Library
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, union## Warning: package 'corrplot' was built under R version 4.0.2## corrplot 0.84 loaded##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
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## select## Warning: package 'caret' was built under R version 4.0.2## Loading required package: lattice1. Data Exploration
The “moneyball” data set contains 2276 rows and 17 columns, including variables such as TARGET_WINS, TEAM_BATTING, TEAN_BASERUN, etc. Running a summary() function on the data set, we are able to get the mean, median, first and third quartile and the minimum and maximum values for each variable. We included a correlation plot and pairs plot to visualize the relationship among the variables. Histograms were created for each type of hits to observe the normality of the variables. We explored the structure of the variables for both the training and evaluation data sets and finally observed how TARGET_WINS are affected by other factors.
See a summary of each column in the train_dfing set
## 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 :286
For types of hits, see a histogram of each
par(mfrow=c(2,2))
hist(train_df$TEAM_BATTING_H,
main = "hits histogram", xlab = "hits (season)",
breaks = 20)
hist(train_df$TEAM_BATTING_2B,
main = "doubles histogram", xlab = "doubles (season)",
breaks = 20)
hist(train_df$TEAM_BATTING_3B,
main = "triples histogram", xlab = "triples (season)",
breaks = 20)
hist(train_df$TEAM_BATTING_HR,
main = "homeruns histogram", xlab = "homeruns (season)",
breaks = 20)
pairs(~ TARGET_WINS + TEAM_BATTING_H + TEAM_BATTING_2B
+ TEAM_BATTING_3B + TEAM_BATTING_HR, data = train_df)
## 'data.frame': 2276 obs. of 17 variables:
## $ INDEX : int 1 2 3 4 5 6 7 8 11 12 ...
## $ TARGET_WINS : int 39 70 86 70 82 75 80 85 86 76 ...
## $ TEAM_BATTING_H : int 1445 1339 1377 1387 1297 1279 1244 1273 1391 1271 ...
## $ TEAM_BATTING_2B : int 194 219 232 209 186 200 179 171 197 213 ...
## $ TEAM_BATTING_3B : int 39 22 35 38 27 36 54 37 40 18 ...
## $ TEAM_BATTING_HR : int 13 190 137 96 102 92 122 115 114 96 ...
## $ TEAM_BATTING_BB : int 143 685 602 451 472 443 525 456 447 441 ...
## $ TEAM_BATTING_SO : int 842 1075 917 922 920 973 1062 1027 922 827 ...
## $ TEAM_BASERUN_SB : int NA 37 46 43 49 107 80 40 69 72 ...
## $ TEAM_BASERUN_CS : int NA 28 27 30 39 59 54 36 27 34 ...
## $ TEAM_BATTING_HBP: int NA NA NA NA NA NA NA NA NA NA ...
## $ TEAM_PITCHING_H : int 9364 1347 1377 1396 1297 1279 1244 1281 1391 1271 ...
## $ TEAM_PITCHING_HR: int 84 191 137 97 102 92 122 116 114 96 ...
## $ TEAM_PITCHING_BB: int 927 689 602 454 472 443 525 459 447 441 ...
## $ TEAM_PITCHING_SO: int 5456 1082 917 928 920 973 1062 1033 922 827 ...
## $ TEAM_FIELDING_E : int 1011 193 175 164 138 123 136 112 127 131 ...
## $ TEAM_FIELDING_DP: int NA 155 153 156 168 149 186 136 169 159 ...## function (expr, envir = parent.frame(), enclos = if (is.list(envir) ||
## is.pairlist(envir)) parent.frame() else baseenv())# lets observe how targets_win are effected by other factors
hist(train_df$TARGET_WINS,xlab="TARGET_WINS",main="")
2. Data Preparation
We addressed issues with imperfect data before building models or performing statistical analysis. We observed that several variables have high numbers of NA or missing values. EAM_BATTING_HBP has the highest number of missing cases i.e., 2085 (~ 90%). Assuming that NA can be filled in by 0, we created additional columns for each variable to flag the original NAs.
- We are told everything is standardized to match a 162 game season, so it is my preference to make TARGET_WINS a decimal of 162
train_target_wins = train_df$TARGET_WINS
#train_df$TARGET_WINS = train_df$TARGET_WINS/162.
