HW1
Adam Gersowitz
3/1/2021
Libraries
library(knitr)
library(tidyverse)
library(reshape2)
library(VIM)
library(corrplot)
library(naniar)
library(tidyverse)
library(skimr)
library(funModeling)
library(fastDummies)Data
In this homework assignment, we are asked to explore, analyze and model a baseball data set containing approximately 2200 records. Each record represents a professional baseball team from the years 1871 to 2006 inclusive. Each record has the performance of the team for the given year, with all of the statistics adjusted to match the performance of a 162 game season.
Our objective is to build a multiple linear regression model on the training data to predict the number of wins for the team based on the variables given or variables that derive from the variables provided. Below is a short description of the variables of interest in the data set:
Load Data
test <- read_csv("https://raw.githubusercontent.com/agersowitz/DATA-621/main/mb_eval.csv")## Parsed with column specification:
## cols(
## INDEX = col_double(),
## TEAM_BATTING_H = col_double(),
## TEAM_BATTING_2B = col_double(),
## TEAM_BATTING_3B = col_double(),
## TEAM_BATTING_HR = col_double(),
## TEAM_BATTING_BB = col_double(),
## TEAM_BATTING_SO = col_double(),
## TEAM_BASERUN_SB = col_double(),
## TEAM_BASERUN_CS = col_double(),
## TEAM_BATTING_HBP = col_double(),
## TEAM_PITCHING_H = col_double(),
## TEAM_PITCHING_HR = col_double(),
## TEAM_PITCHING_BB = col_double(),
## TEAM_PITCHING_SO = col_double(),
## TEAM_FIELDING_E = col_double(),
## TEAM_FIELDING_DP = col_double()
## )test <- data.frame(eval)
yr <- read_csv("https://raw.githubusercontent.com/agersowitz/DATA-621/main/year%20predict.csv")## Parsed with column specification:
## cols(
## Year = col_double(),
## H = col_double(),
## `2B` = col_double(),
## `3B` = col_double(),
## HR = col_double(),
## SB = col_double(),
## BB = col_double(),
## SO = col_double()
## )yr <- data.frame(yr)
train <- read_csv("https://raw.githubusercontent.com/agersowitz/DATA-621/main/mb_train.csv")## Parsed with column specification:
## cols(
## INDEX = col_double(),
## TARGET_WINS = col_double(),
## TEAM_BATTING_H = col_double(),
## TEAM_BATTING_2B = col_double(),
## TEAM_BATTING_3B = col_double(),
## TEAM_BATTING_HR = col_double(),
## TEAM_BATTING_BB = col_double(),
## TEAM_BATTING_SO = col_double(),
## TEAM_BASERUN_SB = col_double(),
## TEAM_BASERUN_CS = col_double(),
## TEAM_BATTING_HBP = col_double(),
## TEAM_PITCHING_H = col_double(),
## TEAM_PITCHING_HR = col_double(),
## TEAM_PITCHING_BB = col_double(),
## TEAM_PITCHING_SO = col_double(),
## TEAM_FIELDING_E = col_double(),
## TEAM_FIELDING_DP = col_double()
## )train <- data.frame(train)skim(train)| Name | train |
| Number of rows | 2276 |
| Number of columns | 17 |
| _______________________ | |
| Column type frequency: | |
| numeric | 17 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| INDEX | 0 | 1.00 | 1268.46 | 736.35 | 1 | 630.75 | 1270.5 | 1915.50 | 2535 | ▇▇▇▇▇ |
