.134 28.584 203.038
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -187.197711 25.610401 -7.309 0.000000000000391 ***
## TEAM_BATTING_3B 0.518983 0.076096 6.820 0.000000000012126 ***
## TEAM_BATTING_HR -0.408387 0.032612 -12.522 < 0.0000000000000002 ***
## TEAM_BATTING_BB 0.039905 0.013760 2.900 0.00377 **
## TEAM_BATTING_SO 0.176199 0.009475 18.596 < 0.0000000000000002 ***
## TEAM_FIELDING_E 0.357907 0.026237 13.642 < 0.0000000000000002 ***
## TEAM_BATTING_1B 0.091768 0.018135 5.060 0.000000458248716 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.49 on 1930 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3474, Adjusted R-squared: 0.3454
## F-statistic: 171.2 on 6 and 1930 DF, p-value: < 0.00000000000000022#eliminate walks
SB.7 <- lm(data=mb2, TEAM_BASERUN_SB~. - INDEX -TEAM_FIELDING_DP -TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H - TEAM_BATTING_2B - TEAM_BATTING_BB)
summary(SB.7)##
## Call:
## lm(formula = TEAM_BASERUN_SB ~ . - INDEX - TEAM_FIELDING_DP -
## TEAM_PITCHING_BB - TARGET_WINS - TEAM_PITCHING_SO - TEAM_PITCHING_H -
## TEAM_BATTING_2B - TEAM_BATTING_BB, data = mb2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.972 -32.412 -5.034 29.206 206.559
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -160.935881 24.001884 -6.705 0.0000000000263 ***
## TEAM_BATTING_3B 0.519666 0.076241 6.816 0.0000000000125 ***
## TEAM_BATTING_HR -0.380719 0.031245 -12.185 < 0.0000000000000002 ***
## TEAM_BATTING_SO 0.171459 0.009351 18.336 < 0.0000000000000002 ***
## TEAM_FIELDING_E 0.345292 0.025923 13.320 < 0.0000000000000002 ***
## TEAM_BATTING_1B 0.089234 0.018148 4.917 0.0000009536160 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.58 on 1931 degrees of freedom
## (339 observations deleted due to missingness)
## Multiple R-squared: 0.3446, Adjusted R-squared: 0.3429
## F-statistic: 203 on 5 and 1931 DF, p-value: < 0.00000000000000022#all low P value and F statistic of 202.9 with adj R squared of 0.3427
#take a look
par(mfrow=c(2,2))
plot(SB.7)
#place back in the data base with imputed data for SB's
pred.SB <- round(predict(SB.7, mb2))
SB.imp <- impute(mb2$TEAM_BASERUN_SB, pred.SB)
# impute the evaluation data
pred_eval.SB <- round(predict(SB.7, eval_data.2))
eval.SB.imp <- impute(eval_data.2$TEAM_BASERUN_SB, pred_eval.SB)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb2$TEAM_BASERUN_SB)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 66.0 101.0 124.8 156.0 697.0 131summary(SB.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 67.0 106.0 137.8 172.0 697.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb2$TEAM_BASERUN_SB, breaks = 200)
hist(SB.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.2$TEAM_BASERUN_SB)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 59.0 92.0 123.7 151.8 580.0 13summary(eval.SB.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 60.5 96.0 134.9 164.5 580.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.2$TEAM_BASERUN_SB, breaks = 30)
hist(eval.SB.imp, breaks = 30)
###################################################
# update dataframes with imputed values
mb3 <- mb2
mb3$TEAM_BASERUN_SB <- SB.imp
eval_data.3 <- eval_data.2
eval_data.3$TEAM_BASERUN_SB <- eval.SB.imp
Build model to replace DP
#remove target wins
DP.1 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS)
summary(DP.1)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.685 -13.815 -0.923 13.056 64.642
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 119.570410 11.008885 10.861 < 0.0000000000000002 ***
