BHao_HW1
train_raw = read.csv("~/Google Drive/CUNY/git/DATA621/HW1/moneyball-training-data.csv")Data Exploration
Our primary objectives for data exploration are two fold:
- To get a general sense for our data via summary statistics and visualizations
- To highlight potential data integrity issues that will need to be addressed in the following data preparation phase
Note: data exploration, data preparation and model building may be somewhat iterative processes
- We start by summarizing our data. A couple things immediately jump out:
- 0 minimum values, especially in the TARGET_WINS column
- NAs in several columns
- 0 minimum values, especially in the TARGET_WINS column
## 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- Next, let’s look at each column’s distribution graphically with some box plots and outline the highlights below:
- TARGET_WINS: There are a large number of outliers
- TEAM_BATTING_H: There are a large number of outliers, especially in the higher values
- TEAM_BATTING_3B: The lower whisker is close to zero, and there are many outliers in the higher values
- TEAM_BATTING_BB: The IQR is relatively tight; there are a large number of outliers
- TEAM_BASERUN_SB: There are a large number of outliers in the higher values
- TEAM_BASERUN_CS: There are a large number of outliers in the higher values
- TEAM_PITCHING_H: There are an extremely large number of outliers in the higher values
- TEAM_PITCHING_BB: There are an extremely large number of outliers in the higher values
- TEAM_PITCHING_SO: There are an extremely large number of outliers in the higher values
- TEAM_FIELDING_E: There are an extremely large number of outliers in the higher values
- TARGET_WINS: There are a large number of outliers
Note: obviously, not having access to the data providers makes it more difficult to make sense of these potential anomalies; however, knowing the total number of at bats and pitches would be very helpful to this end.
- Next, we examine the correlation between each column and the response variable TARGET_WINS:
- TEAM_BATTING_H exhibits the highest correlation to the response variable, while TEAM_FIELDING_E exhibits the lowest correlation
- Surprisingly both TEAM_PITCHING_HR and TEAM_PITCHING_BB exhibit positive correlations to the response variable; we will revisit these anomalies after the data cleansing process to see if they still appear
- TEAM_BATTING_H exhibits the highest correlation to the response variable, while TEAM_FIELDING_E exhibits the lowest correlation
## rowname With NAs Ignoring NAs
## 1 TEAM_BATTING_H 0.3887675 0.38876752
## 2 TEAM_BATTING_2B 0.2891036 0.28910365
## 3 TEAM_BATTING_BB 0.2325599 0.23255986
## 4 TEAM_PITCHING_HR 0.1890137 0.18901373
## 5 TEAM_BATTING_HR 0.1761532 0.17615320
## 6 TEAM_BATTING_3B 0.1426084 0.14260841
## 7 TEAM_BASERUN_SB NA 0.13513892
## 8 TEAM_PITCHING_BB 0.1241745 0.12417454
## 9 TEAM_BATTING_HBP NA 0.07350424
## 10 TEAM_BASERUN_CS NA 0.02240407
## 11 TEAM_BATTING_SO NA -0.03175071
## 12 TEAM_FIELDING_DP NA -0.03485058
## 13 TEAM_PITCHING_SO NA -0.07843609
## 14 TEAM_PITCHING_H -0.1099371 -0.10993705
## 15 TEAM_FIELDING_E -0.1764848 -0.17648476- Data exploration summary: The exploration phase revealed that there are a number of potential data issues that will need to be addressed in the data preparation phase:
- 0 values
- Missing values
- Outliers
- Missing variables - again, it would be very helpful to have the total number of ‘at bats’ and ‘pitches’; however, we can make do without those variables
- 0 values
Data Preparation
In this phase, we will look at each anomaly and decide how best to address it so that our models can work correctly.
