DATA 621 Business And Data Analytics - Assignment 1 - Moneyball
Luisa Velasco
September 30 2018
Section 1 - Data Exploration
The original data was loaded containing 2276 rows and 16 columns related to batting, base run, pitching, and fielding. A summary and boxplots of all variables suggest some columns have missing data, and some may contain outliers.
A visual relationship of the target variable (TARGET_WINS) and the rest of the possible predictor variables were plotted; and correlation values suggest individual relationships with the target variable are not very strong, there appeared neither an obvious positive nor negative linear trend.
In contrast, a correlation matrix among possible predictors suggests some variables with strong relationships (e.g. TEAM_BATTING_SO and TEAM_PITCHING_SO).
library(ggcorrplot)
library(dplyr)
library(car)
# Read the training data
df <- read.csv("https://raw.githubusercontent.com/L-Velasco/DATA621_FA18/master/HW1/moneyball-training-data.csv", stringsAsFactors = FALSE)
# Exclude the INDEX column
tr <- df[-1]1.1 Size, Summary and Boxplots of the Data
dim(tr)## [1] 2276 16summary(tr)## 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.: 548.0 1st Qu.: 66.0
## Median :102.00 Median :512.0 Median : 750.0 Median :101.0
## Mean : 99.61 Mean :501.6 Mean : 735.6 Mean :124.8
## 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 930.0 3rd Qu.:156.0
## Max. :264.00 Max. :878.0 Max. :1399.0 Max. :697.0
## NA's :102 NA's :131
## TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## Min. : 0.0 Min. :29.00 Min. : 1137 Min. : 0.0
## 1st Qu.: 38.0 1st Qu.:50.50 1st Qu.: 1419 1st Qu.: 50.0
## Median : 49.0 Median :58.00 Median : 1518 Median :107.0
## Mean : 52.8 Mean :59.36 Mean : 1779 Mean :105.7
## 3rd Qu.: 62.0 3rd Qu.:67.00 3rd Qu.: 1682 3rd Qu.:150.0
## Max. :201.0 Max. :95.00 Max. :30132 Max. :343.0
## NA's :772 NA's :2085
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## Min. : 0.0 Min. : 0.0 Min. : 65.0 Min. : 52.0
## 1st Qu.: 476.0 1st Qu.: 615.0 1st Qu.: 127.0 1st Qu.:131.0
## Median : 536.5 Median : 813.5 Median : 159.0 Median :149.0
## Mean : 553.0 Mean : 817.7 Mean : 246.5 Mean :146.4
## 3rd Qu.: 611.0 3rd Qu.: 968.0 3rd Qu.: 249.2 3rd Qu.:164.0
## Max. :3645.0 Max. :19278.0 Max. :1898.0 Max. :228.0
## NA's :102 NA's :286boxplot(tr$TARGET_WINS, xlab = "TARGET_WINS")
par(mfrow=c(3,5))
x <- c(2:16)
for (val in x) {
boxplot(tr[,val], xlab=names(tr[val]))
}
par(mfrow=c(1,1))1.2 Relationships and Correlations with Response Variable (TARGET WINS)
#### Target Wins vs all variables
par(mfrow=c(3,5))
x <- c(2:16)
for (val in x) {
plot(tr[,val],tr$TARGET_WINS, xlab=names(tr[val]))
}
par(mfrow=c(1,1))
cor(tr, use = "complete.obs")[,1]## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## 1.00000000 0.46994665 0.31298400 -0.12434586
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## 0.42241683 0.46868793 -0.22889273 0.01483639
## TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## -0.17875598 0.07350424 0.47123431 0.42246683
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 0.46839882 -0.22936481 -0.38668800 -0.195866011.3 Correlations Among Possible Predictor Variables