## TEAM_BATTING_2B 0.015947 0.013100 1.217 0.22360
## TEAM_BATTING_3B -0.095545 0.031158 -3.066 0.00220 **
## TEAM_BATTING_HR 0.062465 0.016446 3.798 0.00015 ***
## TEAM_BATTING_BB 0.195238 0.027750 7.036 0.00000000000272 ***
## TEAM_BATTING_SO -0.107809 0.015781 -6.831 0.00000000001116 ***
## TEAM_BASERUN_SB -0.126130 0.009838 -12.820 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.009159 0.004069 2.251 0.02448 *
## TEAM_PITCHING_BB -0.153349 0.025468 -6.021 0.00000000205698 ***
## TEAM_PITCHING_SO 0.090351 0.014318 6.310 0.00000000034296 ***
## TEAM_FIELDING_E -0.068602 0.009653 -7.107 0.00000000000165 ***
## TEAM_BATTING_1B 0.024316 0.010083 2.412 0.01598 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.05 on 1978 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4185, Adjusted R-squared: 0.4153
## F-statistic: 129.4 on 11 and 1978 DF, p-value: < 0.00000000000000022#remove batting 2B's
DP.2 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS - TEAM_BATTING_2B)
summary(DP.2)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.620 -14.051 -1.043 12.979 64.061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 120.547069 10.980952 10.978 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.087844 0.030513 -2.879 0.00403 **
## TEAM_BATTING_HR 0.065419 0.016268 4.021 0.00006003296882195 ***
## TEAM_BATTING_BB 0.200115 0.027463 7.287 0.00000000000045639 ***
## TEAM_BATTING_SO -0.107359 0.015779 -6.804 0.00000000001344522 ***
## TEAM_BASERUN_SB -0.126208 0.009839 -12.827 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.010913 0.003806 2.868 0.00418 **
## TEAM_PITCHING_BB -0.157287 0.025265 -6.226 0.00000000058410192 ***
## TEAM_PITCHING_SO 0.090027 0.014318 6.288 0.00000000039501280 ***
## TEAM_FIELDING_E -0.072227 0.009183 -7.865 0.00000000000000601 ***
## TEAM_BATTING_1B 0.024008 0.010081 2.381 0.01734 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.06 on 1979 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4181, Adjusted R-squared: 0.4152
## F-statistic: 142.2 on 10 and 1979 DF, p-value: < 0.00000000000000022# results show that EVERYTHING ELSE is statistically signficant, so:
# run vif to check for collinearity
vif(DP.2)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## 2.378033 4.489647 40.081217 61.937276
## TEAM_BASERUN_SB TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_PITCHING_SO
## 2.207539 10.533005 33.459414 51.795257
## TEAM_FIELDING_E TEAM_BATTING_1B
## 6.392623 4.748132# results show TEAM_BATTING_SO should be removed
# remove TEAM_BATTING_SO
DP.3 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO)
summary(DP.3)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -70.858 -14.365 -0.308 13.180 68.663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.364168 10.931590 9.821 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.075566 0.030806 -2.453 0.01425 *
## TEAM_BATTING_HR 0.049820 0.016289 3.059 0.00225 **
## TEAM_BATTING_BB 0.059620 0.018312 3.256 0.00115 **
## TEAM_BASERUN_SB -0.135254 0.009860 -13.717 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.016359 0.003763 4.348 0.000014452154 ***
## TEAM_PITCHING_BB -0.022297 0.015820 -1.409 0.15887
## TEAM_PITCHING_SO -0.003527 0.004037 -0.874 0.38244
## TEAM_FIELDING_E -0.057520 0.009027 -6.372 0.000000000231 ***
## TEAM_BATTING_1B 0.020596 0.010183 2.023 0.04326 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.28 on 1980 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4045, Adjusted R-squared: 0.4018
## F-statistic: 149.4 on 9 and 1980 DF, p-value: < 0.00000000000000022# p-value says remove TEAM_PITCHING_SO;
# remove TEAM_PITCHING_SO
DP.4 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TEAM_BATTING_2B -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO)
summary(DP.4)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TEAM_BATTING_2B -
## TARGET_WINS - TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.801 -14.399 -0.536 13.355 68.091
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 100.469748 7.563815 13.283 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.067701 0.029459 -2.298 0.021658 *
## TEAM_BATTING_HR 0.045067 0.015352 2.936 0.003368 **
## TEAM_BATTING_BB 0.063875 0.017651 3.619 0.000303 ***
## TEAM_BASERUN_SB -0.138490 0.009137 -15.157 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.015675 0.003680 4.259 0.000021452526 ***
