Data 621 Project 1
Moneyball Data Modeling
Data Exploration
Data Load
Exploring data by implementing statistical measures & plots
moneyball_df <- read.csv("https://raw.githubusercontent.com/josephsimone/Data621/master/HW1/moneyball-training-data.csv")
count(moneyball_df)## # A tibble: 1 x 1
## n
## <int>
## 1 2276## [1] "INDEX" "TARGET_WINS" "TEAM_BATTING_H" "TEAM_BATTING_2B"
## [5] "TEAM_BATTING_3B" "TEAM_BATTING_HR" "TEAM_BATTING_BB" "TEAM_BATTING_SO"
## [9] "TEAM_BASERUN_SB" "TEAM_BASERUN_CS" "TEAM_BATTING_HBP" "TEAM_PITCHING_H"
## [13] "TEAM_PITCHING_HR" "TEAM_PITCHING_BB" "TEAM_PITCHING_SO" "TEAM_FIELDING_E"
## [17] "TEAM_FIELDING_DP"## INDEX TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B
## Min. : 1.0 Min. : 0.00 Min. : 891 Min. : 69.0
## 1st Qu.: 630.8 1st Qu.: 71.00 1st Qu.:1383 1st Qu.:208.0
## Median :1270.5 Median : 82.00 Median :1454 Median :238.0
## Mean :1268.5 Mean : 80.79 Mean :1469 Mean :241.2
## 3rd Qu.:1915.5 3rd Qu.: 92.00 3rd Qu.:1537 3rd Qu.:273.0
## Max. :2535.0 Max. :146.00 Max. :2554 Max. :458.0
##
## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## Min. : 0.00 Min. : 0.00 Min. : 0.0 Min. : 0.0
## 1st Qu.: 34.00 1st Qu.: 42.00 1st Qu.:451.0 1st Qu.: 548.0
## Median : 47.00 Median :102.00 Median :512.0 Median : 750.0
## Mean : 55.25 Mean : 99.61 Mean :501.6 Mean : 735.6
## 3rd Qu.: 72.00 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 930.0
## Max. :223.00 Max. :264.00 Max. :878.0 Max. :1399.0
## NA's :102
## TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H
## Min. : 0.0 Min. : 0.0 Min. :29.00 Min. : 1137
## 1st Qu.: 66.0 1st Qu.: 38.0 1st Qu.:50.50 1st Qu.: 1419
## Median :101.0 Median : 49.0 Median :58.00 Median : 1518
## Mean :124.8 Mean : 52.8 Mean :59.36 Mean : 1779
## 3rd Qu.:156.0 3rd Qu.: 62.0 3rd Qu.:67.00 3rd Qu.: 1682
## Max. :697.0 Max. :201.0 Max. :95.00 Max. :30132
## NA's :131 NA's :772 NA's :2085
## TEAM_PITCHING_HR TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E
## Min. : 0.0 Min. : 0.0 Min. : 0.0 Min. : 65.0
## 1st Qu.: 50.0 1st Qu.: 476.0 1st Qu.: 615.0 1st Qu.: 127.0
## Median :107.0 Median : 536.5 Median : 813.5 Median : 159.0
## Mean :105.7 Mean : 553.0 Mean : 817.7 Mean : 246.5
## 3rd Qu.:150.0 3rd Qu.: 611.0 3rd Qu.: 968.0 3rd Qu.: 249.2
## Max. :343.0 Max. :3645.0 Max. :19278.0 Max. :1898.0
## NA's :102
## TEAM_FIELDING_DP
## Min. : 52.0
## 1st Qu.:131.0
## Median :149.0
## Mean :146.4
## 3rd Qu.:164.0
## Max. :228.0
## NA's :286The MoneyBall Data-Set is made up of 17 elements, with 2276 distinct cases.
A signifcant amount of variables contain ‘Na’s’ values or missing data points
TEAM-BATTING_HBP has the highest ‘NA’s’ values.
Exploring Outliers
ggplot(stack(moneyball_df), aes(x = ind, y = values)) +
geom_boxplot() +
coord_cartesian(ylim = c(0, 1000)) +
theme(legend.position="none") +
theme(axis.text.x=element_text(angle=45, hjust=1)) +
theme(panel.background = element_rect(fill = 'grey'))
Skewness in the data
moneyball_df1 = melt(moneyball_df)
ggplot(moneyball_df1, aes(x= value)) +
geom_density(fill='blue') + facet_wrap(~variable, scales = 'free') 
There are several variables that are skewed
In addition, there are some outliers.