# TARGET_WINS now a decimal of games won in 162 game season
hist(train_df$TARGET_WINS,xlab="TARGET_WINS",main="")
## 'data.frame': 2276 obs. of 17 variables:
## $ INDEX : int 1 2 3 4 5 6 7 8 11 12 ...
## $ TARGET_WINS : int 39 70 86 70 82 75 80 85 86 76 ...
## $ TEAM_BATTING_H : int 1445 1339 1377 1387 1297 1279 1244 1273 1391 1271 ...
## $ TEAM_BATTING_2B : int 194 219 232 209 186 200 179 171 197 213 ...
## $ TEAM_BATTING_3B : int 39 22 35 38 27 36 54 37 40 18 ...
## $ TEAM_BATTING_HR : int 13 190 137 96 102 92 122 115 114 96 ...
## $ TEAM_BATTING_BB : int 143 685 602 451 472 443 525 456 447 441 ...
## $ TEAM_BATTING_SO : int 842 1075 917 922 920 973 1062 1027 922 827 ...
## $ TEAM_BASERUN_SB : int NA 37 46 43 49 107 80 40 69 72 ...
## $ TEAM_BASERUN_CS : int NA 28 27 30 39 59 54 36 27 34 ...
## $ TEAM_BATTING_HBP: int NA NA NA NA NA NA NA NA NA NA ...
## $ TEAM_PITCHING_H : int 9364 1347 1377 1396 1297 1279 1244 1281 1391 1271 ...
## $ TEAM_PITCHING_HR: int 84 191 137 97 102 92 122 116 114 96 ...
## $ TEAM_PITCHING_BB: int 927 689 602 454 472 443 525 459 447 441 ...
## $ TEAM_PITCHING_SO: int 5456 1082 917 928 920 973 1062 1033 922 827 ...
## $ TEAM_FIELDING_E : int 1011 193 175 164 138 123 136 112 127 131 ...
## $ TEAM_FIELDING_DP: int NA 155 153 156 168 149 186 136 169 159 ...- Assuming that everything that is NA can be filled by 0 based on the description of variables, create columns flagging if original values were NA (e.g. create TEAM_BATTING_HBP_NA column and value is 1 if TEAM_BATTING_HBP is NA and 0 otherwise meaning it wasn’t NA and had a value. Do this for all columns)
3. Build Models
First we started a model with the backward elimination process with the data. In this process, we will be rejecting predictors with p-value greater than 0.05 with the backward elimination process. We will stop after all the predictors are less than 0.05. TEAM_PITCHING_HR, TEAM_BATTING_2B, TEAM_BATTING_BB, TEAM_BASERUN_CS, TEAM_BASERUN_SB. We also eliminate the variables that have a lot of NA values.
The second model we decided to go with the stepwise selection which includes a semi-automated process of building a model by adding or removing variables based solely on the t-statistics of their estimated coefficients. Removed TEAM_BATTING_HBP, TEAM_BASERUN_CS, TEAM_PITCHING_BB, TEAM_PITCHING_HR.
For our third model we noticed one of the variables, TEAM_PITCHING_SO, have a p-value greater than 0.05 so we decided to investigate. When we removed the variable, TEAM_PITCHING_SO, and the R squared dropped slightly.