## TEAM_PITCHING_BB -0.025444 0.015403 -1.652 0.098711 .
## TEAM_FIELDING_E -0.055612 0.008758 -6.350 0.000000000266 ***
## TEAM_BATTING_1B 0.025138 0.008755 2.871 0.004134 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.28 on 1981 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4043, Adjusted R-squared: 0.4018
## F-statistic: 168 on 8 and 1981 DF, p-value: < 0.00000000000000022vif(DP.4)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.167319 3.909442 16.189150 1.861261
## TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_FIELDING_E TEAM_BATTING_1B
## 9.630593 12.159984 5.684878 3.501740# P values and vif both indicate remove TEAM_PITCHING_BB
# remove TEAM_PITCHING_BB
DP.5 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB)
summary(DP.5)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.547 -14.352 -0.402 13.240 66.253
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 98.606000 7.482458 13.178 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.071477 0.029383 -2.433 0.0151 *
## TEAM_BATTING_HR 0.057086 0.013524 4.221 0.000025413117 ***
## TEAM_BATTING_BB 0.036352 0.005830 6.235 0.000000000551 ***
## TEAM_BASERUN_SB -0.138165 0.009139 -15.118 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.011078 0.002409 4.598 0.000004528538 ***
## TEAM_FIELDING_E -0.051135 0.008332 -6.137 0.000000001010 ***
## TEAM_BATTING_1B 0.032220 0.007637 4.219 0.000025688127 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.29 on 1982 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.4034, Adjusted R-squared: 0.4013
## F-statistic: 191.5 on 7 and 1982 DF, p-value: < 0.00000000000000022vif(DP.5)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.154275 3.031272 1.764845 1.860396
## TEAM_PITCHING_H TEAM_FIELDING_E TEAM_BATTING_1B
## 4.123897 5.140583 2.662224# vif says remove TEAM_FIELDING_E; p-values all < .05 so remove TEAM_FIELDING_E
DP.6 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E)
summary(DP.6)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E,
## data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.558 -14.399 -0.152 13.362 64.018
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 86.427823 7.280960 11.870 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.093997 0.029422 -3.195 0.00142 **
## TEAM_BATTING_HR 0.091627 0.012411 7.383 0.00000000000022678 ***
## TEAM_BATTING_BB 0.045730 0.005678 8.053 0.00000000000000138 ***
## TEAM_BASERUN_SB -0.155983 0.008745 -17.836 < 0.0000000000000002 ***
## TEAM_PITCHING_H 0.001250 0.001817 0.688 0.49148
## TEAM_BATTING_1B 0.044340 0.007446 5.955 0.00000000306506646 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.48 on 1983 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.3921, Adjusted R-squared: 0.3903
## F-statistic: 213.2 on 6 and 1983 DF, p-value: < 0.00000000000000022vif(DP.6)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.120678 2.506351 1.643620 1.672663
## TEAM_PITCHING_H TEAM_BATTING_1B
## 2.301907 2.484225# now no collinearity but p-values say remove TEAM_PITCHING_H
DP.7 <- lm(data=mb3, TEAM_FIELDING_DP~. - INDEX -TARGET_WINS -TEAM_BATTING_2B - TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E - TEAM_PITCHING_H)
summary(DP.7)##
## Call:
## lm(formula = TEAM_FIELDING_DP ~ . - INDEX - TARGET_WINS - TEAM_BATTING_2B -
## TEAM_BATTING_SO - TEAM_PITCHING_SO - TEAM_PITCHING_BB - TEAM_FIELDING_E -
## TEAM_PITCHING_H, data = mb3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.58 -14.41 -0.19 13.38 63.83
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 85.333602 7.104233 12.012 < 0.0000000000000002 ***