| TARGET_WINS | 0 | 1.00 | 80.79 | 15.75 | 0 | 71.00 | 82.0 | 92.00 | 146 | ▁▁▇▅▁ |
| TEAM_BATTING_H | 0 | 1.00 | 1469.27 | 144.59 | 891 | 1383.00 | 1454.0 | 1537.25 | 2554 | ▁▇▂▁▁ |
| TEAM_BATTING_2B | 0 | 1.00 | 241.25 | 46.80 | 69 | 208.00 | 238.0 | 273.00 | 458 | ▁▆▇▂▁ |
| TEAM_BATTING_3B | 0 | 1.00 | 55.25 | 27.94 | 0 | 34.00 | 47.0 | 72.00 | 223 | ▇▇▂▁▁ |
| TEAM_BATTING_HR | 0 | 1.00 | 99.61 | 60.55 | 0 | 42.00 | 102.0 | 147.00 | 264 | ▇▆▇▅▁ |
| TEAM_BATTING_BB | 0 | 1.00 | 501.56 | 122.67 | 0 | 451.00 | 512.0 | 580.00 | 878 | ▁▁▇▇▁ |
| TEAM_BATTING_SO | 102 | 0.96 | 735.61 | 248.53 | 0 | 548.00 | 750.0 | 930.00 | 1399 | ▁▆▇▇▁ |
| TEAM_BASERUN_SB | 131 | 0.94 | 124.76 | 87.79 | 0 | 66.00 | 101.0 | 156.00 | 697 | ▇▃▁▁▁ |
| TEAM_BASERUN_CS | 772 | 0.66 | 52.80 | 22.96 | 0 | 38.00 | 49.0 | 62.00 | 201 | ▃▇▁▁▁ |
| TEAM_BATTING_HBP | 2085 | 0.08 | 59.36 | 12.97 | 29 | 50.50 | 58.0 | 67.00 | 95 | ▂▇▇▅▁ |
| TEAM_PITCHING_H | 0 | 1.00 | 1779.21 | 1406.84 | 1137 | 1419.00 | 1518.0 | 1682.50 | 30132 | ▇▁▁▁▁ |
| TEAM_PITCHING_HR | 0 | 1.00 | 105.70 | 61.30 | 0 | 50.00 | 107.0 | 150.00 | 343 | ▇▇▆▁▁ |
| TEAM_PITCHING_BB | 0 | 1.00 | 553.01 | 166.36 | 0 | 476.00 | 536.5 | 611.00 | 3645 | ▇▁▁▁▁ |
| TEAM_PITCHING_SO | 102 | 0.96 | 817.73 | 553.09 | 0 | 615.00 | 813.5 | 968.00 | 19278 | ▇▁▁▁▁ |
| TEAM_FIELDING_E | 0 | 1.00 | 246.48 | 227.77 | 65 | 127.00 | 159.0 | 249.25 | 1898 | ▇▁▁▁▁ |
| TEAM_FIELDING_DP | 286 | 0.87 | 146.39 | 26.23 | 52 | 131.00 | 149.0 | 164.00 | 228 | ▁▂▇▆▁ |
As the first step in data exploration I use the skim function form the skimr package. This shows missing data, mean, percentiles and a histogram of the distribution of all of the data fields all in one output.
We can see there are numerous fields that are missing data. We will replace these values with the median value for that field.
str(train)## 'data.frame': 2276 obs. of 17 variables:
## $ INDEX : num 1 2 3 4 5 6 7 8 11 12 ...
## $ TARGET_WINS : num 39 70 86 70 82 75 80 85 86 76 ...
## $ TEAM_BATTING_H : num 1445 1339 1377 1387 1297 ...
## $ TEAM_BATTING_2B : num 194 219 232 209 186 200 179 171 197 213 ...
## $ TEAM_BATTING_3B : num 39 22 35 38 27 36 54 37 40 18 ...
## $ TEAM_BATTING_HR : num 13 190 137 96 102 92 122 115 114 96 ...
## $ TEAM_BATTING_BB : num 143 685 602 451 472 443 525 456 447 441 ...
## $ TEAM_BATTING_SO : num 842 1075 917 922 920 ...
## $ TEAM_BASERUN_SB : num NA 37 46 43 49 107 80 40 69 72 ...
## $ TEAM_BASERUN_CS : num NA 28 27 30 39 59 54 36 27 34 ...
## $ TEAM_BATTING_HBP: num NA NA NA NA NA NA NA NA NA NA ...
## $ TEAM_PITCHING_H : num 9364 1347 1377 1396 1297 ...
## $ TEAM_PITCHING_HR: num 84 191 137 97 102 92 122 116 114 96 ...
## $ TEAM_PITCHING_BB: num 927 689 602 454 472 443 525 459 447 441 ...
## $ TEAM_PITCHING_SO: num 5456 1082 917 928 920 ...
## $ TEAM_FIELDING_E : num 1011 193 175 164 138 ...
## $ TEAM_FIELDING_DP: num NA 155 153 156 168 149 186 136 169 159 ...All the variables are integer and TEAM_BATTING_HBP has a lot of missing values. Let’s look at the summary of the data.