Model 1 - Backward Elimination Process
We will be rejecting predictors with p-value greater than 0.05 with the backward elimination process. We will stop after all the predictors are less than 0.05
model <- lm(TARGET_WINS ~ TEAM_BATTING_H + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_PITCHING_H + TEAM_PITCHING_HR + TEAM_PITCHING_BB + TEAM_FIELDING_E, data=train_df)
summary(train_df)## 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.: 524.0
## Median : 47.00 Median :102.00 Median :512.0 Median : 728.0
## Mean : 55.25 Mean : 99.61 Mean :501.6 Mean : 702.6
## 3rd Qu.: 72.00 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 925.0
## Max. :223.00 Max. :264.00 Max. :878.0 Max. :1399.0
## TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H
## Min. : 0.0 Min. : 0.00 Min. : 0.000 Min. : 1137
## 1st Qu.: 60.0 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 1419
## Median : 97.0 Median : 38.00 Median : 0.000 Median : 1518
## Mean :117.6 Mean : 34.89 Mean : 4.981 Mean : 1779
## 3rd Qu.:151.0 3rd Qu.: 54.25 3rd Qu.: 0.000 3rd Qu.: 1682
## Max. :697.0 Max. :201.00 Max. :95.000 Max. :30132
## 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.: 587.8 1st Qu.: 127.0
## Median :107.0 Median : 536.5 Median : 797.0 Median : 159.0
## Mean :105.7 Mean : 553.0 Mean : 781.1 Mean : 246.5
## 3rd Qu.:150.0 3rd Qu.: 611.0 3rd Qu.: 957.0 3rd Qu.: 249.2
## Max. :343.0 Max. :3645.0 Max. :19278.0 Max. :1898.0
## TEAM_FIELDING_DP TEAM_BATTING_SO_NA TEAM_BASERUN_SB_NA TEAM_BASERUN_CS_NA
## Min. : 0.0 Min. :0.00000 Min. :0.00000 Min. :0.0000
## 1st Qu.:118.0 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :145.0 Median :0.00000 Median :0.00000 Median :0.0000
## Mean :128.0 Mean :0.04482 Mean :0.05756 Mean :0.3392
## 3rd Qu.:161.2 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:1.0000
## Max. :228.0 Max. :1.00000 Max. :1.00000 Max. :1.0000
## TEAM_BATTING_HBP_NA TEAM_PITCHING_SO_NA TEAM_FIELDING_DP_NA
## Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:1.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :1.0000 Median :0.00000 Median :0.0000
## Mean :0.9161 Mean :0.04482 Mean :0.1257
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000##
## Call:
## lm(formula = TARGET_WINS ~ TEAM_BATTING_H + TEAM_BATTING_2B +
## TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_PITCHING_H + TEAM_PITCHING_HR +
## TEAM_PITCHING_BB + TEAM_FIELDING_E, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.273 -8.832 0.127 8.886 55.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.526453 3.423988 1.906 0.0568 .
## TEAM_BATTING_H 0.048766 0.003208 15.200 < 2e-16 ***
## TEAM_BATTING_2B -0.026072 0.009050 -2.881 0.0040 **
## TEAM_BATTING_3B 0.102196 0.016708 6.116 1.12e-09 ***
## TEAM_BATTING_HR 0.054383 0.024691 2.203 0.0277 *
## TEAM_PITCHING_H -0.001282 0.000327 -3.922 9.05e-05 ***
## TEAM_PITCHING_HR -0.016991 0.022575 -0.753 0.4517
## TEAM_PITCHING_BB 0.010755 0.002036 5.283 1.40e-07 ***
## TEAM_FIELDING_E -0.016351 0.002287 -7.149 1.18e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.48 on 2267 degrees of