Finding correlations:
## [1] "TARGET_WINS" "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B"
## [5] "TEAM_BATTING_HR" "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB"
## [9] "TEAM_BASERUN_CS" "TEAM_BATTING_HBP" "TEAM_PITCHING_H" "TEAM_PITCHING_HR"
## [13] "TEAM_PITCHING_BB" "TEAM_PITCHING_SO" "TEAM_FIELDING_E" "TEAM_FIELDING_DP"## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## TARGET_WINS 1.00000000 0.46994665 0.31298400 -0.12434586
## TEAM_BATTING_H 0.46994665 1.00000000 0.56177286 0.21391883
## TEAM_BATTING_2B 0.31298400 0.56177286 1.00000000 0.04203441
## TEAM_BATTING_3B -0.12434586 0.21391883 0.04203441 1.00000000
## TEAM_BATTING_HR 0.42241683 0.39627593 0.25099045 -0.21879927
## TEAM_BATTING_BB 0.46868793 0.19735234 0.19749256 -0.20584392
## TEAM_BATTING_SO -0.22889273 -0.34174328 -0.06415123 -0.19291841
## TEAM_BASERUN_SB 0.01483639 0.07167495 -0.18768279 0.16946086
## TEAM_BASERUN_CS -0.17875598 -0.09377545 -0.20413884 0.23213978
## TEAM_BATTING_HBP 0.07350424 -0.02911218 0.04608475 -0.17424715
## TEAM_PITCHING_H 0.47123431 0.99919269 0.56045355 0.21250322
## TEAM_PITCHING_HR 0.42246683 0.39495630 0.24999875 -0.21973263
## TEAM_PITCHING_BB 0.46839882 0.19529071 0.19592157 -0.20675383
## TEAM_PITCHING_SO -0.22936481 -0.34445001 -0.06616615 -0.19386654
## TEAM_FIELDING_E -0.38668800 -0.25381638 -0.19427027 -0.06513145
## TEAM_FIELDING_DP -0.19586601 0.01776946 -0.02488808 0.13314758
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## TARGET_WINS 0.42241683 0.46868793 -0.22889273
## TEAM_BATTING_H 0.39627593 0.19735234 -0.34174328
## TEAM_BATTING_2B 0.25099045 0.19749256 -0.06415123
## TEAM_BATTING_3B -0.21879927 -0.20584392 -0.19291841
## TEAM_BATTING_HR 1.00000000 0.45638161 0.21045444
## TEAM_BATTING_BB 0.45638161 1.00000000 0.21833871
## TEAM_BATTING_SO 0.21045444 0.21833871 1.00000000
## TEAM_BASERUN_SB -0.19021893 -0.08806123 -0.07475974
## TEAM_BASERUN_CS -0.27579838 -0.20878051 -0.05613035
## TEAM_BATTING_HBP 0.10618116 0.04746007 0.22094219
## TEAM_PITCHING_H 0.39549390 0.19848687 -0.34145321
## TEAM_PITCHING_HR 0.99993259 0.45659283 0.21111617
## TEAM_PITCHING_BB 0.45542468 0.99988140 0.21895783
## TEAM_PITCHING_SO 0.20829574 0.21793253 0.99976835
## TEAM_FIELDING_E 0.01567397 -0.07847126 0.30814540
## TEAM_FIELDING_DP -0.06182222 -0.07929078 -0.12319072
## TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP
## TARGET_WINS 0.01483639 -0.178755979 0.07350424
## TEAM_BATTING_H 0.07167495 -0.093775445 -0.02911218
## TEAM_BATTING_2B -0.18768279 -0.204138837 0.04608475
## TEAM_BATTING_3B 0.16946086 0.232139777 -0.17424715
## TEAM_BATTING_HR -0.19021893 -0.275798375 0.10618116
## TEAM_BATTING_BB -0.08806123 -0.208780510 0.04746007
## TEAM_BATTING_SO -0.07475974 -0.056130355 0.22094219
## TEAM_BASERUN_SB 1.00000000 0.624737808 -0.06400498
## TEAM_BASERUN_CS 0.62473781 1.000000000 -0.07051390
## TEAM_BATTING_HBP -0.06400498 -0.070513896 1.00000000
## TEAM_PITCHING_H 0.07395373 -0.092977893 -0.02769699
## TEAM_PITCHING_HR -0.18948057 -0.275471495 0.10675878
## TEAM_PITCHING_BB -0.08741902 -0.208470154 0.04785137
## TEAM_PITCHING_SO -0.07351325 -0.055308336 0.22157375
## TEAM_FIELDING_E 0.04292341 0.207701189 0.04178971
## TEAM_FIELDING_DP -0.13023054 -0.006764233 -0.07120824
## TEAM_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## TARGET_WINS 0.47123431 0.42246683 0.46839882
## TEAM_BATTING_H 0.99919269 0.39495630 0.19529071
## TEAM_BATTING_2B 0.56045355 0.24999875 0.19592157
## TEAM_BATTING_3B 0.21250322 -0.21973263 -0.20675383
## TEAM_BATTING_HR 0.39549390 0.99993259 0.45542468
## TEAM_BATTING_BB 0.19848687 0.45659283 0.99988140
## TEAM_BATTING_SO -0.34145321 0.21111617 0.21895783
## TEAM_BASERUN_SB 0.07395373 -0.18948057 -0.08741902
## TEAM_BASERUN_CS -0.09297789 -0.27547150 -0.20847015
## TEAM_BATTING_HBP -0.02769699 0.10675878 0.04785137
## TEAM_PITCHING_H 1.00000000 0.39463199 0.19703302
## TEAM_PITCHING_HR 0.39463199 1.00000000 0.45580983
## TEAM_PITCHING_BB 0.19703302 0.45580983 1.00000000
## TEAM_PITCHING_SO -0.34330646 0.20920115 0.21887700
## TEAM_FIELDING_E -0.25073028 0.01689330 -0.07692315
## TEAM_FIELDING_DP 0.01416807 -0.06292475 -0.08040645
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## TARGET_WINS -0.22936481 -0.38668800 -0.195866006
## TEAM_BATTING_H -0.34445001 -0.25381638 0.017769456
## TEAM_BATTING_2B -0.06616615 -0.19427027 -0.024888081
## TEAM_BATTING_3B -0.19386654 -0.06513145 0.133147578
## TEAM_BATTING_HR 0.20829574 0.01567397 -0.061822219
## TEAM_BATTING_BB 0.21793253 -0.07847126 -0.079290775
## TEAM_BATTING_SO 0.99976835 0.30814540 -0.123190715
## TEAM_BASERUN_SB -0.07351325 0.04292341 -0.130230537
## TEAM_BASERUN_CS -0.05530834 0.20770119 -0.006764233
## TEAM_BATTING_HBP 0.22157375 0.04178971 -0.071208241
## TEAM_PITCHING_H -0.34330646 -0.25073028 0.014168073
## TEAM_PITCHING_HR 0.20920115 0.01689330 -0.062924751
## TEAM_PITCHING_BB 0.21887700 -0.07692315 -0.080406452
## TEAM_PITCHING_SO 1.00000000 0.31008407 -0.124923213
## TEAM_FIELDING_E 0.31008407 1.00000000 0.040205814
## TEAM_FIELDING_DP -0.12492321 0.04020581 1.000000000
There are both Positively and Negatively Correlated Variables in this Data-Set
Data Preperation
Removing variables
## [1] "TARGET_WINS" "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B"
## [5] "TEAM_BATTING_HR" "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB"
## [9] "TEAM_BASERUN_CS" "TEAM_BATTING_HBP" "TEAM_PITCHING_H" "TEAM_PITCHING_HR"
## [13] "TEAM_PITCHING_BB" "TEAM_PITCHING_SO" "TEAM_FIELDING_E" "TEAM_FIELDING_DP"The variable TEAM_BATTING_HBP is mostly made up of missing values
Therefore, this variable will be removed completely.