summary(train)## 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 :286g = melt(train)
ggplot(g, aes(x= value)) +
geom_density(fill='blue') +
facet_wrap(~variable, scales = 'free') +
theme_light()
Check for rows with missing values
sum(complete.cases(train))## [1] 191Check how many rows with missing values in terms of percentage
sum(complete.cases(train))/(nrow(train)) *100## [1] 8.391916missing_plot <- aggr(train, col=c('blue','red'),numbers=TRUE, sortVars=TRUE,labels=names(train), cex.axis=.7,gap=3, ylab=c("Missing data","Pattern"))
##
## Variables sorted by number of missings:
## Variable Count
## TEAM_BATTING_HBP 0.91608084
## TEAM_BASERUN_CS 0.33919156
## TEAM_FIELDING_DP 0.12565905
## TEAM_BASERUN_SB 0.05755712
## TEAM_BATTING_SO 0.04481547
## TEAM_PITCHING_SO 0.04481547
## INDEX 0.00000000
## TARGET_WINS 0.00000000
## TEAM_BATTING_H 0.00000000
## TEAM_BATTING_2B 0.00000000
## TEAM_BATTING_3B 0.00000000
## TEAM_BATTING_HR 0.00000000
## TEAM_BATTING_BB 0.00000000
## TEAM_PITCHING_H 0.00000000
## TEAM_PITCHING_HR 0.00000000
## TEAM_PITCHING_BB 0.00000000
## TEAM_FIELDING_E 0.00000000Six of the variable has missing values.
Outliers
ggplot(stack(train[,-1]), aes(x = ind, y = values, fill=ind)) +
geom_boxplot(outlier.colour = "red", outlier.alpha=.3) +
coord_cartesian(ylim = c(0, 1000)) +
theme_light()+
theme(axis.text.x=element_text(angle=45, hjust=1)) 
Correlations
train %>%
cor(., use = "complete.obs") %>%
corrplot(., method = "color", type = "upper", tl.col = "black", tl.cex=.8, diag = FALSE)
cleanup <- function(df, outlier_mult = 1.5) {
#Outlier_mult is what mutliple of the IQR a value needs to be away from the median to be considered an outlier
#Change NA to median where appropriate
df<- df %>% replace_na(list(TEAM_BATTING_SO = median(df$TEAM_BATTING_SO[(is.na(df$TEAM_BATTING_SO) == FALSE)]),
TEAM_BASERUN_SB = median(df$TEAM_BASERUN_SB[(is.na(df$TEAM_BASERUN_SB) == FALSE)]),
TEAM_BASERUN_CS = median(df$TEAM_BASERUN_CS[(is.na(df$TEAM_BASERUN_CS) == FALSE)]),
TEAM_PITCHING_SO = median(df$TEAM_PITCHING_SO[(is.na(df$TEAM_PITCHING_SO) == FALSE)]),
TEAM_FIELDING_DP = median(df$TEAM_FIELDING_DP[(is.na(df$TEAM_FIELDING_DP) == FALSE)])
))
#Drop column with too many NA
df$TEAM_BATTING_HBP <- NULL
#Removes with outliers
i = 1 #Skip the index
k = 0 #Count of outliers changed
while (i < length(colnames(df))) { #Column cycle
i = i+1
iqr= IQR(df[,i])
med = median(df[,i])
max_range = c(med - iqr * outlier_mult, med + iqr * outlier_mult) #Defines the maximum range, outside of which values are considered outliers
j = 0
while (j < length(df[,i])) { #Row cycle
j = j + 1
if (df[j,i] < max_range[1] || df[j,i] > max_range[2] ) {
df[j,i] <- med #Sets outliers to median column value
k = k + 1
}
}
}
print(paste("set",k, "outliers to median"))
return(df)
}
#cleanup(train)
#Change NA to median where appropriate
train<- train %>% replace_na(list(TEAM_BATTING_SO = median(train$TEAM_BATTING_SO[(is.na(train$TEAM_BATTING_SO) == FALSE)]),