freedom
## Multiple R-squared: 0.2702, Adjusted R-squared: 0.2677
## F-statistic: 104.9 on 8 and 2267 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = TARGET_WINS ~ TEAM_BATTING_H + TEAM_BATTING_2B +
## TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_PITCHING_H + TEAM_PITCHING_BB +
## TEAM_FIELDING_E, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.763 -8.861 0.095 8.860 55.469
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.2713462 3.2775220 2.219 0.02662 *
## TEAM_BATTING_H 0.0484775 0.0031849 15.221 < 2e-16 ***
## TEAM_BATTING_2B -0.0258127 0.0090430 -2.854 0.00435 **
## TEAM_BATTING_3B 0.1010776 0.0166406 6.074 1.46e-09 ***
## TEAM_BATTING_HR 0.0366916 0.0075591 4.854 1.29e-06 ***
## TEAM_PITCHING_H -0.0013088 0.0003251 -4.026 5.87e-05 ***
## TEAM_PITCHING_BB 0.0103207 0.0019522 5.287 1.36e-07 ***
## TEAM_FIELDING_E -0.0166263 0.0022577 -7.364 2.48e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.48 on 2268 degrees of freedom
## Multiple R-squared: 0.27, Adjusted R-squared: 0.2678
## F-statistic: 119.9 on 7 and 2268 DF, p-value: < 2.2e-16
## [1] "INDEX" "TEAM_BATTING_H" "TEAM_BATTING_2B"
## [4] "TEAM_BATTING_3B" "TEAM_BATTING_HR" "TEAM_BATTING_BB"
## [7] "TEAM_BATTING_SO" "TEAM_BASERUN_SB" "TEAM_BASERUN_CS"
## [10] "TEAM_BATTING_HBP" "TEAM_PITCHING_H" "TEAM_PITCHING_HR"
## [13] "TEAM_PITCHING_BB" "TEAM_PITCHING_SO" "TEAM_FIELDING_E"
## [16] "TEAM_FIELDING_DP" "TEAM_BATTING_SO_NA" "TEAM_BASERUN_SB_NA"
## [19] "TEAM_BASERUN_CS_NA" "TEAM_BATTING_HBP_NA" "TEAM_PITCHING_SO_NA"
## [22] "TEAM_FIELDING_DP_NA"#remove the predictors that have negative effect to the target wins
new_eval_model = subset(test_df, select=c(TEAM_BATTING_H, TEAM_BATTING_2B, TEAM_BATTING_3B, TEAM_BATTING_HR, TEAM_PITCHING_H, TEAM_PITCHING_BB, TEAM_FIELDING_E))
# Turn the NA values in 0
new_eval_model[is.na(new_eval_model)] = 0
# prediction model
prediction_model <- predict(model, newdata=new_eval_model)
prediction_model## 1 2 3 4 5 6 7 8
## 68.57679 70.20767 77.35107 83.60728 66.44188 67.44392 74.01699 72.52290
## 9 10 11 12 13 14 15 16
## 72.07908 75.86204 76.14127 85.66302 84.25863 82.11244 79.28366 80.65313
## 17 18 19 20 21 22 23 24
## 72.72498 80.73209 68.24429 93.15727 84.03790 86.72537 83.94422 76.45507
## 25 26 27 28 29 30 31 32
## 82.33443 84.46690 53.99437 77.34772 83.55037 76.54752 89.64897 87.49762
## 33 34 35 36 37 38 39 40
## 86.39979 88.63464 83.07959 82.97654 76.59917 90.98962 88.25264 89.93392
## 41 42 43 44 45 46 47 48
## 81.06430 86.65244 32.00565 93.94542 84.49850 91.12091 95.25990 72.55215
## 49 50 51 52 53 54 55 56
## 70.71842 77.42567 80.56279 86.18097 79.54452 75.66770 76.77920 78.91475
## 57 58 59 60 61 62 63 64
## 87.00232 70.24445 62.43238 76.94456 85.57690 82.32992 84.10415 84.08464
## 65 66 67 68 69 70 71 72
## 81.72510 88.61128 77.01994 84.45808 75.03575 84.58887 93.11545 78.11656
## 73 74 75 76 77 78 79 80
## 83.60987 87.48446 83.25982 87.59647 81.10361 79.45530 69.17038 75.34361
## 81 82 83 84 85 86 87 88
## 86.58620 91.02278 98.65784 83.24041 86.29588 81.38914 77.81345 83.29427
## 89 90 91 92 