corr<- round(cor(tr[-1], use="complete.obs"),1)
ggcorrplot(corr, lab = TRUE)
corr## TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## TEAM_BATTING_H 1.0 0.6 0.2
## TEAM_BATTING_2B 0.6 1.0 0.0
## TEAM_BATTING_3B 0.2 0.0 1.0
## TEAM_BATTING_HR 0.4 0.3 -0.2
## TEAM_BATTING_BB 0.2 0.2 -0.2
## TEAM_BATTING_SO -0.3 -0.1 -0.2
## TEAM_BASERUN_SB 0.1 -0.2 0.2
## TEAM_BASERUN_CS -0.1 -0.2 0.2
## TEAM_BATTING_HBP 0.0 0.0 -0.2
## TEAM_PITCHING_H 1.0 0.6 0.2
## TEAM_PITCHING_HR 0.4 0.2 -0.2
## TEAM_PITCHING_BB 0.2 0.2 -0.2
## TEAM_PITCHING_SO -0.3 -0.1 -0.2
## TEAM_FIELDING_E -0.3 -0.2 -0.1
## TEAM_FIELDING_DP 0.0 0.0 0.1
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO
## TEAM_BATTING_H 0.4 0.2 -0.3
## TEAM_BATTING_2B 0.3 0.2 -0.1
## TEAM_BATTING_3B -0.2 -0.2 -0.2
## TEAM_BATTING_HR 1.0 0.5 0.2
## TEAM_BATTING_BB 0.5 1.0 0.2
## TEAM_BATTING_SO 0.2 0.2 1.0
## TEAM_BASERUN_SB -0.2 -0.1 -0.1
## TEAM_BASERUN_CS -0.3 -0.2 -0.1
## TEAM_BATTING_HBP 0.1 0.0 0.2
## TEAM_PITCHING_H 0.4 0.2 -0.3
## TEAM_PITCHING_HR 1.0 0.5 0.2
## TEAM_PITCHING_BB 0.5 1.0 0.2
## TEAM_PITCHING_SO 0.2 0.2 1.0
## TEAM_FIELDING_E 0.0 -0.1 0.3
## TEAM_FIELDING_DP -0.1 -0.1 -0.1
## TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP
## TEAM_BATTING_H 0.1 -0.1 0.0
## TEAM_BATTING_2B -0.2 -0.2 0.0
## TEAM_BATTING_3B 0.2 0.2 -0.2
## TEAM_BATTING_HR -0.2 -0.3 0.1
## TEAM_BATTING_BB -0.1 -0.2 0.0
## TEAM_BATTING_SO -0.1 -0.1 0.2
## TEAM_BASERUN_SB 1.0 0.6 -0.1
## TEAM_BASERUN_CS 0.6 1.0 -0.1
## TEAM_BATTING_HBP -0.1 -0.1 1.0
## TEAM_PITCHING_H 0.1 -0.1 0.0
## TEAM_PITCHING_HR -0.2 -0.3 0.1
## TEAM_PITCHING_BB -0.1 -0.2 0.0
## TEAM_PITCHING_SO -0.1 -0.1 0.2
## TEAM_FIELDING_E 0.0 0.2 0.0
## TEAM_FIELDING_DP -0.1 0.0 -0.1
## TEAM_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## TEAM_BATTING_H 1.0 0.4 0.2
## TEAM_BATTING_2B 0.6 0.2 0.2
## TEAM_BATTING_3B 0.2 -0.2 -0.2
## TEAM_BATTING_HR 0.4 1.0 0.5
## TEAM_BATTING_BB 0.2 0.5 1.0
## TEAM_BATTING_SO -0.3 0.2 0.2
## TEAM_BASERUN_SB 0.1 -0.2 -0.1
## TEAM_BASERUN_CS -0.1 -0.3 -0.2
## TEAM_BATTING_HBP 0.0 0.1 0.0
## TEAM_PITCHING_H 1.0 0.4 0.2
## TEAM_PITCHING_HR 0.4 1.0 0.5
## TEAM_PITCHING_BB 0.2 0.5 1.0
## TEAM_PITCHING_SO -0.3 0.2 0.2
## TEAM_FIELDING_E -0.3 0.0 -0.1
## TEAM_FIELDING_DP 0.0 -0.1 -0.1
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## TEAM_BATTING_H -0.3 -0.3 0.0
## TEAM_BATTING_2B -0.1 -0.2 0.0
## TEAM_BATTING_3B -0.2 -0.1 0.1
## TEAM_BATTING_HR 0.2 0.0 -0.1
## TEAM_BATTING_BB 0.2 -0.1 -0.1
## TEAM_BATTING_SO 1.0 0.3 -0.1
## TEAM_BASERUN_SB -0.1 0.0 -0.1
## TEAM_BASERUN_CS -0.1 0.2 0.0
## TEAM_BATTING_HBP 0.2 0.0 -0.1
## TEAM_PITCHING_H -0.3 -0.3 0.0
## TEAM_PITCHING_HR 0.2 0.0 -0.1
## TEAM_PITCHING_BB 0.2 -0.1 -0.1
## TEAM_PITCHING_SO 1.0 0.3 -0.1
## TEAM_FIELDING_E 0.3 1.0 0.0
## TEAM_FIELDING_DP -0.1 0.0 1.0Section 2 - Data Preparation
To prepare the data for modeling, variables will be added, removed, imputed, and treated for outliers.