TEAM_BASERUN_SB = median(train$TEAM_BASERUN_SB[(is.na(train$TEAM_BASERUN_SB) == FALSE)]),
TEAM_BASERUN_CS = median(train$TEAM_BASERUN_CS[(is.na(train$TEAM_BASERUN_CS) == FALSE)]),
TEAM_PITCHING_SO = median(train$TEAM_PITCHING_SO[(is.na(train$TEAM_PITCHING_SO) == FALSE)]),
TEAM_FIELDING_DP = median(train$TEAM_FIELDING_DP[(is.na(train$TEAM_FIELDING_DP) == FALSE)])
))
#Drop column with too many NA
train$TEAM_BATTING_HBP <- NULL##Build Models
INTERACTION TERMS BY ERA
##correlation_table(train, target = "TARGET_WINS")
#true<-lm(TARGET_WINS ~ hr_era+hr_era_p, data = train)
train$X2B=(train$TEAM_BATTING_2B/162)
train$X3B=(train$TEAM_BATTING_3B/162)
train$BB=((train$TEAM_BATTING_BB/162)+(train$TEAM_PITCHING_BB/162))/2
train$SO=((train$TEAM_BATTING_SO/162)+(train$TEAM_PITCHING_SO/162))/2
year<-lm(Year ~ X2B+X3B+BB+SO, data = yr)
#summary(year)
#plot(year)
predicted_year<- predict(year, newdata = train)
train<-cbind(train,predicted_year)
train$era = ifelse(train$predicted_year>= 1994,"Modern",
ifelse(train$predicted_year> 1977 & train$predicted_year<1993, "FreeAgency",
ifelse(train$predicted_year> 1961 & train$predicted_yea<1976, "Expansion",
ifelse(train$predicted_year> 1942 & train$predicted_yea<1960, "Integration",
ifelse(train$predicted_year> 1920 & train$predicted_yea<1941, "LiveBall",
"DeadBall")))))
train<-dummy_cols(train,select_columns=c("era"))
#skim(train)
train$H_era_m <- (train$TEAM_BATTING_H)*train$era_Modern
train$H_era_fa <- (train$TEAM_BATTING_H)*train$era_FreeAgency
train$H_era_e <- (train$TEAM_BATTING_H)*train$era_Expansion
train$H_era_i <- (train$TEAM_BATTING_H)*train$era_Integration
train$H_era_lb <- (train$TEAM_BATTING_H)*train$era_LiveBall
train$H_era_db <- (train$TEAM_BATTING_H)*train$era_DeadBall
train$H_era_m_p <- (train$TEAM_PITCHING_H)*train$era_Modern
train$H_era_fa_p <- (train$TEAM_PITCHING_H)*train$era_FreeAgency
train$H_era_e_p <- (train$TEAM_PITCHING_H)*train$era_Expansion
train$H_era_i_p <- (train$TEAM_PITCHING_H)*train$era_Integration
train$H_era_lb_p <- (train$TEAM_PITCHING_H)*train$era_LiveBall
train$H_era_db_p <- (train$TEAM_PITCHING_H)*train$era_DeadBall
train$bb_era_m <- (train$TEAM_BATTING_BB)*train$era_Modern
train$bb_era_fa <- (train$TEAM_BATTING_BB)*train$era_FreeAgency
train$bb_era_e <- (train$TEAM_BATTING_BB)*train$era_Expansion
train$bb_era_i <- (train$TEAM_BATTING_BB)*train$era_Integration
train$bb_era_lb <- (train$TEAM_BATTING_BB)*train$era_LiveBall
train$bb_era_db <- (train$TEAM_BATTING_BB)*train$era_DeadBall
train$bb_era_m_p <- (train$TEAM_PITCHING_BB)*train$era_Modern
train$bb_era_fa_p <- (train$TEAM_PITCHING_BB)*train$era_FreeAgency
train$bb_era_e_p <- (train$TEAM_PITCHING_BB)*train$era_Expansion
train$bb_era_i_p <- (train$TEAM_PITCHING_BB)*train$era_Integration
train$bb_era_lb_p <- (train$TEAM_PITCHING_BB)*train$era_LiveBall
train$bb_era_db_p <- (train$TEAM_PITCHING_BB)*train$era_DeadBall