## [1] "TARGET_WINS" "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B"
## [5] "TEAM_BATTING_HR" "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB"
## [9] "TEAM_BASERUN_CS" "TEAM_PITCHING_H" "TEAM_PITCHING_HR" "TEAM_PITCHING_BB"
## [13] "TEAM_PITCHING_SO" "TEAM_FIELDING_E" "TEAM_FIELDING_DP"TEAM_PITCHING_HR and TEAM_BATTING_HR are highly correlated, therefore we will remove one of them.
## [1] "TARGET_WINS" "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B"
## [5] "TEAM_BATTING_HR" "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB"
## [9] "TEAM_BASERUN_CS" "TEAM_PITCHING_H" "TEAM_PITCHING_BB" "TEAM_PITCHING_SO"
## [13] "TEAM_FIELDING_E" "TEAM_FIELDING_DP"Imputing the ‘NA’s’ values
##
## iter imp variable
## 1 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO TEAM_FIELDING_DP## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## Min. : 0.00 Min. : 891 Min. : 69.0 Min. : 0.00
## 1st Qu.: 71.00 1st Qu.:1383 1st Qu.:208.0 1st Qu.: 34.00
## Median : 82.00 Median :1454 Median :238.0 Median : 47.00
## Mean : 80.79 Mean :1469 Mean :241.2 Mean : 55.25
## 3rd Qu.: 92.00 3rd Qu.:1537 3rd Qu.:273.0 3rd Qu.: 72.00
## Max. :146.00 Max. :2554 Max. :458.0 Max. :223.00
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 42.00 1st Qu.:451.0 1st Qu.: 545.0 1st Qu.: 67.0
## Median :102.00 Median :512.0 Median : 735.5 Median :106.0
## Mean : 99.61 Mean :501.6 Mean : 728.6 Mean :137.6
## 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 925.0 3rd Qu.:170.2
## Max. :264.00 Max. :878.0 Max. :1399.0 Max. :697.0
## TEAM_BASERUN_CS TEAM_PITCHING_H TEAM_PITCHING_BB TEAM_PITCHING_SO
## Min. : 0.00 Min. : 1137 Min. : 0.0 Min. : 0.0
## 1st Qu.: 43.00 1st Qu.: 1419 1st Qu.: 476.0 1st Qu.: 611.0
## Median : 57.00 Median : 1518 Median : 536.5 Median : 805.5
## Mean : 75.38 Mean : 1779 Mean : 553.0 Mean : 811.6
## 3rd Qu.: 91.00 3rd Qu.: 1682 3rd Qu.: 611.0 3rd Qu.: 958.2
## Max. :201.00 Max. :30132 Max. :3645.0 Max. :19278.0
## TEAM_FIELDING_E TEAM_FIELDING_DP
## Min. : 65.0 Min. : 52.0
## 1st Qu.: 127.0 1st Qu.:125.0
## Median : 159.0 Median :146.0
## Mean : 246.5 Mean :141.8
## 3rd Qu.: 249.2 3rd Qu.:162.0
## Max. :1898.0 Max. :228.0Scaling & Centering
mb = preProcess(imputed_moneyball_df_Data,
c("BoxCox", "center", "scale"))
moneyball_df_final = data.frame(
mb = predict(mb, imputed_moneyball_df_Data))
summary(moneyball_df_final)## mb.TARGET_WINS mb.TEAM_BATTING_H mb.TEAM_BATTING_2B mb.TEAM_BATTING_3B
## Min. :-5.12888 Min. :-7.537074 Min. :-4.48108 Min. :-1.9776
## 1st Qu.:-0.62156 1st Qu.:-0.573089 1st Qu.:-0.68949 1st Qu.:-0.7606
## Median : 0.07676 Median :-0.003988 Median :-0.03019 Median :-0.2953
## Mean : 0.00000 Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.71159 3rd Qu.: 0.586908 3rd Qu.: 0.69827 3rd Qu.: 0.5995
## Max. : 4.13970 Max. : 4.390097 Max. : 4.05391 Max. : 6.0042
## mb.TEAM_BATTING_HR mb.TEAM_BATTING_BB mb.TEAM_BATTING_SO mb.TEAM_BASERUN_SB
## Min. :-1.64521 Min. :-4.08866 Min. :-2.95701 Min. :-1.3047
## 1st Qu.:-0.95153 1st Qu.:-0.41215 1st Qu.:-0.74525 1st Qu.:-0.6695
## Median : 0.03944 Median : 0.08511 Median : 0.02785 Median :-0.2997
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.78267 3rd Qu.: 0.63944 3rd Qu.: 0.79689 3rd Qu.: 0.3094
## Max. : 2.71505 Max. : 3.06871 Max. : 2.72051 Max. : 5.3033
## mb.TEAM_BASERUN_CS mb.TEAM_PITCHING_H mb.TEAM_PITCHING_BB mb.TEAM_PITCHING_SO
## Min. :-1.5092 Min. :-2.8556 Min. :-3.32422 Min. :-1.49634
## 1st Qu.:-0.6483 1st Qu.:-0.6710 1st Qu.:-0.46291 1st Qu.:-0.36981
## Median :-0.3680 Median :-0.1765 Median :-0.09923 Median :-0.01121
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.3128 3rd Qu.: 0.4602 3rd Qu.: 0.34860 3rd Qu.: 0.27042
## Max. : 2.5152 Max. : 3.2387 Max. :18.58645 Max. :34.04726
## mb.TEAM_FIELDING_E mb.TEAM_FIELDING_DP
## Min. :-3.3092 Min. :-2.59195
## 1st Qu.:-0.7163 1st Qu.:-0.61598
## Median :-0.1424 Median : 0.09239
## Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.7096 3rd Qu.: 0.66785
## Max. : 2.1432 Max. : 3.33606moneyball_df_final1 = melt(moneyball_df_final)
ggplot(moneyball_df_final1, aes(x= value)) +
geom_density(fill='blue') + facet_wrap(~variable, scales = 'free') 