- Since the TEAM_BATTING_H column is inclusive of three other columns, we will start by replacing it with a TEAM_BATTING_1B column
We’ll replace TEAM_BATTING_H with TEAM_BATTING_1B = TEAM_BATTING_H - TEAM_BATTING_2B - TEAM_BATTING_3B - TEAM_BATTING_HR.
train_clean = train_raw
train_clean = train_clean %>% mutate(TEAM_BATTING_1B = TEAM_BATTING_H - TEAM_BATTING_2B - TEAM_BATTING_3B - TEAM_BATTING_HR) %>%
select(-TEAM_BATTING_H)- Let’s next look at the row with 0 wins
- Most of its columns are either 0 or NA
- Furthermore, it has a value for TEAM_PITCHING_H (24057) which just does not make sense as that would equate to giving up 148.5 hits on average over 162 games. The median for this field is 1518 which is close to the median value for TEAM_BATTING_H of 1454 - which makes sense as they should be nearly mirror images of each other on average
It’s safe to assume that this row contains faulty data and should be removed.
train_clean %>% filter(TARGET_WINS == 0)## INDEX TARGET_WINS TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR
## 1 1347 0 135 0 0
## TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB TEAM_BASERUN_CS
## 1 0 0 0 0
## TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## 1 NA 24057 0 0
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 1 0 1890 NA 756train_clean = train_clean %>% filter(TARGET_WINS != 0)- Let’s turn our attention to columns with missing data
- Specifically let’s start with TEAM_BATTING_SO and TEAM_PITCHING_SO, both of which are missing values for the same 102 rows
- These two columns should be nearly mirror images of each other on average
We’ll fill in the missing values using their respective median values.
train_clean = train_clean %>% mutate(
TEAM_PITCHING_SO = ifelse(is.na(TEAM_PITCHING_SO), median(TEAM_PITCHING_SO, na.rm = TRUE), TEAM_PITCHING_SO),
TEAM_BATTING_SO = ifelse(is.na(TEAM_BATTING_SO), median(TEAM_BATTING_SO, na.rm = TRUE), TEAM_BATTING_SO))We’ll use the same approach to fill in the missing values for TEAM_BASERUN_SB, TEAM_BASERUN_CS and TEAM_FIELDING_DP. While we could have used the ratio of average ‘stolen bases’ to ‘caught steals’ multiplied by the ‘stolen bases’ column, we would often then be estimating based on an estimate when the ‘stolen bases’ itself was filled in.
train_clean = train_clean %>% mutate(
TEAM_BASERUN_SB = ifelse(is.na(TEAM_BASERUN_SB), median(TEAM_BASERUN_SB, na.rm = TRUE), TEAM_BASERUN_SB),
TEAM_BASERUN_CS = ifelse(is.na(TEAM_BASERUN_CS), median(TEAM_BASERUN_CS, na.rm = TRUE), TEAM_BASERUN_CS),
TEAM_FIELDING_DP = ifelse(is.na(TEAM_FIELDING_DP), median(TEAM_FIELDING_DP, na.rm = TRUE), TEAM_FIELDING_DP))- Missing data (cont.)
- The final column with NAs is the TEAM_BATTING_HBP. Since there are 2084 rows with missing data, it may be best to create a categorical variable to indicate whether TEAM_BATTING_HBP exists or not
We’ll add a new variable TEAM_BATTING_HBP_YN that is 1 when the TEAM_BATTING_HBP exists and 0 when it does not.