tr_prep <- tr2.1 Add variable
A new variable TEAM_TOTAL_BASES will be added to represent number for total bases with formula derived from https://baseballtips.com/glossary/index.html/
Total Bases = [H + 2B + (2 X 3B) + (3 X HR)]
Below shows the first few rows after adding the new variable at the end:
#add variable
tr_prep <- tr_prep %>%
mutate(TEAM_TOTAL_BASES =
TEAM_BATTING_H + TEAM_BATTING_2B
+ (2 * TEAM_BATTING_3B) + (3 * TEAM_BATTING_HR))
head(tr_prep)## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## 1 39 1445 194 39
## 2 70 1339 219 22
## 3 86 1377 232 35
## 4 70 1387 209 38
## 5 82 1297 186 27
## 6 75 1279 200 36
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## 1 13 143 842 NA
## 2 190 685 1075 37
## 3 137 602 917 46
## 4 96 451 922 43
## 5 102 472 920 49
## 6 92 443 973 107
## TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## 1 NA NA 9364 84
## 2 28 NA 1347 191
## 3 27 NA 1377 137
## 4 30 NA 1396 97
## 5 39 NA 1297 102
## 6 59 NA 1279 92
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## 1 927 5456 1011 NA
## 2 689 1082 193 155
## 3 602 917 175 153
## 4 454 928 164 156
## 5 472 920 138 168
## 6 443 973 123 149
## TEAM_TOTAL_BASES
## 1 1756
## 2 2172
## 3 2090
## 4 1960
## 5 1843
## 6 18272.2 Remove variables
Due to almost 92% missing values on TEAM_BATTING_HBP, it will be removed from the dataset.
Due to the addition of aggregate variable TEAM_TOTAL_BASES, the contributing variables will be removed: TEAM_BATTING_H, TEAM_BATTING_2B, TEAM_BATTING_3B, TEAM_BATTING_HR.
Below shows the dataset’s size and variables after this step:
#remove variable
tr_prep = select(tr_prep,
-TEAM_BATTING_H,
-TEAM_BATTING_2B,
-TEAM_BATTING_3B,
-TEAM_BATTING_HR,
-TEAM_BATTING_HBP)
dim(tr_prep)## [1] 2276 12names(tr_prep)## [1] "TARGET_WINS" "TEAM_BATTING_BB" "TEAM_BATTING_SO"
## [4] "TEAM_BASERUN_SB" "TEAM_BASERUN_CS" "TEAM_PITCHING_H"
## [7] "TEAM_PITCHING_HR" "TEAM_PITCHING_BB" "TEAM_PITCHING_SO"
## [10] "TEAM_FIELDING_E" "TEAM_FIELDING_DP" "TEAM_TOTAL_BASES"2.3 Impute missing data
Below are the variables with missing data which will be populated with the variable’s mean.