Build Models
Model1
All Vatiables
##
## Call:
## lm(formula = mb.TARGET_WINS ~ ., data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5427 -0.5134 -0.0043 0.5188 3.9201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.459e-11 1.691e-02 0.000 1.0000
## mb.TEAM_BATTING_H 3.893e-01 3.628e-02 10.729 < 2e-16 ***
## mb.TEAM_BATTING_2B -2.724e-02 2.738e-02 -0.995 0.3200
## mb.TEAM_BATTING_3B 1.545e-01 2.985e-02 5.177 2.46e-07 ***
## mb.TEAM_BATTING_HR 2.400e-01 3.788e-02 6.336 2.83e-10 ***
## mb.TEAM_BATTING_BB 1.590e-01 3.434e-02 4.632 3.83e-06 ***
## mb.TEAM_BATTING_SO -3.712e-01 4.049e-02 -9.167 < 2e-16 ***
## mb.TEAM_BASERUN_SB 2.692e-01 3.196e-02 8.422 < 2e-16 ***
## mb.TEAM_BASERUN_CS 8.049e-02 3.282e-02 2.452 0.0143 *
## mb.TEAM_PITCHING_H -1.796e-01 3.802e-02 -4.723 2.47e-06 ***
## mb.TEAM_PITCHING_BB -2.562e-02 3.257e-02 -0.787 0.4315
## mb.TEAM_PITCHING_SO 1.242e-01 2.905e-02 4.273 2.01e-05 ***
## mb.TEAM_FIELDING_E -4.990e-01 3.810e-02 -13.097 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.749e-01 2.310e-02 -7.571 5.35e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8066 on 2262 degrees of freedom
## Multiple R-squared: 0.3532, Adjusted R-squared: 0.3494
## F-statistic: 95 on 13 and 2262 DF, p-value: < 2.2e-16Model2
Significant Variables
model2 <- lm(mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B + mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO + mb.TEAM_BASERUN_SB + mb.TEAM_PITCHING_SO + mb.TEAM_PITCHING_H + mb.TEAM_PITCHING_SO + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP, moneyball_df_final)
summary(model2)##
## Call:
## lm(formula = mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B +
## mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO +
## mb.TEAM_BASERUN_SB + mb.TEAM_PITCHING_SO + mb.TEAM_PITCHING_H +
## mb.TEAM_PITCHING_SO + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP,
## data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7964 -0.5098 0.0067 0.5120 3.8462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.572e-11 1.693e-02 0.000 1
## mb.TEAM_BATTING_H 3.705e-01 3.028e-02 12.234 < 2e-16 ***
## mb.TEAM_BATTING_3B 1.693e-01 2.931e-02 5.777 8.67e-09 ***
## mb.TEAM_BATTING_HR 2.341e-01 3.752e-02 6.239 5.23e-10 ***
## mb.TEAM_BATTING_BB 1.385e-01 2.213e-02 6.259 4.61e-10 ***
## mb.TEAM_BATTING_SO -3.729e-01 3.895e-02 -9.573 < 2e-16 ***
## mb.TEAM_BASERUN_SB 3.159e-01 2.628e-02 12.022 < 2e-16 ***
## mb.TEAM_PITCHING_SO 1.011e-01 2.174e-02 4.648 3.54e-06 ***
## mb.TEAM_PITCHING_H -1.970e-01 3.498e-02 -5.631 2.01e-08 ***
## mb.TEAM_FIELDING_E -4.852e-01 3.738e-02 -12.981 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.856e-01 2.275e-02 -8.155 5.72e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8075 on 2265 degrees of freedom
## Multiple R-squared: 0.3509, Adjusted R-squared: 0.348
## F-statistic: 122.4 on 10 and 2265 DF, p-value: < 2.2e-16Model3
Reduction of Variables
TEAM_PITCHING_SO & TEAM_BATTING_SO are highly correlated
TEAM_BATTING_H & TEAM_PITCHING_H are also highly correlated
TEAM_BATTING_SO $ TEAM_PITCHING_SO are also highly correlated
model3 <- lm(mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B + mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO + mb.TEAM_BASERUN_SB + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP, moneyball_df_final)
summary(model3)##
## Call:
## lm(formula = mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B +
## mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO +
## mb.TEAM_BASERUN_SB + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP,
## data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7794 -0.5153 -0.0075 0.5215 3.8388
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.324e-12 1.706e-02 0.000 1