93 94 95 96
## 82.14307 85.78844 77.31626 90.17090 74.92238 80.27929 76.63840 76.41073
## 97 98 99 100 101 102 103 104
## 83.76351 101.49146 90.66066 91.80633 85.67709 75.74458 85.85636 82.51112
## 105 106 107 108 109 110 111 112
## 80.28514 75.74648 59.21657 80.05705 83.36447 63.89810 81.69559 80.89442
## 113 114 115 116 117 118 119 120
## 90.51339 88.42404 82.00004 79.88766 89.12636 79.28716 78.32773 70.56117
## 121 122 123 124 125 126 127 128
## 88.18073 64.83877 68.79647 62.89740 70.53486 89.14903 93.52098 77.13546
## 129 130 131 132 133 134 135 136
## 89.76420 96.00349 87.87496 79.55286 74.18762 83.65916 84.63120 67.92567
## 137 138 139 140 141 142 143 144
## 76.76088 79.31622 80.25903 79.00221 65.97271 70.88566 93.96534 80.09868
## 145 146 147 148 149 150 151 152
## 75.63502 76.66057 79.09194 81.58381 85.45157 81.03183 83.18578 79.69117
## 153 154 155 156 157 158 159 160
## 32.00533 74.74922 76.72696 73.53798 83.62346 70.38656 90.86799 71.82949
## 161 162 163 164 165 166 167 168
## 103.86302 102.94796 91.40787 103.43996 96.25437 92.15061 87.44536 83.28689
## 169 170 171 172 173 174 175 176
## 73.88550 80.44850 87.53529 83.90489 81.81791 91.73197 83.62750 78.62979
## 177 178 179 180 181 182 183 184
## 78.72177 78.62720 77.61974 80.23747 75.75891 82.42463 82.50687 83.40560
## 185 186 187 188 189 190 191 192
## 93.86719 84.08224 84.88270 59.90440 62.71131 106.61875 70.30532 79.80179
## 193 194 195 196 197 198 199 200
## 77.50981 80.91032 82.33698 71.26555 77.85090 81.87750 80.77272 86.39044
## 201 202 203 204 205 206 207 208
## 80.67028 82.42010 76.24716 85.64095 77.63218 78.86158 80.18659 76.75479
## 209 210 211 212 213 214 215 216
## 78.45877 74.04968 102.73424 94.95937 83.50166 71.04174 76.47425 88.75922
## 217 218 219 220 221 222 223 224
## 87.14607 86.32952 77.07959 76.85061 79.78128 75.26852 82.97115 79.90219
## 225 226 227 228 229 230 231 232
## 88.18673 76.73958 79.38705 80.08819 80.21071 76.68290 71.78995 94.28243
## 233 234 235 236 237 238 239 240
## 83.96099 86.59268 79.03424 74.35427 81.44309 78.25418 92.42152 75.30730
## 241 242 243 244 245 246 247 248
## 90.78059 88.86296 85.17144 83.49939 63.68535 86.98493 79.74425 82.77956
## 249 250 251 252 253 254 255 256
## 76.14821 84.12894 82.43395 59.19506 90.43189 46.23627 70.80823 77.18288
## 257 258 259
## 75.82183 77.87520 77.54615Model 2 - Stepwise Regression
# Try stepwise regression as mentioned in http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
full_model = lm(TARGET_WINS ~ ., data=train_df)
step.model <- stepAIC(full_model, direction = "both",
trace = FALSE)
summary(step.model)##
## Call:
## lm(formula = TARGET_WINS ~ TEAM_BATTING_H + TEAM_BATTING_2B +
## TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO +
## TEAM_BASERUN_SB + TEAM_PITCHING_H + TEAM_PITCHING_SO + TEAM_FIELDING_E +
## TEAM_FIELDING_DP + TEAM_BASERUN_SB_NA + TEAM_BATTING_HBP_NA +
## TEAM_FIELDING_DP_NA, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.693 -8.067 0.330 7.875 49.924
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.820e+01 4.192e+00 4.340 1.49e-05 ***