colnames(tr_prep)[colSums(is.na(tr_prep)) > 0]## [1] "TEAM_BATTING_SO" "TEAM_BASERUN_SB" "TEAM_BASERUN_CS"
## [4] "TEAM_PITCHING_SO" "TEAM_FIELDING_DP"Below is a summary of the dataset after filling up the missing values:
#impute
tr_prep = tr_prep %>%
mutate(TEAM_BASERUN_CS =
ifelse(is.na(TEAM_BASERUN_CS),
mean(TEAM_BASERUN_CS, na.rm=TRUE), TEAM_BASERUN_CS)) %>%
mutate(TEAM_BASERUN_SB =
ifelse(is.na(TEAM_BASERUN_SB),
mean(TEAM_BASERUN_SB, na.rm=TRUE), TEAM_BASERUN_SB)) %>%
mutate(TEAM_PITCHING_SO =
ifelse(is.na(TEAM_PITCHING_SO),
mean(TEAM_PITCHING_SO, na.rm=TRUE), TEAM_PITCHING_SO)) %>%
mutate(TEAM_BATTING_SO =
ifelse(is.na(TEAM_BATTING_SO),
mean(TEAM_BATTING_SO, na.rm=TRUE), TEAM_BATTING_SO)) %>%
mutate(TEAM_FIELDING_DP =
ifelse(is.na(TEAM_FIELDING_DP),
mean(TEAM_FIELDING_DP, na.rm=TRUE), TEAM_FIELDING_DP))
summary(tr_prep)## TARGET_WINS TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 71.00 1st Qu.:451.0 1st Qu.: 556.8 1st Qu.: 67.0
## Median : 82.00 Median :512.0 Median : 735.6 Median :106.0
## Mean : 80.79 Mean :501.6 Mean : 735.6 Mean :124.8
## 3rd Qu.: 92.00 3rd Qu.:580.0 3rd Qu.: 925.0 3rd Qu.:151.0
## Max. :146.00 Max. :878.0 Max. :1399.0 Max. :697.0
## TEAM_BASERUN_CS TEAM_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## Min. : 0.00 Min. : 1137 Min. : 0.0 Min. : 0.0
## 1st Qu.: 44.00 1st Qu.: 1419 1st Qu.: 50.0 1st Qu.: 476.0
## Median : 52.80 Median : 1518 Median :107.0 Median : 536.5
## Mean : 52.80 Mean : 1779 Mean :105.7 Mean : 553.0
## 3rd Qu.: 54.25 3rd Qu.: 1682 3rd Qu.:150.0 3rd Qu.: 611.0
## Max. :201.00 Max. :30132 Max. :343.0 Max. :3645.0
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_TOTAL_BASES
## Min. : 0.0 Min. : 65.0 Min. : 52.0 Min. :1026
## 1st Qu.: 626.0 1st Qu.: 127.0 1st Qu.:134.0 1st Qu.:1947
## Median : 817.7 Median : 159.0 Median :146.4 Median :2126
## Mean : 817.7 Mean : 246.5 Mean :146.4 Mean :2120
## 3rd Qu.: 957.0 3rd Qu.: 249.2 3rd Qu.:161.2 3rd Qu.:2285
## Max. :19278.0 Max. :1898.0 Max. :228.0 Max. :32902.4 Cap Outliers
Any outliers outside of lower 1.5IQR would be capped at 5th %ile, and observations above the upper 1.5IQR would be capped at 95th %ile. Reference from http://r-statistics.co/Outlier-Treatment-With-R.html
# Outlier Capping
tr_prep2 <- tr_prep
id <- c(2:12)
for (val in id) {
qnt <- quantile(tr_prep2[,val], probs=c(.25, .75), na.rm = T)
caps <- quantile(tr_prep2[,val], probs=c(.05, .95), na.rm = T)
H <- 1.5 * IQR(tr_prep2[,val], na.rm = T)
tr_prep2[,val][tr_prep2[,val] < (qnt[1] - H)] <- caps[1]
tr_prep2[,val][tr_prep2[,val] > (qnt[2] + H)] <- caps[2]
}After these 4 data preparation tasks, below displays the correlations of all possible predictor variables:
corr<- round(cor(tr_prep2[-1]),1)
ggcorrplot(corr, lab = TRUE)
corr## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## TEAM_BATTING_BB 1.0 0.3 -0.1