## mb.TEAM_BATTING_H 2.656e-01 2.451e-02 10.838 < 2e-16 ***
## mb.TEAM_BATTING_3B 1.752e-01 2.943e-02 5.952 3.05e-09 ***
## mb.TEAM_BATTING_HR 1.946e-01 3.720e-02 5.232 1.84e-07 ***
## mb.TEAM_BATTING_BB 1.739e-01 2.090e-02 8.321 < 2e-16 ***
## mb.TEAM_BATTING_SO -2.693e-01 3.507e-02 -7.678 2.39e-14 ***
## mb.TEAM_BASERUN_SB 2.842e-01 2.516e-02 11.295 < 2e-16 ***
## mb.TEAM_FIELDING_E -5.207e-01 3.641e-02 -14.301 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.857e-01 2.260e-02 -8.219 3.40e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8139 on 2267 degrees of freedom
## Multiple R-squared: 0.3399, Adjusted R-squared: 0.3376
## F-statistic: 145.9 on 8 and 2267 DF, p-value: < 2.2e-16Select Model
##
## Call:
## lm(formula = mb.TARGET_WINS ~ ., data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5427 -0.5134 -0.0043 0.5188 3.9201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.459e-11 1.691e-02 0.000 1.0000
## mb.TEAM_BATTING_H 3.893e-01 3.628e-02 10.729 < 2e-16 ***
## mb.TEAM_BATTING_2B -2.724e-02 2.738e-02 -0.995 0.3200
## mb.TEAM_BATTING_3B 1.545e-01 2.985e-02 5.177 2.46e-07 ***
## mb.TEAM_BATTING_HR 2.400e-01 3.788e-02 6.336 2.83e-10 ***
## mb.TEAM_BATTING_BB 1.590e-01 3.434e-02 4.632 3.83e-06 ***
## mb.TEAM_BATTING_SO -3.712e-01 4.049e-02 -9.167 < 2e-16 ***
## mb.TEAM_BASERUN_SB 2.692e-01 3.196e-02 8.422 < 2e-16 ***
## mb.TEAM_BASERUN_CS 8.049e-02 3.282e-02 2.452 0.0143 *
## mb.TEAM_PITCHING_H -1.796e-01 3.802e-02 -4.723 2.47e-06 ***
## mb.TEAM_PITCHING_BB -2.562e-02 3.257e-02 -0.787 0.4315
## mb.TEAM_PITCHING_SO 1.242e-01 2.905e-02 4.273 2.01e-05 ***
## mb.TEAM_FIELDING_E -4.990e-01 3.810e-02 -13.097 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.749e-01 2.310e-02 -7.571 5.35e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8066 on 2262 degrees of freedom
## Multiple R-squared: 0.3532, Adjusted R-squared: 0.3494
## F-statistic: 95 on 13 and 2262 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B +
## mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO +
## mb.TEAM_BASERUN_SB + mb.TEAM_PITCHING_SO + mb.TEAM_PITCHING_H +
## mb.TEAM_PITCHING_SO + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP,
## data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7964 -0.5098 0.0067 0.5120 3.8462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.572e-11 1.693e-02 0.000 1
## mb.TEAM_BATTING_H 3.705e-01 3.028e-02 12.234 < 2e-16 ***
## mb.TEAM_BATTING_3B 1.693e-01 2.931e-02 5.777 8.67e-09 ***
## mb.TEAM_BATTING_HR 2.341e-01 3.752e-02 6.239 5.23e-10 ***
## mb.TEAM_BATTING_BB 1.385e-01 2.213e-02 6.259 4.61e-10 ***
## mb.TEAM_BATTING_SO -3.729e-01 3.895e-02 -9.573 < 2e-16 ***
## mb.TEAM_BASERUN_SB 3.159e-01 2.628e-02 12.022 < 2e-16 ***
## mb.TEAM_PITCHING_SO 1.011e-01 2.174e-02 4.648 3.54e-06 ***
## mb.TEAM_PITCHING_H -1.970e-01 3.498e-02 -5.631 2.01e-08 ***
## mb.TEAM_FIELDING_E -4.852e-01 3.738e-02 -12.981 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.856e-01 2.275e-02 -8.155 5.72e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8075 on 2265 degrees of freedom
## Multiple R-squared: 0.3509, Adjusted R-squared: 0.348
## F-statistic: 122.4 on 10 and 2265 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = mb.TARGET_WINS ~ mb.TEAM_BATTING_H + mb.TEAM_BATTING_3B +
## mb.TEAM_BATTING_HR + mb.TEAM_BATTING_BB + mb.TEAM_BATTING_SO +
## mb.TEAM_BASERUN_SB + mb.TEAM_FIELDING_E + mb.TEAM_FIELDING_DP,
## data = moneyball_df_final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7794 -0.5153 -0.0075 0.5215 3.8388
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.324e-12 1.706e-02 0.000 1
## mb.TEAM_BATTING_H 2.656e-01 2.451e-02 10.838 < 2e-16 ***
## mb.TEAM_BATTING_3B 1.752e-01 2.943e-02 5.952 3.05e-09 ***
## mb.TEAM_BATTING_HR 1.946e-01 3.720e-02 5.232 1.84e-07 ***
## mb.TEAM_BATTING_BB 1.739e-01 2.090e-02 8.321 < 2e-16 ***
## mb.TEAM_BATTING_SO -2.693e-01 3.507e-02 -7.678 2.39e-14 ***
## mb.TEAM_BASERUN_SB 2.842e-01 2.516e-02 11.295 < 2e-16 ***
## mb.TEAM_FIELDING_E -5.207e-01 3.641e-02 -14.301 < 2e-16 ***
## mb.TEAM_FIELDING_DP -1.857e-01 2.260e-02 -8.219 3.40e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8139 on 2267 degrees of freedom
## Multiple R-squared: 0.3399, Adjusted R-squared: 0.3376
## F-statistic: 145.9 on 8 and 2267 DF, p-value: < 2.2e-16After exploring these three models, it is clear to use model3 for the predictions.
This is due to the fact that this model is more parsimonious.
In additon, There is no significant difference in \(R2\), Adjusted \(R2\) and \(RMSE\).