## TEAM_BATTING_H 4.682e-02 3.212e-03 14.578 < 2e-16 ***
## TEAM_BATTING_2B -2.757e-02 8.973e-03 -3.073 0.002147 **
## TEAM_BATTING_3B 5.424e-02 1.547e-02 3.507 0.000461 ***
## TEAM_BATTING_HR 7.549e-02 8.642e-03 8.736 < 2e-16 ***
## TEAM_BATTING_BB 2.398e-02 3.239e-03 7.404 1.86e-13 ***
## TEAM_BATTING_SO -1.025e-02 1.776e-03 -5.771 8.97e-09 ***
## TEAM_BASERUN_SB 5.014e-02 4.457e-03 11.249 < 2e-16 ***
## TEAM_PITCHING_H 1.980e-03 3.339e-04 5.930 3.49e-09 ***
## TEAM_PITCHING_SO -1.096e-03 6.613e-04 -1.657 0.097666 .
## TEAM_FIELDING_E -5.685e-02 3.370e-03 -16.873 < 2e-16 ***
## TEAM_FIELDING_DP -1.045e-01 1.309e-02 -7.985 2.21e-15 ***
## TEAM_BASERUN_SB_NA 3.969e+01 2.048e+00 19.385 < 2e-16 ***
## TEAM_BATTING_HBP_NA 3.277e+00 1.071e+00 3.059 0.002244 **
## TEAM_FIELDING_DP_NA -1.073e+01 1.948e+00 -5.507 4.07e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.1 on 2261 degrees of freedom
## Multiple R-squared: 0.4135, Adjusted R-squared: 0.4098
## F-statistic: 113.9 on 14 and 2261 DF, p-value: < 2.2e-16# Train model
train_control = trainControl(method = "cv", number = 10)
step_model = train(TARGET_WINS ~ ., data=train_df,
method = "lmStepAIC",
trControl = train_control,
trace=FALSE)
# Model accuracy
step_model$results## parameter RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 none 12.2621 0.3901083 9.64169 0.5608981 0.06517879 0.3265393##
## Call:
## lm(formula = .outcome ~ TEAM_BATTING_H + TEAM_BATTING_2B + TEAM_BATTING_3B +
## TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO + TEAM_BASERUN_SB +
## TEAM_PITCHING_H + TEAM_PITCHING_SO + TEAM_FIELDING_E + TEAM_FIELDING_DP +
## TEAM_BASERUN_SB_NA + TEAM_BATTING_HBP_NA + TEAM_FIELDING_DP_NA,
## data = dat)
##
## Coefficients:
## (Intercept) TEAM_BATTING_H TEAM_BATTING_2B
## 18.196340 0.046820 -0.027572
## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 0.054244 0.075494 0.023983
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## -0.010247 0.050139 0.001980
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## -0.001096 -0.056855 -0.104532
## TEAM_BASERUN_SB_NA TEAM_BATTING_HBP_NA TEAM_FIELDING_DP_NA
## 39.693780 3.277467 -10.727882##
## Call:
## lm(formula = .outcome ~ TEAM_BATTING_H + TEAM_BATTING_2B + TEAM_BATTING_3B +
## TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO + TEAM_BASERUN_SB +
## TEAM_PITCHING_H + TEAM_PITCHING_SO + TEAM_FIELDING_E + TEAM_FIELDING_DP +
## TEAM_BASERUN_SB_NA + TEAM_BATTING_HBP_NA + TEAM_FIELDING_DP_NA,
## data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.693 -8.067 0.330 7.875 49.924
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.820e+01 4.192e+00 4.340 1.49e-05 ***