## TEAM_BATTING_SO 0.3 1.0 -0.2
## TEAM_BASERUN_SB -0.1 -0.2 1.0
## TEAM_BASERUN_CS -0.1 -0.2 0.4
## TEAM_PITCHING_H -0.4 -0.5 0.3
## TEAM_PITCHING_HR 0.5 0.6 -0.4
## TEAM_PITCHING_BB 0.8 0.0 0.1
## TEAM_PITCHING_SO 0.1 0.9 -0.1
## TEAM_FIELDING_E -0.5 -0.6 0.5
## TEAM_FIELDING_DP 0.3 0.1 -0.4
## TEAM_TOTAL_BASES 0.3 0.1 -0.2
## TEAM_BASERUN_CS TEAM_PITCHING_H TEAM_PITCHING_HR
## TEAM_BATTING_BB -0.1 -0.4 0.5
## TEAM_BATTING_SO -0.2 -0.5 0.6
## TEAM_BASERUN_SB 0.4 0.3 -0.4
## TEAM_BASERUN_CS 1.0 0.0 -0.3
## TEAM_PITCHING_H 0.0 1.0 -0.2
## TEAM_PITCHING_HR -0.3 -0.2 1.0
## TEAM_PITCHING_BB -0.1 0.1 0.3
## TEAM_PITCHING_SO -0.2 -0.2 0.5
## TEAM_FIELDING_E 0.1 0.7 -0.6
## TEAM_FIELDING_DP -0.1 -0.1 0.4
## TEAM_TOTAL_BASES -0.2 0.2 0.7
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E
## TEAM_BATTING_BB 0.8 0.1 -0.5
## TEAM_BATTING_SO 0.0 0.9 -0.6
## TEAM_BASERUN_SB 0.1 -0.1 0.5
## TEAM_BASERUN_CS -0.1 -0.2 0.1
## TEAM_PITCHING_H 0.1 -0.2 0.7
## TEAM_PITCHING_HR 0.3 0.5 -0.6
## TEAM_PITCHING_BB 1.0 0.1 -0.1
## TEAM_PITCHING_SO 0.1 1.0 -0.3
## TEAM_FIELDING_E -0.1 -0.3 1.0
## TEAM_FIELDING_DP 0.3 0.0 -0.3
## TEAM_TOTAL_BASES 0.3 0.1 -0.2
## TEAM_FIELDING_DP TEAM_TOTAL_BASES
## TEAM_BATTING_BB 0.3 0.3
## TEAM_BATTING_SO 0.1 0.1
## TEAM_BASERUN_SB -0.4 -0.2
## TEAM_BASERUN_CS -0.1 -0.2
## TEAM_PITCHING_H -0.1 0.2
## TEAM_PITCHING_HR 0.4 0.7
## TEAM_PITCHING_BB 0.3 0.3
## TEAM_PITCHING_SO 0.0 0.1
## TEAM_FIELDING_E -0.3 -0.2
## TEAM_FIELDING_DP 1.0 0.4
## TEAM_TOTAL_BASES 0.4 1.0Section 3 - Build Models
3.1 All variables Included
Below shows the summary, vif and diagnostics plot when all variables are included.
### Model 1 - All variables included
model1 <- lm(TARGET_WINS ~., data = tr_prep2)
summary(model1)##
## Call:
## lm(formula = TARGET_WINS ~ ., data = tr_prep2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.040 -8.368 0.167 8.333 64.423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.947444 5.025463 6.158 8.68e-10 ***
## TEAM_BATTING_BB 0.053735 0.008897 6.040 1.80e-09 ***
## TEAM_BATTING_SO -0.015663 0.005052 -3.100 0.00196 **
## TEAM_BASERUN_SB 0.060483 0.006071 9.962 < 2e-16 ***
## TEAM_BASERUN_CS -0.058439 0.023006 -2.540 0.01115 *
## TEAM_PITCHING_H 0.008907 0.002095 4.253 2.20e-05 ***
## TEAM_PITCHING_HR -0.004984 0.012015 -0.415 0.67832
## TEAM_PITCHING_BB -0.034361 0.007981 -4.305 1.74e-05 ***
## TEAM_PITCHING_SO 0.005110 0.004562 1.120 0.26285
## TEAM_FIELDING_E -0.022199 0.002982 -7.444 1.38e-13 ***
## TEAM_FIELDING_DP -0.109811 0.014798 -7.421 1.64e-13 ***
## TEAM_TOTAL_BASES 0.024669 0.002417 10.208 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.43 on 2264 degrees of freedom
## Multiple R-squared: 0.2765, Adjusted R-squared: 0.273
## F-statistic: 78.66 on 11 and 2264 DF, p-value: < 2.2e-16vif(model1)## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS
## 11.582096 17.849283 2.294852 1.326458
## TEAM_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB TEAM_PITCHING_SO
## 6.475854 6.725598 8.705859 13.284509
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_TOTAL_BASES
## 4.325928 1.419217 4.555244par(mfrow=c(2,2))
plot(model1)
par(mfrow=c(1,1))3.2 Excludes variables based on possible Multicollinearity
Below shows the summary, vif and diagnostics plot when TEAM_BATTING_SO, TEAM_PITCHING_BB, TEAM_PITCHING_H, TEAM_PITCHING_HR variables are excluded.