Predictive Values
moneyball_evaulated_df <- read.csv("https://raw.githubusercontent.com/josephsimone/Data621/master/HW1/moneyball-evaluation-data.csv")Removing variables
## [1] "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B" "TEAM_BATTING_HR"
## [5] "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB" "TEAM_BASERUN_CS"
## [9] "TEAM_BATTING_HBP" "TEAM_PITCHING_H" "TEAM_PITCHING_HR" "TEAM_PITCHING_BB"
## [13] "TEAM_PITCHING_SO" "TEAM_FIELDING_E" "TEAM_FIELDING_DP"## [1] "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B" "TEAM_BATTING_HR"
## [5] "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB" "TEAM_BASERUN_CS"
## [9] "TEAM_BATTING_HBP" "TEAM_PITCHING_HR" "TEAM_PITCHING_BB" "TEAM_PITCHING_SO"
## [13] "TEAM_FIELDING_E" "TEAM_FIELDING_DP"## [1] "TEAM_BATTING_H" "TEAM_BATTING_2B" "TEAM_BATTING_3B" "TEAM_BATTING_HR"
## [5] "TEAM_BATTING_BB" "TEAM_BATTING_SO" "TEAM_BASERUN_SB" "TEAM_BASERUN_CS"
## [9] "TEAM_BATTING_HBP" "TEAM_PITCHING_HR" "TEAM_PITCHING_SO" "TEAM_FIELDING_E"
## [13] "TEAM_FIELDING_DP"Imputing ‘NA’s’ values
imputed_moneyball_evaulated_df_Data <- mice(moneyball_evaulated_df_f, m=5, maxit = 5, method = 'pmm')##
## iter imp variable
## 1 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 1 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 2 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 3 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 4 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 1 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 2 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 3 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 4 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP
## 5 5 TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_SO TEAM_FIELDING_DP## Warning: Number of logged events: 25imputed_moneyball_evaulated_df_Data <- complete(imputed_moneyball_evaulated_df_Data)
summary(imputed_moneyball_evaulated_df_Data)## TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR
## Min. : 819 Min. : 44.0 Min. : 14.00 Min. : 0.00
## 1st Qu.:1387 1st Qu.:210.0 1st Qu.: 35.00 1st Qu.: 44.50
## Median :1455 Median :239.0 Median : 52.00 Median :101.00
## Mean :1469 Mean :241.3 Mean : 55.91 Mean : 95.63
## 3rd Qu.:1548 3rd Qu.:278.5 3rd Qu.: 72.00 3rd Qu.:135.50
## Max. :2170 Max. :376.0 Max. :155.00 Max. :242.00
## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS
## Min. : 15.0 Min. : 0.0 Min. : 0.0 Min. : 0.00
## 1st Qu.:436.5 1st Qu.: 527.0 1st Qu.: 59.5 1st Qu.: 41.00
## Median :509.0 Median : 675.0 Median : 96.0 Median : 56.00
## Mean :499.0 Mean : 698.0 Mean :130.3 Mean : 65.23
## 3rd Qu.:565.5 3rd Qu.: 904.5 3rd Qu.:159.0 3rd Qu.: 76.00
## Max. :792.0 Max. :1268.0 Max. :580.0 Max. :154.00
## TEAM_BATTING_HBP TEAM_PITCHING_HR TEAM_PITCHING_SO TEAM_FIELDING_E
## Min. :42.0 Min. : 0.0 Min. : 0.0 Min. : 73.0
## 1st Qu.:49.0 1st Qu.: 52.0 1st Qu.: 621.5 1st Qu.: 131.0
## Median :62.0 Median :104.0 Median : 758.0 Median : 163.0
## Mean :61.4 Mean :102.1 Mean : 805.8 Mean : 249.7
## 3rd Qu.:67.0 3rd Qu.:142.5 3rd Qu.: 955.5 3rd Qu.: 252.0
## Max. :96.0 Max. :336.0 Max. :9963.0 Max. :1568.0
## TEAM_FIELDING_DP
## Min. : 69.0
## 1st Qu.:123.0
## Median :146.0
## Mean :140.7
## 3rd Qu.:160.5
## Max. :204.0Scaling & Centering
mb = preProcess(imputed_moneyball_evaulated_df_Data,
c("BoxCox", "center", "scale"))
moneyball_evaulated_df_final = data.frame(
mb = predict(mb, imputed_moneyball_evaulated_df_Data))
summary(moneyball_evaulated_df_final)## mb.TEAM_BATTING_H mb.TEAM_BATTING_2B mb.TEAM_BATTING_3B mb.TEAM_BATTING_HR
## Min. :-5.07603 Min. :-3.26217 Min. :-2.64215 Min. :-1.69766
## 1st Qu.:-0.52836 1st Qu.:-0.67016 1st Qu.:-0.73771 1st Qu.:-0.90771
## Median :-0.06571 Median :-0.09057 Median : 0.08513 Median : 0.09527
## Mean : 0.00000 Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.54648 3rd Qu.: 0.74495 3rd Qu.: 0.76149 3rd Qu.: 0.70771
## Max. : 4.16429 Max. : 3.00896 Max. : 2.35514 Max. : 2.59828
## mb.TEAM_BATTING_BB mb.TEAM_BATTING_SO mb.TEAM_BASERUN_SB mb.TEAM_BASERUN_CS
## Min. :-2.859388 Min. :-2.91029 Min. :-1.3132 Min. :-1.8451
## 1st Qu.:-0.619108 1st Qu.:-0.71287 1st Qu.:-0.7136 1st Qu.:-0.6854
## Median : 0.008141 Median :-0.09576 Median :-0.3457 Median :-0.2611
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.536019 3rd Qu.: 0.86118 3rd Qu.: 0.2892 3rd Qu.: 0.3046