## TEAM_BATTING_3B -0.094593 0.029405 -3.217 0.00132 **
## TEAM_BATTING_HR 0.094530 0.011670 8.100 0.000000000000000947 ***
## TEAM_BATTING_BB 0.044401 0.005339 8.316 < 0.0000000000000002 ***
## TEAM_BASERUN_SB -0.153554 0.008000 -19.194 < 0.0000000000000002 ***
## TEAM_BATTING_1B 0.047370 0.006003 7.892 0.000000000000004884 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.48 on 1984 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.3919, Adjusted R-squared: 0.3904
## F-statistic: 255.8 on 5 and 1984 DF, p-value: < 0.00000000000000022vif(DP.7)## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## 2.118844 2.216648 1.453424 1.400175
## TEAM_BATTING_1B
## 1.615010# no collinearity, all p-values < .05 so stop
#all low P value and F statistic of 255.8 with adj R squared of 0.3904
#take a look
par(mfrow=c(2,2))
plot(DP.7)
#place back in the data base with imputed data for SB's
# NOTE: Changed DP.4 to DP.7 here
pred.DP <- round(predict(DP.7, mb3))
DP.imp <- impute(mb3$TEAM_FIELDING_DP, pred.DP)
# impute the evaluation data
pred_eval.DP <- round(predict(DP.7, eval_data.3))
eval.DP.imp <- impute(eval_data.3$TEAM_FIELDING_DP, pred_eval.DP)
###################################################
# Jims added code for diagnostics of imputation
# first, check summaries to ensure similar values
summary(mb3$TEAM_FIELDING_DP)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 52.0 131.0 149.0 146.4 164.0 228.0 286summary(DP.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 48.0 124.0 145.0 141.5 162.0 228.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(mb3$TEAM_FIELDING_DP, breaks = 200)
hist(DP.imp, breaks = 200)
# ------------------ eval data checks ------------------------
# first, check summaries to ensure similar values
summary(eval_data.3$TEAM_FIELDING_DP)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 69.0 131.0 148.0 146.1 164.0 204.0 31summary(eval.DP.imp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 52.0 123.5 146.0 141.3 160.5 204.0# now plot side-by-side histograms to check similarity of distributions
par(mfrow = c(2,2))
hist(eval_data.3$TEAM_FIELDING_DP, breaks = 30)
hist(eval.DP.imp, breaks = 30)
###################################################
# update data frames with imputed values
mb4 <- mb3
mb4$TEAM_FIELDING_DP <- DP.imp
eval_data.4 <- eval_data.3
eval_data.4$TEAM_FIELDING_DP <- eval.DP.imp
Eliminate unhistorical outliers - DO THIS FOR THE EVAL DATA AS WELL
# check rowcount before removal of outliers
nrow(mb4)## [1] 2276nrow(eval_data.4)## [1] 259############## TEAM PITCHING_SO ############################
#most pitching SO's is 1450. So delete all records with more than 1450 pitching SO's
mb5 <- mb4
# fixed error in this line: dataframe in 'which' call was mb1 so changed to mb5
mb5 <- mb5[which(mb5$TEAM_PITCHING_SO < 1450),]
# eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_PITCHING_SO < 1450),]
# check rowcount
nrow(mb5)## [1] 2251nrow(eval_data.4)## [1] 259############ TEAM_PITCHING_H ##############################
#most ever hits by a team is 1730. So delete all pitching hits >3000 to be conservative with the median
mb6 <- mb5
mb6 <- mb6[which(mb6$TEAM_PITCHING_H < 3001),]
# eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_PITCHING_H < 3001),]
# check rowcount
nrow(mb6)## [1] 2174nrow(eval_data.4)## [1] 259############ TEAM_FIELDING_E ##############################
#most ever errors by a team is 639 by 1883 Philadelphia. Prorating to 162 games gives a value of 1046.
mb7 <- mb6
mb7 <- mb7[which(mb7$TEAM_FIELDING_E < 1047),]
# eval_data.4 <- eval_data.4[which(eval_data.4$TEAM_FIELDING_E < 1047),]
# ----------------------------------------------------------------------
# ----------------------------------------------------------------------
# check rowcount: result is 2172 => removed total of 104 rows
nrow(mb7)## [1] 2172nrow(eval_data.4)## [1] 259dim(mb)-dim(mb7)## [1] 104 0#we removed 104 rows total due to outliers in TRAINING data set.