train_clean = train_clean %>% mutate(TEAM_BATTING_HBP_YN = ifelse(is.na(TEAM_BATTING_HBP), 0, 1))
summary(train_clean)## INDEX TARGET_WINS TEAM_BATTING_2B TEAM_BATTING_3B
## Min. : 1.0 Min. : 12.00 Min. : 69.0 Min. : 0.00
## 1st Qu.: 630.5 1st Qu.: 71.00 1st Qu.:208.0 1st Qu.: 34.00
## Median :1270.0 Median : 82.00 Median :238.0 Median : 47.00
## Mean :1268.4 Mean : 80.83 Mean :241.3 Mean : 55.27
## 3rd Qu.:1916.0 3rd Qu.: 92.00 3rd Qu.:273.0 3rd Qu.: 72.00
## Max. :2535.0 Max. :146.00 Max. :458.0 Max. :223.00
##
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## Min. : 0.00 Min. : 12.0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 42.00 1st Qu.:451.0 1st Qu.: 557.5 1st Qu.: 67.0
## Median :102.00 Median :512.0 Median : 750.0 Median :101.0
## Mean : 99.66 Mean :501.8 Mean : 736.6 Mean :123.4
## 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 925.0 3rd Qu.:151.0
## Max. :264.00 Max. :878.0 Max. :1399.0 Max. :697.0
##
## TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## Min. : 7.00 Min. :29.00 Min. : 1137 Min. : 0.0
## 1st Qu.: 44.00 1st Qu.:50.50 1st Qu.: 1419 1st Qu.: 50.0
## Median : 49.00 Median :58.00 Median : 1518 Median :107.0
## Mean : 51.54 Mean :59.36 Mean : 1769 Mean :105.7
## 3rd Qu.: 54.50 3rd Qu.:67.00 3rd Qu.: 1682 3rd Qu.:150.0
## Max. :201.00 Max. :95.00 Max. :30132 Max. :343.0
## NA's :2084
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## Min. : 119.0 Min. : 0.0 Min. : 65.0 Min. : 52.0
## 1st Qu.: 476.0 1st Qu.: 626.0 1st Qu.: 127.0 1st Qu.:134.0
## Median : 537.0 Median : 814.0 Median : 159.0 Median :149.0
## Mean : 553.3 Mean : 817.9 Mean : 245.8 Mean :146.7
## 3rd Qu.: 611.0 3rd Qu.: 957.0 3rd Qu.: 249.0 3rd Qu.:161.5
## Max. :3645.0 Max. :19278.0 Max. :1898.0 Max. :228.0
##
## TEAM_BATTING_1B TEAM_BATTING_HBP_YN
## Min. : 709 Min. :0.00000
## 1st Qu.: 991 1st Qu.:0.00000
## Median :1050 Median :0.00000
## Mean :1073 Mean :0.08396
## 3rd Qu.:1129 3rd Qu.:0.00000
## Max. :2112 Max. :1.00000
## - Looking deeper into the TEAM_PITCHING_H column, we see that it contains a large number of outliers
- Quantifying that shows 213 rows with TEAM_PITCHING_H values greater than 1.5 IQRs above the 3rd quartile
Instead of removing these rows since they still might contain useful data in the other columns, let’s create a flag to indicate which rows contain outliers in this particular column - this happens to address outliers across all of the pitcher-related columns. Let’s also do the same for other column categories as well.
plot(density(train_clean$TEAM_PITCHING_H))
train_clean %>% filter(TEAM_PITCHING_H > quantile(TEAM_PITCHING_H, 0.75) + 1.5 * IQR(TEAM_PITCHING_H)) %>%
summarise(n = n())## n
## 1 213train_clean = train_clean %>%
mutate('PITCHER_OUTLIER_YN' = ifelse(TEAM_PITCHING_H > quantile(TEAM_PITCHING_H, 0.75) + 1.5 * IQR(TEAM_PITCHING_H) |
TEAM_PITCHING_H < quantile(TEAM_PITCHING_H, 0.25) - 1.5 * IQR(TEAM_PITCHING_H),
1, 0))
train_clean = train_clean %>%