## Max. : 2.968415 Max. : 2.37686 Max. : 4.5320 Max. : 2.5109
## mb.TEAM_BATTING_HBP mb.TEAM_PITCHING_HR mb.TEAM_PITCHING_SO mb.TEAM_FIELDING_E
## Min. :-1.6759 Min. :-1.77169 Min. :-1.30863 Min. :-3.1354
## 1st Qu.:-0.8697 1st Qu.:-0.86977 1st Qu.:-0.29934 1st Qu.:-0.7317
## Median : 0.2258 Median : 0.03214 Median :-0.07767 Median :-0.1378
## Mean : 0.0000 Mean : 0.00000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.5543 3rd Qu.: 0.69991 3rd Qu.: 0.24306 3rd Qu.: 0.7208
## Max. : 1.8928 Max. : 4.05609 Max. :14.87078 Max. : 2.0409
## mb.TEAM_FIELDING_DP
## Min. :-2.2272
## 1st Qu.:-0.6576
## Median : 0.1361
## Mean : 0.0000
## 3rd Qu.: 0.6704
## Max. : 2.4173eval_data <- predict(model3, newdata = moneyball_evaulated_df_final, interval="prediction")
eval_data## fit lwr upr
## 1 -1.204949252 -2.804458e+00 0.3945591
## 2 -0.960662791 -2.558789e+00 0.6374631
## 3 -0.611825601 -2.209369e+00 0.9857180
## 4 0.315243395 -1.282535e+00 1.9130216
## 5 -1.400574520 -3.001878e+00 0.2007290
## 6 -0.915830796 -2.515180e+00 0.6835183
## 7 0.209721898 -1.390966e+00 1.8104099
## 8 -0.714386909 -2.312684e+00 0.8839099
## 9 -0.683470016 -2.282011e+00 0.9150705
## 10 -0.587747895 -2.185055e+00 1.0095596
## 11 -0.901102931 -2.500176e+00 0.6979703
## 12 -0.017203229 -1.616737e+00 1.5823303
## 13 0.082370396 -1.518493e+00 1.6832337
## 14 0.022760225 -1.576903e+00 1.6224232
## 15 0.335425224 -1.265790e+00 1.9366400
## 16 -0.464435055 -2.062919e+00 1.1340486
## 17 -0.746101161 -2.344771e+00 0.8525690
## 18 -0.093865927 -1.691478e+00 1.5037457
## 19 -0.654852196 -2.254144e+00 0.9444392
## 20 0.353391307 -1.245425e+00 1.9522076
## 21 0.307083399 -1.291443e+00 1.9056100
## 22 0.189559866 -1.408885e+00 1.7880046
## 23 0.045089922 -1.553121e+00 1.6433012
## 24 -0.700977855 -2.299208e+00 0.8972526
## 25 0.177069732 -1.421693e+00 1.7758323
## 26 0.516501772 -1.083281e+00 2.1162849
## 27 -0.819534057 -2.428090e+00 0.7890223
## 28 -0.570680125 -2.168184e+00 1.0268233
## 29 0.242472629 -1.356831e+00 1.8417765
## 30 -0.610275689 -2.209812e+00 0.9892606
## 31 0.650435535 -9.487651e-01 2.2496361
## 32 0.344455555 -1.253178e+00 1.9420887
## 33 0.319923113 -1.278839e+00 1.9186857
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## 104 0.234158253 -1.364170e+00 1.8324865
## 105 -0.502703219 -2.103342e+00 1.0979360
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## 110 -1.410583645 -3.011998e+00 0.1908305
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## 133 -0.675729323 -2.278628e+00 0.9271692
## 134 -0.087958962 -1.686797e+00 1.5108788
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## 136 -0.355234712 -1.954719e+00 1.2442498
## 137 -0.225545687 -1.823626e+00 1.3725344
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## 140 -0.042361791 -1.640111e+00 1.5553871
## 141 -1.277065157 -2.877153e+00 0.3230223
## 142 -0.618337709 -2.216868e+00 0.9801921
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## 144 -0.620175512 -2.218688e+00 0.9783365
## 145 -0.190834347 -1.789472e+00 1.4078033
## 146 -0.411376130 -2.008644e+00 1.1858913
## 147 -0.440422685 -2.038531e+00 1.1576857
## 148 0.048700576 -1.548894e+00 1.6462956
## 149 -0.080452432 -1.679419e+00 1.5185141
## 150 0.331455840 -1.266059e+00 1.9289711
## 151 0.134686524 -1.463962e+00 1.7333348
## 152 0.492004037 -1.108879e+00 2.0928874
## 153 -1.282374628 -2.893204e+00 0.3284546
## 154 -1.099684261 -2.698677e+00 0.4993083
## 155 -0.023012790 -1.621459e+00 1.5754331
## 156 -0.935779404 -2.534900e+00 0.6633414
## 157 0.847286252 -7.520373e-01 2.4466098
## 158 -0.365896728 -1.964675e+00 1.2328812
## 159 0.485855027 -1.112615e+00 2.0843249
## 160 -0.374704365 -1.972750e+00 1.2233411
## 161 1.112886482 -4.891293e-01 2.7149023
## 162 1.602568555 -1.058603e-05 3.2051477
## 163 0.913340147 -6.857612e-01 2.5124415
## 164 1.312776860 -2.898140e-01 2.9153677
## 165 1.021487822 -5.809024e-01 2.6238781
## 166 0.927866237 -6.729192e-01 2.5286516
## 167 0.182600977 -1.416352e+00 1.7815538
## 168 0.223829928 -1.375694e+00 1.8233538
## 169 -0.664015385 -2.262914e+00 0.9348837
## 170 