train$hr_era_m <- (train$TEAM_BATTING_HR)*train$era_Modern
train$hr_era_fa <- (train$TEAM_BATTING_HR)*train$era_FreeAgency
train$hr_era_e <- (train$TEAM_BATTING_HR)*train$era_Expansion
train$hr_era_i <- (train$TEAM_BATTING_HR)*train$era_Integration
train$hr_era_lb <- (train$TEAM_BATTING_HR)*train$era_LiveBall
train$hr_era_db <- (train$TEAM_BATTING_HR)*train$era_DeadBall
train$hr_era_m_p <- (train$TEAM_PITCHING_HR)*train$era_Modern
train$hr_era_fa_p <- (train$TEAM_PITCHING_HR)*train$era_FreeAgency
train$hr_era_e_p <- (train$TEAM_PITCHING_HR)*train$era_Expansion
train$hr_era_i_p <- (train$TEAM_PITCHING_HR)*train$era_Integration
train$hr_era_lb_p <- (train$TEAM_PITCHING_HR)*train$era_LiveBall
train$hr_era_db_p <- (train$TEAM_PITCHING_HR)*train$era_DeadBall
train$so_era_m <- (train$TEAM_BATTING_SO)*train$era_Modern
train$so_era_fa <- (train$TEAM_BATTING_SO)*train$era_FreeAgency
train$so_era_e <- (train$TEAM_BATTING_SO)*train$era_Expansion
train$so_era_i <- (train$TEAM_BATTING_SO)*train$era_Integration
train$so_era_lb <- (train$TEAM_BATTING_SO)*train$era_LiveBall
train$so_era_db <- (train$TEAM_BATTING_SO)*train$era_DeadBall
train$so_era_m_p <- (train$TEAM_PITCHING_SO)*train$era_Modern
train$so_era_fa_p <- (train$TEAM_PITCHING_SO)*train$era_FreeAgency
train$so_era_e_p <- (train$TEAM_PITCHING_SO)*train$era_Expansion
train$so_era_i_p <- (train$TEAM_PITCHING_SO)*train$era_Integration
train$so_era_lb_p <- (train$TEAM_PITCHING_SO)*train$era_LiveBall
train$so_era_db_p <- (train$TEAM_PITCHING_SO)*train$era_DeadBall
train$x2b_era_m <- (train$TEAM_BATTING_2B)*train$era_Modern
train$x2b_era_fa <- (train$TEAM_BATTING_2B)*train$era_FreeAgency
train$x2b_era_e <- (train$TEAM_BATTING_2B)*train$era_Expansion
train$x2b_era_i <- (train$TEAM_BATTING_2B)*train$era_Integration
train$x2b_era_lb <- (train$TEAM_BATTING_2B)*train$era_LiveBall
train$x2b_era_db <- (train$TEAM_BATTING_2B)*train$era_DeadBall
train$x3b_era_m <- (train$TEAM_BATTING_3B)*train$era_Modern
train$x3b_era_fa <- (train$TEAM_BATTING_3B)*train$era_FreeAgency
train$x3b_era_e <- (train$TEAM_BATTING_3B)*train$era_Expansion
train$x3b_era_i <- (train$TEAM_BATTING_3B)*train$era_Integration
train$x3b_era_lb <- (train$TEAM_BATTING_3B)*train$era_LiveBall
train$x3b_era_db <- (train$TEAM_BATTING_3B)*train$era_DeadBall
train$sb_era_m <- (train$TEAM_BASERUN_SB)*train$era_Modern
train$sb_era_fa <- (train$TEAM_BASERUN_SB)*train$era_FreeAgency
train$sb_era_e <- (train$TEAM_BASERUN_SB)*train$era_Expansion
train$sb_era_i <- (train$TEAM_BASERUN_SB)*train$era_Integration
train$sb_era_lb <- (train$TEAM_BASERUN_SB)*train$era_LiveBall
train$sb_era_db <- (train$TEAM_BASERUN_SB)*train$era_DeadBall
train$cs_era_m <- (train$TEAM_BASERUN_CS)*train$era_Modern
train$cs_era_fa <- (train$TEAM_BASERUN_CS)*train$era_FreeAgency
train$cs_era_e <- (train$TEAM_BASERUN_CS)*train$era_Expansion
train$cs_era_i <- (train$TEAM_BASERUN_CS)*train$era_Integration