mutate('BATTING_OUTLIER_YN' = ifelse(TEAM_BATTING_1B > quantile(TEAM_BATTING_1B, 0.75) + 1.5 * IQR(TEAM_BATTING_1B) |
TEAM_BATTING_1B < quantile(TEAM_BATTING_1B, 0.25) - 1.5 * IQR(TEAM_BATTING_1B),
1, 0))
train_clean = train_clean %>%
mutate('BATTING_OUTLIER_YN' = ifelse(TEAM_BATTING_1B > quantile(TEAM_BATTING_1B, 0.75) + 1.5 * IQR(TEAM_BATTING_1B) |
TEAM_BATTING_1B < quantile(TEAM_BATTING_1B, 0.25) - 1.5 * IQR(TEAM_BATTING_1B),
1, 0))
train_clean = train_clean %>%
mutate('BASERUN_OUTLIER_YN' = ifelse(TEAM_BASERUN_SB > quantile(TEAM_BASERUN_SB, 0.75) + 1.5 * IQR(TEAM_BASERUN_SB) |
TEAM_BASERUN_SB < quantile(TEAM_BASERUN_SB, 0.25) - 1.5 * IQR(TEAM_BASERUN_SB),
1, 0))
train_clean = train_clean %>%
mutate('FIELDING_OUTLIER_YN' = ifelse(TEAM_FIELDING_E > quantile(TEAM_FIELDING_E, 0.75) + 1.5 * IQR(TEAM_FIELDING_E) |
TEAM_FIELDING_E < quantile(TEAM_FIELDING_E, 0.25) - 1.5 * IQR(TEAM_FIELDING_E),
1, 0))- Next, we’ll create some new variables based on ratios of the existing variables. Not only will this scale and normalize the variables, it may also create variables that have a better explain the response variable
- TARGET_WINS_Ratio = TARGET_WINS / 162 (i.e. the percentage of wins)
- TEAM_H_Ratio = (TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR) / TEAM_PITCHING_H (i.e. the ratio of hits earned to hits allowed)
- TEAM_BASERUN_Ratio = TEAM_BASERUN_SB / TEAM_BASERUN_CS (i.e. the ratio of successful steals to unsuccessful ones)
- TEAM_HR_SO_Ratio = TEAM_BATTING_HR / TEAM_BATTING_SO (i.e. the ratio of home runs to strikeouts)
- TARGET_WINS_Ratio = TARGET_WINS / 162 (i.e. the percentage of wins)
train_clean = train_clean %>%
mutate(TARGET_WINS_Ratio = TARGET_WINS / 162,
TEAM_H_Ratio = (TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR) / TEAM_PITCHING_H,
TEAM_BASERUN_Ratio = TEAM_BASERUN_SB / TEAM_BASERUN_CS,
TEAM_HR_SO_Ratio = TEAM_BATTING_HR / ifelse(TEAM_BATTING_SO == 0, median(TEAM_BATTING_SO), TEAM_BATTING_SO))- Let’s now revisit our earlier data explorations. Well, we certainly removed the missing values, but it does not yet look like our new variables will be very promising
## INDEX TARGET_WINS TEAM_BATTING_2B TEAM_BATTING_3B
## Min. : 1.0 Min. : 12.00 Min. : 69.0 Min. : 0.00
## 1st Qu.: 630.5 1st Qu.: 71.00 1st Qu.:208.0 1st Qu.: 34.00
## Median :1270.0 Median : 82.00 Median :238.0 Median : 47.00
## Mean :1268.4 Mean : 80.83 Mean :241.3 Mean : 55.27
## 3rd Qu.:1916.0 3rd Qu.: 92.00 3rd Qu.:273.0 3rd Qu.: 72.00
## Max. :2535.0 Max. :146.00 Max. :458.0 Max. :223.00
##
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BATTING_SO TEAM_BASERUN_SB