### Model 2 - Excludes multicollinearity
model2 <- lm(TARGET_WINS ~ .
- TEAM_BATTING_SO
- TEAM_PITCHING_BB
- TEAM_PITCHING_H
- TEAM_PITCHING_HR, data = tr_prep2)
summary(model2)##
## Call:
## lm(formula = TARGET_WINS ~ . - TEAM_BATTING_SO - TEAM_PITCHING_BB -
## TEAM_PITCHING_H - TEAM_PITCHING_HR, data = tr_prep2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -60.259 -8.687 0.165 8.520 58.288
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 35.777053 3.731338 9.588 < 2e-16 ***
## TEAM_BATTING_BB 0.014466 0.003454 4.189 2.91e-05 ***
## TEAM_BASERUN_SB 0.051170 0.005770 8.869 < 2e-16 ***
## TEAM_BASERUN_CS -0.030529 0.022776 -1.340 0.18
## TEAM_PITCHING_SO -0.009154 0.001334 -6.864 8.59e-12 ***
## TEAM_FIELDING_E -0.010721 0.002169 -4.944 8.22e-07 ***
## TEAM_FIELDING_DP -0.123429 0.014658 -8.421 < 2e-16 ***
## TEAM_TOTAL_BASES 0.028888 0.001281 22.559 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.57 on 2268 degrees of freedom
## Multiple R-squared: 0.2604, Adjusted R-squared: 0.2581
## F-statistic: 114 on 7 and 2268 DF, p-value: < 2.2e-16vif(model2)## TEAM_BATTING_BB TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_PITCHING_SO
## 1.710103 2.030921 1.273957 1.112149
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_TOTAL_BASES
## 2.241362 1.364467 1.253293par(mfrow=c(2,2))
plot(model2)
par(mfrow=c(1,1))3.3 Excludes variable based on insignificant P-value
Below shows the summary, vif and diagnostics plot when TEAM_BASERUN_CS variable is excluded.
### Model 3 - Excludes Insignificant variables
model3 <- lm(TARGET_WINS ~ .
- TEAM_BATTING_SO
- TEAM_PITCHING_BB
- TEAM_PITCHING_H
- TEAM_PITCHING_HR
- TEAM_BASERUN_CS, data = tr_prep2)
summary(model3)##
## Call:
## lm(formula = TARGET_WINS ~ . - TEAM_BATTING_SO - TEAM_PITCHING_BB -
## TEAM_PITCHING_H - TEAM_PITCHING_HR - TEAM_BASERUN_CS, data = tr_prep2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -60.045 -8.733 0.227 8.558 58.198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.637350 3.373213 9.972 < 2e-16 ***
## TEAM_BATTING_BB 0.015397 0.003384 4.551 5.63e-06 ***
## TEAM_BASERUN_SB 0.047982 0.005257 9.127 < 2e-16 ***
## TEAM_PITCHING_SO -0.008846 0.001314 -6.733 2.10e-11 ***
## TEAM_FIELDING_E -0.009889 0.002078 -4.758 2.07e-06 ***
## TEAM_FIELDING_DP -0.124931 0.014617 -8.547 < 2e-16 ***
## TEAM_TOTAL_BASES 0.028997 0.001278 22.687 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.57 on 2269 degrees of freedom
## Multiple R-squared: 0.2598, Adjusted R-squared: 0.2578
## F-statistic: 132.7 on 6 and 2269 DF, p-value: < 2.2e-16vif(model3)## TEAM_BATTING_BB TEAM_BASERUN_SB TEAM_PITCHING_SO TEAM_FIELDING_E
## 1.640901 1.685747 1.079243 2.058003
## TEAM_FIELDING_DP TEAM_TOTAL_BASES
## 1.356490 1.248182par(mfrow=c(2,2))
plot(model3)
par(mfrow=c(1,1))Section 4 - Select Model
Based on the 3 models, the 3rd one will be selected although the R-squared value is not the highest because possible multicollinearity is addressed and all included variables appear to contribute significantly to the model. The predictor coefficients makes sense
The TARGET_WINS of the evaluation data set will be predicted using this Model 3.