train$cs_era_lb <- (train$TEAM_BASERUN_CS)*train$era_LiveBall
train$cs_era_db <- (train$TEAM_BASERUN_CS)*train$era_DeadBall
train$e_era_m <- (train$TEAM_FIELDING_E)*train$era_Modern
train$e_era_fa <- (train$TEAM_FIELDING_E)*train$era_FreeAgency
train$e_era_e <- (train$TEAM_FIELDING_E)*train$era_Expansion
train$e_era_i <- (train$TEAM_FIELDING_E)*train$era_Integration
train$e_era_lb <- (train$TEAM_FIELDING_E)*train$era_LiveBall
train$e_era_db <- (train$TEAM_FIELDING_E)*train$era_DeadBall
train$dp_era_m <- (train$TEAM_FIELDING_DP)*train$era_Modern
train$dp_era_fa <- (train$TEAM_FIELDING_DP)*train$era_FreeAgency
train$dp_era_e <- (train$TEAM_FIELDING_DP)*train$era_Expansion
train$dp_era_i <- (train$TEAM_FIELDING_DP)*train$era_Integration
train$dp_era_lb <- (train$TEAM_FIELDING_DP)*train$era_LiveBall
train$dp_era_db <- (train$TEAM_FIELDING_DP)*train$era_DeadBall
era<-lm(TARGET_WINS ~ H_era_m+H_era_fa+H_era_e+H_era_i+H_era_lb+H_era_db+
H_era_m_p+H_era_fa_p+H_era_e_p+H_era_i_p+H_era_lb_p+H_era_db_p+
bb_era_m+bb_era_fa+bb_era_e+bb_era_i+bb_era_lb+bb_era_db+
bb_era_m_p+bb_era_fa_p+bb_era_e_p+bb_era_i_p+bb_era_lb_p+bb_era_db_p+
hr_era_m+hr_era_fa+hr_era_e+hr_era_i+hr_era_lb+hr_era_db+
hr_era_m_p+hr_era_fa_p+hr_era_e_p+hr_era_i_p+hr_era_lb_p+hr_era_db_p+
so_era_m+so_era_fa+so_era_e+so_era_i+so_era_lb+so_era_db+
so_era_m_p+so_era_fa_p+so_era_e_p+so_era_i_p+so_era_lb_p+so_era_db_p+
x2b_era_m+x2b_era_fa+x2b_era_e+x2b_era_i+x2b_era_lb+x2b_era_db+
x3b_era_m+x3b_era_fa+x3b_era_e+x3b_era_i+x3b_era_lb+x3b_era_db+
e_era_m+e_era_fa+e_era_e+e_era_i+e_era_lb+e_era_db+
dp_era_m+dp_era_fa+dp_era_e+dp_era_i+dp_era_lb+dp_era_db+
sb_era_m+sb_era_fa+sb_era_e+sb_era_i+sb_era_lb+sb_era_db
, data = train)
summary(era)##
## Call:
## lm(formula = TARGET_WINS ~ H_era_m + H_era_fa + H_era_e + H_era_i +
## H_era_lb + H_era_db + H_era_m_p + H_era_fa_p + H_era_e_p +
## H_era_i_p + H_era_lb_p + H_era_db_p + bb_era_m + bb_era_fa +
## bb_era_e + bb_era_i + bb_era_lb + bb_era_db + bb_era_m_p +
## bb_era_fa_p + bb_era_e_p + bb_era_i_p + bb_era_lb_p + bb_era_db_p +
## hr_era_m + hr_era_fa + hr_era_e + hr_era_i + hr_era_lb +
## hr_era_db + hr_era_m_p + hr_era_fa_p + hr_era_e_p + hr_era_i_p +
## hr_era_lb_p + hr_era_db_p + so_era_m + so_era_fa + so_era_e +
## so_era_i + so_era_lb + so_era_db + so_era_m_p + so_era_fa_p +
## so_era_e_p + so_era_i_p + so_era_lb_p + so_era_db_p + x2b_era_m +
## x2b_era_fa + x2b_era_e + x2b_era_i + x2b_era_lb + x2b_era_db +
## x3b_era_m + x3b_era_fa + x3b_era_e + x3b_era_i + x3b_era_lb +
## x3b_era_db + e_era_m + e_era_fa + e_era_e + e_era_i + e_era_lb +
## e_era_db + dp_era_m + dp_era_fa + dp_era_e + dp_era_i + dp_era_lb +
## dp_era_db + sb_era_m + sb_era_fa + sb_era_e + sb_era_i +
## sb_era_lb + sb_era_db, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.346 -7.716 0.025 7.535 55.109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.5149454 6.3583950 4.170 3.16e-05 ***