## Min. : 0.00 Min. : 12.0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 42.00 1st Qu.:451.0 1st Qu.: 557.5 1st Qu.: 67.0
## Median :102.00 Median :512.0 Median : 750.0 Median :101.0
## Mean : 99.66 Mean :501.8 Mean : 736.6 Mean :123.4
## 3rd Qu.:147.00 3rd Qu.:580.0 3rd Qu.: 925.0 3rd Qu.:151.0
## Max. :264.00 Max. :878.0 Max. :1399.0 Max. :697.0
##
## TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H TEAM_PITCHING_HR
## Min. : 7.00 Min. :29.00 Min. : 1137 Min. : 0.0
## 1st Qu.: 44.00 1st Qu.:50.50 1st Qu.: 1419 1st Qu.: 50.0
## Median : 49.00 Median :58.00 Median : 1518 Median :107.0
## Mean : 51.54 Mean :59.36 Mean : 1769 Mean :105.7
## 3rd Qu.: 54.50 3rd Qu.:67.00 3rd Qu.: 1682 3rd Qu.:150.0
## Max. :201.00 Max. :95.00 Max. :30132 Max. :343.0
## NA's :2084
## TEAM_PITCHING_BB TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## Min. : 119.0 Min. : 0.0 Min. : 65.0 Min. : 52.0
## 1st Qu.: 476.0 1st Qu.: 626.0 1st Qu.: 127.0 1st Qu.:134.0
## Median : 537.0 Median : 814.0 Median : 159.0 Median :149.0
## Mean : 553.3 Mean : 817.9 Mean : 245.8 Mean :146.7
## 3rd Qu.: 611.0 3rd Qu.: 957.0 3rd Qu.: 249.0 3rd Qu.:161.5
## Max. :3645.0 Max. :19278.0 Max. :1898.0 Max. :228.0
##
## TEAM_BATTING_1B TEAM_BATTING_HBP_YN PITCHER_OUTLIER_YN BATTING_OUTLIER_YN
## Min. : 709 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.: 991 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :1050 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :1073 Mean :0.08396 Mean :0.09363 Mean :0.03341
## 3rd Qu.:1129 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :2112 Max. :1.00000 Max. :1.00000 Max. :1.00000
##
## BASERUN_OUTLIER_YN FIELDING_OUTLIER_YN TARGET_WINS_Ratio
## Min. :0.00000 Min. :0.0000 Min. :0.07407
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.43827
## Median :0.00000 Median :0.0000 Median :0.50617
## Mean :0.05978 Mean :0.1327 Mean :0.49893
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.56790
## Max. :1.00000 Max. :1.0000 Max. :0.90123
##
## TEAM_H_Ratio TEAM_BASERUN_Ratio TEAM_HR_SO_Ratio
## Min. :0.04938 Min. : 0.000 Min. :0.00000
## 1st Qu.:0.93223 1st Qu.: 1.448 1st Qu.:0.08543
## Median :0.95069 Median : 2.059 Median :0.13463
## Mean :0.91475 Mean : 2.466 Mean :0.13034
## 3rd Qu.:1.00000 3rd Qu.: 2.806 3rd Qu.:0.17306
## Max. :1.01854 Max. :14.224 Max. :0.54545
## ## rowname TARGET_WINS
## 1 TARGET_WINS_Ratio 1.000000000
## 2 TEAM_BATTING_2B 0.285964582
## 3 TEAM_HR_SO_Ratio 0.276486605
## 4 TEAM_BATTING_BB 0.225471523
## 5 TEAM_BATTING_1B 0.213402040
## 6 TEAM_PITCHING_HR 0.186326615
## 7 TEAM_BATTING_HR 0.173551988
## 8 TEAM_BATTING_3B 0.139073830
## 9 BATTING_OUTLIER_YN 0.128735272
## 10 TEAM_BASERUN_SB 0.121110012
## 11 TEAM_BASERUN_Ratio 0.119491785
## 12 TEAM_PITCHING_BB 0.117643912
## 13 BASERUN_OUTLIER_YN 0.102242413
## 14 TEAM_H_Ratio 0.083696128
## 15 PITCHER_OUTLIER_YN 0.046631794
## 16 TEAM_BASERUN_CS 0.009835166
## 17 TEAM_BATTING_HBP_YN 0.001939440
## 18 TEAM_FIELDING_DP -0.030050754
## 19 TEAM_BATTING_SO -0.037712096
## 20 FIELDING_OUTLIER_YN -0.053236802
## 21 TEAM_PITCHING_H -0.079145655
## 22 TEAM_PITCHING_SO -0.079711792
## 23 TEAM_FIELDING_E -0.163022098
## 24 TEAM_BATTING_HBP NA- Let’s also revisit our box plots filtered to exclude the outliers. Although some outliers remain, the vast majority of them have been filtered out
Build Model