# we removed 11 rows from the EVALUATION data set
# now renumber rows of dataframe so that there are no gaps in row numbers
rownames(mb7) <- 1:nrow(mb7)
rownames(eval_data.4) <- 1:nrow(eval_data.4)
# drop INDEX column from training set
# mb7 <- mb7[,-1]
# now drop dummy column from evaluation data
# eval_data.4 <- eval_data.4[,-14]
# create CSV files containing updated data setswrite.csv(mb7, file = "C:/SQLData/621-HW1-Clean-Data.csv", row.names = FALSE, col.names = TRUE)
write.csv(eval_data.4, file = "C:/SQLData/621-HW1-Clean-EvalData-.csv", row.names = FALSE, col.names = TRUE)Model 5: Box-Cox First
Eliminate HBP, CS, and pitching HR’s.
Build model for batting SO using Gelman approach
Build model for Pitching SO
Build model for SB
Build model to replace DP
Eliminate unhistorical outliers - DO THIS FOR THE EVAL DATA AS WELL
# create CSV files containing updated data sets
write.csv(mb7, file = "/Users/scottkarr/IS621Summer2016/HW1/621-HW1-Clean-Data.csv", row.names = FALSE, col.names = TRUE)
write.csv(eval_data.4, file = "/Users/scottkarr/IS621Summer2016/HW1/621-HW1-Clean-EvalData-.csv", row.names = FALSE, col.names = TRUE)SINGLE PREDICTOR ANALYSIS & TRANSFORMATIONS
Model SMK Generlized Equation
Review descriptive statistics to confirm each variable is within acceptable bounds and contains no missing data. Review Density plots of 13 variables for skewness to identify which may require transformation.
Evaluate Correlations
Evaluate Correlation between predictors so as to not introduce collinearity into the model. 
## [1] 2157Model Selection Strategy
Two common strategies for adding or removing variables in a multiple regression model are called backward elimination and forward selection. These techniques are often referred to as stepwise model selection strategies, because they add or delete one variable at a time as they âstepâ through the candidate predictors. Model 1 uses the forward selection strategy which adds variables two-at-a-time until variables cannot be found that improve the model as measured by adjusted \(R^2\). Diez, D.M., Barr, C.D., & Ãetinkaya-Rundel, M. (2015). OpenIntro Statistics (3rd Ed). pg. 378
Start with p.Hits & p.Walks
Add b.Singles & b.Doubles
Removed p.Hits
Added Stolen Bases and Double Plays
Added b.Walks and p.Strikeouts
Remove b.Walks
Add b.StrikeOuts, & b.Slugging
Add b.Fielding
\[ \begin{aligned} \widehat{wins} &= \hat{\beta}_0 + \hat{\beta}_1 \times p.Walks \hat{\beta}_2 \times b.Singles + \hat{\beta}_3 \times b.Doubles + \hat{\beta}_4 \times b.Stolen Bases + \end{aligned} \] \[ \begin{aligned} \hat{\beta}_5 \times f.Double Plays + \hat{\beta}_6 \times b.Strike Outs + \hat{\beta}_7 \times b.Slugging + \hat{\beta}_8 \times b.Fielding Yield + \end{aligned} \] nrow(lm.smk)
#VARIABLES
#variables have been transformed first as individual predictors
Wins <- mW
Index <- lm.smk$INDEX
p.Walks <- tmp.BB
b.Singles <- tmb.1B
b.Doubles <- tmb.2B
b.StolenBases <- tmb.SB
b.StrikeOuts <- tmb.SO
b.Slugging <- tmb.SL
f.Fielding <- tmf.FY
m1 <- lm(Wins ~ -Index+p.Walks+b.Singles+b.Doubles+b.StolenBases+b.StrikeOuts+b.Slugging+f.Fielding)
#PAIRWISE PLOT
par(mfrow=c(1,1))
pairs(Wins ~ p.Walks+b.Singles+b.StolenBases+b.StrikeOuts+b.Slugging+f.Fielding)