## TEAM_BATTING_H 4.682e-02 3.212e-03 14.578 < 2e-16 ***
## TEAM_BATTING_2B -2.757e-02 8.973e-03 -3.073 0.002147 **
## TEAM_BATTING_3B 5.424e-02 1.547e-02 3.507 0.000461 ***
## TEAM_BATTING_HR 7.549e-02 8.642e-03 8.736 < 2e-16 ***
## TEAM_BATTING_BB 2.398e-02 3.239e-03 7.404 1.86e-13 ***
## TEAM_BATTING_SO -1.025e-02 1.776e-03 -5.771 8.97e-09 ***
## TEAM_BASERUN_SB 5.014e-02 4.457e-03 11.249 < 2e-16 ***
## TEAM_PITCHING_H 1.980e-03 3.339e-04 5.930 3.49e-09 ***
## TEAM_PITCHING_SO -1.096e-03 6.613e-04 -1.657 0.097666 .
## TEAM_FIELDING_E -5.685e-02 3.370e-03 -16.873 < 2e-16 ***
## TEAM_FIELDING_DP -1.045e-01 1.309e-02 -7.985 2.21e-15 ***
## TEAM_BASERUN_SB_NA 3.969e+01 2.048e+00 19.385 < 2e-16 ***
## TEAM_BATTING_HBP_NA 3.277e+00 1.071e+00 3.059 0.002244 **
## TEAM_FIELDING_DP_NA -1.073e+01 1.948e+00 -5.507 4.07e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.1 on 2261 degrees of freedom
## Multiple R-squared: 0.4135, Adjusted R-squared: 0.4098
## F-statistic: 113.9 on 14 and 2261 DF, p-value: < 2.2e-16
## [1] 743.6606Model 3 - Try removing TEAM_PITCHING_SO
# Train model without TEAM_PITCHING_SO since it has a relatively high p-value
train_control = trainControl(method = "cv", number = 10)
no_TPS = subset(train_df, select=-c(TEAM_PITCHING_SO))
step_model_noTPS = train(TARGET_WINS ~ ., data=no_TPS,
method = "lmStepAIC",
trControl = train_control,
trace=FALSE)
# Model accuracy
step_model_noTPS$results## parameter RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 none 12.2715 0.3955766 9.654802 0.559686 0.04342146 0.3603521##
## Call:
## lm(formula = .outcome ~ TEAM_BATTING_H + TEAM_BATTING_2B + TEAM_BATTING_3B +
## TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO + TEAM_BASERUN_SB +
## TEAM_PITCHING_H + TEAM_FIELDING_E + TEAM_FIELDING_DP + TEAM_BASERUN_SB_NA +
## TEAM_BATTING_HBP_NA + TEAM_FIELDING_DP_NA, data = dat)
##
## Coefficients:
## (Intercept) TEAM_BATTING_H TEAM_BATTING_2B
## 17.475160 0.047857 -0.029176
## TEAM_BATTING_3B TEAM_BATTING_HR TEAM_BATTING_BB
## 0.053032 0.076969 0.023764
## TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_PITCHING_H
## -0.011516 0.049503 0.001683
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BASERUN_SB_NA
## -0.055278 -0.104090 38.683727
## TEAM_BATTING_HBP_NA TEAM_FIELDING_DP_NA
## 3.170394 -11.012818##
## Call:
## lm(formula = .outcome ~ TEAM_BATTING_H + TEAM_BATTING_2B + TEAM_BATTING_3B +
## TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO + TEAM_BASERUN_SB +
## TEAM_PITCHING_H + TEAM_FIELDING_E + TEAM_FIELDING_DP + TEAM_BASERUN_SB_NA +
## TEAM_BATTING_HBP_NA + TEAM_FIELDING_DP_NA, data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.938 -8.049 0.369 7.904 49.371
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.748e+01 4.171e+00 4.189 2.91e-05 ***
## TEAM_BATTING_H 4.786e-02 3.151e-03 15.187 < 2e-16 ***
## TEAM_BATTING_2B -2.918e-02 8.924e-03 -3.269 0.001094 **
## TEAM_BATTING_3B 5.303e-02 1.545e-02 3.432 0.000611 ***
## TEAM_BATTING_HR 7.697e-02 8.599e-03 8.951 < 2e-16 ***
## TEAM_BATTING_BB 2.376e-02 3.238e-03 7.339 2.98e-13 ***
## TEAM_BATTING_SO -1.152e-02 1.603e-03 -7.185 9.12e-13 ***
## TEAM_BASERUN_SB 4.950e-02 4.442e-03 11.144 < 2e-16 ***
## TEAM_PITCHING_H 1.683e-03 2.817e-04 5.974 2.68e-09 ***
## TEAM_FIELDING_E -5.528e-02 3.234e-03 -17.095 < 2e-16 ***
## TEAM_FIELDING_DP -1.041e-01 1.309e-02 -7.950 2.92e-15 ***
## TEAM_BASERUN_SB_NA 3.868e+01 1.956e+00 19.782 < 2e-16 ***
## TEAM_BATTING_HBP_NA 3.170e+00 1.070e+00 2.964 0.003072 **
## TEAM_FIELDING_DP_NA -1.101e+01 1.941e+00 -5.673 1.58e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.11 on 2262 degrees of freedom
## Multiple R-squared: 0.4128, Adjusted R-squared: 0.4094
## F-statistic: 122.3 on 13 and 2262 DF, p-value: < 2.2e-16
4. Predictions on Evaluation Set
Out of the three models we created, the second model created with stepwise selection is the best of the three. The Adjusted R squared is 0.4098 which explains approximately 41% of variation in Target Wins can be explained by our model. This f statistic tells us if there is a relationship between the dependent and independent variables we are testing. Generally, a large F indicates a stronger relationship and here we have 113.9. The normal quantile quantile plot for residuals displays an approximately straight line so the residuals are approximately normally distributed. The MSE is 743.6606. Using this model we were able to make predictions for our evaluation data.
# convert decimals of wins back to number of wins, rounded
test_preds = round(predict(model, newdata=test_df)) #*162
test_df$PRED_TARGET_WINS = test_preds
# write out evaluation data with predictions
write.csv(test_df, 'data/eval_with_preds.csv')
hist(test_preds)