## H_era_m 0.0249513 0.0120527 2.070 0.038552 *
## H_era_fa 0.0067291 0.0293094 0.230 0.818433
## H_era_e -0.0205919 0.0247588 -0.832 0.405668
## H_era_i 0.0388812 0.0084105 4.623 4.00e-06 ***
## H_era_lb 0.0208088 0.0076115 2.734 0.006310 **
## H_era_db 0.0521409 0.0047745 10.921 < 2e-16 ***
## H_era_m_p 0.0038292 0.0045766 0.837 0.402855
## H_era_fa_p 0.0437280 0.0249128 1.755 0.079357 .
## H_era_e_p 0.0573490 0.0217278 2.639 0.008363 **
## H_era_i_p -0.0003111 0.0011637 -0.267 0.789204
## H_era_lb_p 0.0063022 0.0022585 2.791 0.005308 **
## H_era_db_p -0.0009699 0.0005150 -1.883 0.059817 .
## bb_era_m 0.0391196 0.0147350 2.655 0.007991 **
## bb_era_fa 0.1571089 0.0752044 2.089 0.036814 *
## bb_era_e 0.4843324 0.1324373 3.657 0.000261 ***
## bb_era_i 0.0038739 0.0235637 0.164 0.869432
## bb_era_lb -0.0276587 0.0265984 -1.040 0.298518
## bb_era_db -0.0130167 0.0117329 -1.109 0.267369
## bb_era_m_p 0.0083550 0.0084392 0.990 0.322272
## bb_era_fa_p -0.1143946 0.0716431 -1.597 0.110470
## bb_era_e_p -0.4422586 0.1287088 -3.436 0.000601 ***
## bb_era_i_p -0.0001063 0.0221287 -0.005 0.996168
## bb_era_lb_p 0.0394072 0.0214444 1.838 0.066249 .
## bb_era_db_p -0.0122104 0.0080862 -1.510 0.131182
## hr_era_m 0.1449235 0.0442409 3.276 0.001070 **
## hr_era_fa -0.3311064 0.1668553 -1.984 0.047336 *
## hr_era_e -0.5880747 0.5072753 -1.159 0.246468
## hr_era_i -0.0284609 0.2527823 -0.113 0.910365
## hr_era_lb 0.3610345 0.1587916 2.274 0.023084 *
## hr_era_db 0.0325140 0.0606093 0.536 0.591700
## hr_era_m_p -0.0744317 0.0363347 -2.049 0.040629 *
## hr_era_fa_p 0.3691369 0.1595200 2.314 0.020757 *
## hr_era_e_p 0.6626919 0.4950401 1.339 0.180819
## hr_era_i_p 0.0916041 0.2415589 0.379 0.704561
## hr_era_lb_p -0.2160877 0.1439625 -1.501 0.133499
## hr_era_db_p 0.0427567 0.0495391 0.863 0.388182
## so_era_m -0.0191559 0.0078753 -2.432 0.015079 *
## so_era_fa 0.0299327 0.0283780 1.055 0.291640
## so_era_e -0.1383335 0.0563040 -2.457 0.014091 *
## so_era_i -0.0306074 0.0140997 -2.171 0.030054 *
## so_era_lb -0.0835988 0.0171974 -4.861 1.25e-06 ***
## so_era_db 0.0058190 0.0083171 0.700 0.484225
## so_era_m_p -0.0033599 0.0039780 -0.845 0.398408
## so_era_fa_p -0.0571447 0.0265302 -2.154 0.031352 *
## so_era_e_p 0.1313924 0.0548716 2.395 0.016725 *
## so_era_i_p 0.0254026 0.0130496 1.947 0.051708 .