Model1: Backward elimination
- Let’s start with a backward elimination by including all variables (except we’ll remove -INDEX, -TARGET_WINS_Ratio, -TEAM_BATTING_HBP on the first pass since these are either irrelevant or captured in other columns) and then remove variables until we are left with only statistically significant variables
train_model1 = train_clean
train_model1 = train_model1 %>% select(-INDEX, -TARGET_WINS_Ratio, -TEAM_BATTING_HBP)
model1 = train(TARGET_WINS ~ ., data = train_model1, method = 'lm')
summary(model1)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.126 -8.533 0.222 8.115 58.895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.330e+01 8.493e+00 7.453 1.29e-13 ***
## TEAM_BATTING_2B 2.865e-02 7.671e-03 3.735 0.000193 ***
## TEAM_BATTING_3B 1.280e-01 1.598e-02 8.009 1.84e-15 ***
## TEAM_BATTING_HR 2.359e-01 3.245e-02 7.272 4.87e-13 ***
## TEAM_BATTING_BB 1.989e-02 6.226e-03 3.195 0.001418 **
## TEAM_BATTING_SO -2.198e-03 3.326e-03 -0.661 0.508734
## TEAM_BASERUN_SB 4.358e-02 2.403e-02 1.814 0.069867 .
## TEAM_BASERUN_CS -3.547e-02 4.016e-02 -0.883 0.377269
## TEAM_PITCHING_H -3.362e-04 4.557e-04 -0.738 0.460705
## TEAM_PITCHING_HR -1.439e-01 3.266e-02 -4.407 1.10e-05 ***
## TEAM_PITCHING_BB -4.376e-03 4.463e-03 -0.980 0.326960
## TEAM_PITCHING_SO 9.948e-04 9.272e-04 1.073 0.283435
## TEAM_FIELDING_E -4.989e-02 4.111e-03 -12.135 < 2e-16 ***
## TEAM_FIELDING_DP -1.271e-01 1.318e-02 -9.638 < 2e-16 ***
## TEAM_BATTING_1B 4.440e-02 4.293e-03 10.343 < 2e-16 ***
## TEAM_BATTING_HBP_YN -4.078e+00 1.209e+00 -3.375 0.000752 ***
## PITCHER_OUTLIER_YN 5.210e+00 1.740e+00 2.995 0.002775 **
## BATTING_OUTLIER_YN 1.400e+00 2.179e+00 0.642 0.520708
## BASERUN_OUTLIER_YN -1.793e+00 1.882e+00 -0.953 0.340935
## FIELDING_OUTLIER_YN 8.933e+00 1.839e+00 4.857 1.27e-06 ***
## TEAM_H_Ratio -3.578e+01 7.408e+00 -4.830 1.46e-06 ***
## TEAM_BASERUN_Ratio -7.192e-01 1.205e+00 -0.597 0.550746
## TEAM_HR_SO_Ratio 1.548e+01 1.289e+01 1.201 0.230031
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.76 on 2252 degrees of freedom
## Multiple R-squared: 0.3429, Adjusted R-squared: 0.3365
## F-statistic: 53.42 on 22 and 2252 DF, p-value: < 2.2e-16model1$results## intercept RMSE Rsquared RMSESD RsquaredSD
## 1 TRUE 13.82968 0.2670291 0.9587843 0.05415188- We then remove the insignificant columns, -TEAM_HR_SO_Ratio, -TEAM_BASERUN_Ratio, -BASERUN_OUTLIER_YN, -BATTING_OUTLIER_YN, -TEAM_PITCHING_SO, -TEAM_PITCHING_BB, -TEAM_PITCHING_H, -TEAM_BASERUN_CS, -TEAM_BATTING_SO
- Nice, not only do we see that the RMSE decreased slightly but that the RMSESD decreased significantly, which indicates a more precise estimate of the RMSE figure
train_model1 = train_model1 %>% select(-TEAM_HR_SO_Ratio, -TEAM_BASERUN_Ratio, -BASERUN_OUTLIER_YN, -BATTING_OUTLIER_YN,
-TEAM_PITCHING_SO, -TEAM_PITCHING_BB, -TEAM_PITCHING_H, -TEAM_BASERUN_CS,