#MODEL DIAGNOSTICS
summary(m1)##
## Call:
## lm(formula = Wins ~ -Index + p.Walks + b.Singles + b.Doubles +
## b.StolenBases + b.StrikeOuts + b.Slugging + f.Fielding)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.318 -7.845 -0.053 7.816 39.368
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.03042 12.67433 5.289 0.0000001357003
## p.Walks 27.93429 3.00029 9.311 < 0.0000000000000002
## b.Singles -19003746.29526 2670169.82691 -7.117 0.0000000000015
## b.Doubles 0.03065 0.21302 0.144 0.886
## b.StolenBases -121.06738 12.99326 -9.318 < 0.0000000000000002
## b.StrikeOuts -0.07317 0.01409 -5.195 0.0000002239702
## b.Slugging 3.01538 0.18292 16.485 < 0.0000000000000002
## f.Fielding 4032977.37953 225896.61232 17.853 < 0.0000000000000002
##
## (Intercept) ***
## p.Walks ***
## b.Singles ***
## b.Doubles
## b.StolenBases ***
## b.StrikeOuts ***
## b.Slugging ***
## f.Fielding ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.95 on 2149 degrees of freedom
## Multiple R-squared: 0.3168, Adjusted R-squared: 0.3146
## F-statistic: 142.4 on 7 and 2149 DF, p-value: < 0.00000000000000022#DIAGNOSTIC1. show collinearity of variables after checking p-values to < 0.05.
vif(m1)## p.Walks b.Singles b.Doubles b.StolenBases b.StrikeOuts
## 1.106592 2.857435 1.469729 1.205956 3.210354
## b.Slugging f.Fielding
## 1.301083 1.801535#p-values are all < 0.05 and no VIFs > 5
#DIAGNOSTIC2. generate Added Variable Plots: should show linear relationship between response & predictors:
par(mfrow=c(2,2))
avPlots(m1, ~.,ask=FALSE, id.n = 2)
#relationship is linear
#DIAGNOSTIC3. generate Summary Diagnostic Plots
par(mfrow=c(2,2))
plot(m1)
#Upper Left plot "Residuals vs Fitted"
# clear predictable pattern
# uniform variability for all fitted values
#Upper Right
# normality in residuals
#Lower Right plot "Residuals vs. Leverage"
# normal distribution, and uniform distribution of residuals
# no significant leverage points
#DIAGNOSTIC4. generate Standardized Residual Plots against each predictor
par(mfrow=c(2,2))
StanRest <- rstandard(m1)
plot(p.Walks,StanRest,ylab="Standardized Residuals")
plot(b.Singles,StanRest,ylab="Standardized Residuals")
plot(b.Doubles,StanRest,ylab="Standardized Residuals")
plot(b.StolenBases,StanRest,ylab="Standardized Residuals")
plot(f.DoublePlays,StanRest,ylab="Standardized Residuals")
plot(b.StrikeOuts,StanRest,ylab="Standardized Residuals")
plot(b.Slugging,StanRest,ylab="Standardized Residuals")
plot(f.Fielding,StanRest,ylab="Standardized Residuals")
plot(m1$fitted.values,StanRest,ylab="Standardized Residuals",xlab="Fitted Values")
#Examine plots for constant variability of residuals across ALL predictor.
# uniform distribution of residuals
#DIAGNOSTIC5. generate plot of Y "response variable"" against Fitted Values "regression model"
par(mfrow = c(2,2))
plot(m1$fitted.values,Wins,xlab="Fitted Values",ylab=expression(Wins^lambda))
abline(lsfit(m1$fitted.values,Wins))
plot(m1)
# normal distribution, and uniform distribution of residuals
#pred_eval.m1 <- round(predict(m1, eval_data))
#eval.BSO.imp <- impute(eval_data$TARGET_WINS, pred_eval.m1)Part 4. Select Models
#########################################################################################