## so_era_lb_p 0.0856253 0.0148685 5.759 9.66e-09 ***
## so_era_db_p -0.0027319 0.0060722 -0.450 0.652822
## x2b_era_m 0.0440077 0.0305506 1.440 0.149873
## x2b_era_fa -0.0668614 0.0417534 -1.601 0.109445
## x2b_era_e -0.0262660 0.0408917 -0.642 0.520726
## x2b_era_i -0.0306346 0.0346856 -0.883 0.377222
## x2b_era_lb 0.0327525 0.0325232 1.007 0.314022
## x2b_era_db 0.0072839 0.0194255 0.375 0.707721
## x3b_era_m 0.0676848 0.0794700 0.852 0.394472
## x3b_era_fa -0.0304846 0.1048836 -0.291 0.771345
## x3b_era_e 0.1594218 0.0949959 1.678 0.093451 .
## x3b_era_i 0.2696816 0.0841463 3.205 0.001370 **
## x3b_era_lb 0.2008185 0.0724950 2.770 0.005651 **
## x3b_era_db 0.0770310 0.0265484 2.902 0.003750 **
## e_era_m -0.0204063 0.0119897 -1.702 0.088900 .
## e_era_fa 0.0260124 0.0175436 1.483 0.138290
## e_era_e -0.1116542 0.0222972 -5.008 5.95e-07 ***
## e_era_i -0.0451841 0.0128702 -3.511 0.000456 ***
## e_era_lb -0.0905786 0.0094137 -9.622 < 2e-16 ***
## e_era_db -0.0234638 0.0037249 -6.299 3.60e-10 ***
## dp_era_m -0.1112532 0.0369904 -3.008 0.002663 **
## dp_era_fa -0.0806575 0.0390467 -2.066 0.038977 *
## dp_era_e -0.0746975 0.0351085 -2.128 0.033480 *
## dp_era_i -0.0763914 0.0295604 -2.584 0.009823 **
## dp_era_lb -0.1341195 0.0286437 -4.682 3.01e-06 ***
## dp_era_db -0.1420045 0.0247892 -5.728 1.15e-08 ***
## sb_era_m 0.0182889 0.0190365 0.961 0.336795
## sb_era_fa 0.0549168 0.0181246 3.030 0.002474 **
## sb_era_e 0.0314596 0.0158083 1.990 0.046707 *
## sb_era_i 0.0622565 0.0132599 4.695 2.83e-06 ***
## sb_era_lb 0.0911188 0.0105364 8.648 < 2e-16 ***
## sb_era_db 0.0275920 0.0067918 4.063 5.02e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.3 on 2197 degrees of freedom
## Multiple R-squared: 0.4115, Adjusted R-squared: 0.3906
## F-statistic: 19.7 on 78 and 2197 DF, p-value: < 2.2e-16plot(era)