0.012988040 -1.585627e+00 1.6116031
## 171 0.617110859 -9.812179e-01 2.2154396
## 172 0.463766418 -1.134094e+00 2.0616267
## 173 0.070242790 -1.527298e+00 1.6677837
## 174 0.731586309 -8.669259e-01 2.3300986
## 175 -0.047837090 -1.645300e+00 1.5496262
## 176 -0.159163251 -1.757694e+00 1.4393678
## 177 0.109916256 -1.489614e+00 1.7094468
## 178 -0.846834800 -2.445965e+00 0.7522957
## 179 -0.341663318 -1.938606e+00 1.2552793
## 180 -0.160431539 -1.757963e+00 1.4371004
## 181 0.576146282 -1.025595e+00 2.1778873
## 182 0.300814907 -1.298499e+00 1.9001289
## 183 0.496625123 -1.101872e+00 2.0951223
## 184 0.536163677 -1.062069e+00 2.1343967
## 185 1.126569818 -4.763403e-01 2.7294799
## 186 0.992519080 -6.139535e-01 2.5989916
## 187 0.471125638 -1.130288e+00 2.0725389
## 188 -0.626483875 -2.227077e+00 0.9741093
## 189 -0.734675402 -2.333922e+00 0.8645711
## 190 1.536828811 -6.688687e-02 3.1405445
## 191 -0.646892861 -2.244832e+00 0.9510464
## 192 -0.059709576 -1.657108e+00 1.5376887
## 193 -0.607002551 -2.204687e+00 0.9906817
## 194 -0.478316757 -2.076157e+00 1.1195231
## 195 -0.457334155 -2.056597e+00 1.1419283
## 196 -1.092909047 -2.692292e+00 0.5064738
## 197 -0.477634658 -2.075077e+00 1.1198077
## 198 0.758201166 -8.423250e-01 2.3587274
## 199 0.040765300 -1.556962e+00 1.6384923
## 200 0.249795731 -1.348183e+00 1.8477749
## 201 -0.619838453 -2.219870e+00 0.9801927
## 202 0.123013484 -1.475440e+00 1.7214674
## 203 -0.100223039 -1.700626e+00 1.5001797
## 204 0.666719884 -9.311730e-01 2.2646128
## 205 0.098524797 -1.499549e+00 1.6965981
## 206 0.206276827 -1.391607e+00 1.8041610
## 207 0.114884319 -1.483883e+00 1.7136514
## 208 0.163130153 -1.435516e+00 1.7617760
## 209 0.157874422 -1.440160e+00 1.7559086
## 210 -0.176263778 -1.775089e+00 1.4225616
## 211 1.415982632 -1.842105e-01 3.0161757
## 212 0.583673599 -1.015319e+00 2.1826664
## 213 0.010639253 -1.587865e+00 1.6091438
## 214 -1.186660955 -2.785261e+00 0.4119395
## 215 -0.788266563 -2.387646e+00 0.8111128
## 216 0.120957776 -1.476863e+00 1.7187783
## 217 -0.199861304 -1.800655e+00 1.4009321
## 218 0.705616997 -8.927049e-01 2.3039389
## 219 -0.182353112 -1.779851e+00 1.4151448
## 220 0.087041959 -1.510510e+00 1.6845944
## 221 -0.372337360 -1.970585e+00 1.2259104
## 222 -0.556379083 -2.155578e+00 1.0428194
## 223 -0.077922175 -1.675817e+00 1.5199726
## 224 -0.273885312 -1.874472e+00 1.3267009
## 225 0.279445439 -1.332344e+00 1.8912350
## 226 -0.182511395 -1.779925e+00 1.4149021
## 227 -0.153286864 -1.751005e+00 1.4444312
## 228 -0.187254840 -1.786223e+00 1.4117137
## 229 0.429882299 -1.167874e+00 2.0276391
## 230 -0.412827614 -2.012820e+00 1.1871648
## 231 -0.095918941 -1.695166e+00 1.5033285
## 232 0.578135191 -1.020050e+00 2.1763202
## 233 0.049422904 -1.549893e+00 1.6487391
## 234 0.247373323 -1.351775e+00 1.8465216
## 235 -0.244573958 -1.841988e+00 1.3528396
## 236 -0.381578152 -1.978804e+00 1.2156472
## 237 -0.337993406 -1.937842e+00 1.2618554
## 238 0.115072221 -1.483986e+00 1.7141309
## 239 0.765655889 -8.339884e-01 2.3653001
## 240 -0.696054978 -2.293920e+00 0.9018097
## 241 0.263451726 -1.334107e+00 1.8610101
## 242 0.749194083 -8.499319e-01 2.3483201
## 243 0.260973376 -1.337135e+00 1.8590816
## 244 0.203135153 -1.395375e+00 1.8016456
## 245 -1.469623213 -3.071486e+00 0.1322397
## 246 0.132129941 -1.466827e+00 1.7310867
## 247 -0.198780547 -1.796316e+00 1.3987553
## 248 0.182762808 -1.415215e+00 1.7807410
## 249 -0.350022186 -1.947869e+00 1.2478249
## 250 0.475623256 -1.125223e+00 2.0764698
## 251 0.176426003 -1.422044e+00 1.7748962
## 252 -0.908361510 -2.508597e+00 0.6918736
## 253 0.820909307 -7.791909e-01 2.4210095
## 254 -1.920043528 -3.538537e+00 -0.3015502
## 255 -0.793410224 -2.391392e+00 0.8045712
## 256 -0.336833182 -1.937025e+00 1.2633581
## 257 0.220844585 -1.377685e+00 1.8193744
## 258 0.117576791 -1.480076e+00 1.7152297
## 259 -0.344841627 -1.943495e+00 1.2538119## fit lwr upr
## Min. :-1.92004 Min. :-3.53854 Min. :-0.3015
## 1st Qu.:-0.41111 1st Qu.:-2.00916 1st Qu.: 1.1876
## Median : 0.05347 Median :-1.54429 Median : 1.6512
## Mean : 0.00000 Mean :-1.59937 Mean : 1.5994
## 3rd Qu.: 0.38262 3rd Qu.:-1.21616 3rd Qu.: 1.9814
## Max. : 1.68597 Max. : 0.07591 Max. : 3.2960