#
# This file loads our preferred predictive model (TOTAL BASES PLUS)
# and uses that model to predict the TARGET_WINS variable of the MLB Evaluation
# data set.
#
# When finished, two separate files are written to a local hard disk directory:
#
# - one containing the entire EVALUATION data set after the TARGET_WINS variable has
# been updated with the predicted values for each record;
#
# - one containing ONLY the INDEX and TARGET_WINS variables from the EVALUATION data set
#
# - NO screen output is generated at all by this code
#
#########################################################################################
# --------------------------------------------------------------
# read clean data set from Github
mb_clean <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/621-HW1-Clean-Data.csv")
# ---------------------------------------------------------------
# Build a model with Total Bases + SB + BB added and all of the other hitting vars removed
# create new variable and drop its components
mb_t <- mb_clean
mb_t$TB_PLUS <- mb_clean$TEAM_BATTING_1B + (2 * mb_clean$TEAM_BATTING_2B) +
(3 * mb_clean$TEAM_BATTING_3B) + (4 * mb_clean$TEAM_BATTING_HR) +
mb_clean$TEAM_BATTING_BB + mb_clean$TEAM_BASERUN_SB
# par(mfrow = c(1,1))
# hist(mb_t$TB_PLUS, breaks = 200)
# now drop 1B, 2B, 3B, HR, BB, SB
mb_tbp <- mb_t[,c(1, 2, 7, 9, 10, 11, 12, 13, 15)]
# -----------------------------------------------------------------------------------------
# REMOVE OUTLIERS AND REFIT
# Per Cooks Distance, remove items 836, 821, 1920, 1737, 1515
############ FIRST SET OF OUTLIERS ######################
# drop outlier records from data set
mb_rem <- mb_tbp[-c(836, 821, 1920, 1737, 1515),]
# save first data set
mb_tbp_orig <- mb_tbp
# renumber rows
rownames(mb_rem) <- 1:nrow(mb_rem)
# keep the clean data set pure
mb_tbp <- mb_rem
# -------------------------------------------------------------------------------------------
## Now try same model but with FIELD_E transformed using Box-Cox
# TEAM_FIELDING_E: Box-cox says -1 power transform => 1/y
mb_tbp$TEAM_FIELDING_E <- 1/mb_tbp$TEAM_FIELDING_E
# Now refit first model from above: Start with all variables
model.4 <- lm(data=mb_tbp, TARGET_WINS ~ . - INDEX - TEAM_PITCHING_BB - TEAM_PITCHING_H - TEAM_PITCHING_SO)
# summary(model.4)# Now load evaluation data set and predict TARGET WINS
# load EVAL data set
eval.d <- read.csv("https://raw.githubusercontent.com/spsstudent15/2016-02-621-W1/master/621-HW1-Clean-EvalData-.csv")
# save original data
eval.2 <- eval.d
# creaet TB_PLUS and drop component variables
eval.2$TB_PLUS <- eval.2$TEAM_BATTING_1B + (2 * eval.2$TEAM_BATTING_2B) +
(3 * eval.2$TEAM_BATTING_3B) + (4 * eval.2$TEAM_BATTING_HR) +
eval.2$TEAM_BATTING_BB + eval.2$TEAM_BASERUN_SB
# par(mfrow = c(1,1))
# hist(eval.d$TB_PLUS, breaks = 30)
# now drop 1B, 2B, 3B, HR, BB, SB
eval.2 <- eval.2[,c(1, 6, 8, 9, 10, 11, 12, 14, 15)]
# transform TEAM_FIELDING_E using 1/y
eval.2$TEAM_FIELDING_E <- 1/eval.2$TEAM_FIELDING_E
# now predict TARGET_WINS using model.4
pred.TW <- round(predict(model.4, eval.2))
# add predicted variables to TARGET_WINS variable
eval.2$TARGET_WINS <- pred.TW
eval.d$TARGET_WINS <- pred.TW# write entire updated EVAL data set to a CSV
write.csv(eval.d, file = "C:/SQLData/HW1-PRED-EVAL-ALLDATA.csv", row.names = FALSE)
# write full model EVAL data to a CSV file
write.csv(eval.d, file = "C:/SQLData/HW1-PRED-EVAL-ALL_M_DATA.csv", row.names = FALSE)
# now write just INDEX and TARGET_WINS to a separate file
eval.3 <- eval.2[,c(1,8)]
write.csv(eval.3, file = "C:/SQLData/HW1-PRED-EVAL-WINS-ONLY.csv", row.names = FALSE)
# end# clean up objects in memory
rm(list = ls())