-TEAM_BATTING_SO)
model1 = train(TARGET_WINS ~ ., data = train_model1, method = 'lm')
summary(model1)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.778 -8.432 0.132 8.195 57.842
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 53.155060 6.555099 8.109 8.28e-16 ***
## TEAM_BATTING_2B 0.027764 0.007493 3.705 0.000216 ***
## TEAM_BATTING_3B 0.135822 0.015148 8.966 < 2e-16 ***
## TEAM_BATTING_HR 0.251312 0.030586 8.217 3.48e-16 ***
## TEAM_BATTING_BB 0.015211 0.003307 4.600 4.46e-06 ***
## TEAM_BASERUN_SB 0.022143 0.004220 5.248 1.68e-07 ***
## TEAM_PITCHING_HR -0.144617 0.027408 -5.277 1.44e-07 ***
## TEAM_FIELDING_E -0.050733 0.003739 -13.570 < 2e-16 ***
## TEAM_FIELDING_DP -0.126957 0.012828 -9.897 < 2e-16 ***
## TEAM_BATTING_1B 0.048458 0.003122 15.520 < 2e-16 ***
## TEAM_BATTING_HBP_YN -4.651387 1.131601 -4.110 4.09e-05 ***
## PITCHER_OUTLIER_YN 5.538817 1.651010 3.355 0.000807 ***
## FIELDING_OUTLIER_YN 9.414990 1.680125 5.604 2.35e-08 ***
## TEAM_H_Ratio -31.644840 5.914721 -5.350 9.67e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.76 on 2261 degrees of freedom
## Multiple R-squared: 0.3404, Adjusted R-squared: 0.3366
## F-statistic: 89.77 on 13 and 2261 DF, p-value: < 2.2e-16model1$results## intercept RMSE Rsquared RMSESD RsquaredSD
## 1 TRUE 12.92585 0.3241775 0.192913 0.02812984Model2: Ratio-based
- I’m skeptical based on the correlation results, but let’s see how the ratio-based model performs; we’ll throw the TEAM_PITCHING_HR column as well since no pitching columns were converted to ratios and thus also the PITCHER_OUTLIER_YN column
- Since the response variable was converted into a ratio, the RMSE figures are not directly comparable, but based on the R-squared values, this model clearly underperforms the previous model
train_model2 = train_clean
train_model2 = train_model2 %>% select(TARGET_WINS_Ratio, TEAM_H_Ratio, TEAM_BASERUN_Ratio, TEAM_HR_SO_Ratio, TEAM_PITCHING_HR, PITCHER_OUTLIER_YN)
model2 = train(TARGET_WINS_Ratio ~ ., data = train_model2, method = 'lm')
summary(model2)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33772 -0.05691 0.00511 0.05786 0.44478
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.454e-01 2.143e-02 11.453 < 2e-16 ***
## TEAM_H_Ratio 1.718e-01 2.286e-02 7.515 8.12e-14 ***
## TEAM_BASERUN_Ratio 1.271e-02 1.176e-03 10.806 < 2e-16 ***
## TEAM_HR_SO_Ratio 6.113e-01 4.979e-02 12.277 < 2e-16 ***
## TEAM_PITCHING_HR -2.186e-04 5.478e-05 -3.991 6.79e-05 ***
## PITCHER_OUTLIER_YN 9.032e-02 1.114e-02 8.108 8.36e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08913 on 2269 degrees of freedom
## Multiple R-squared: 0.1521, Adjusted R-squared: 0.1502
## F-statistic: 81.41 on 5 and 2269 DF, p-value: < 2.2e-16model2$results## intercept RMSE Rsquared RMSESD RsquaredSD
## 1 TRUE 0.08973831 0.1448375 0.00229784 0.02171559Model3: Remove highly collinear variables
- Time to return to the original model, but we’ll remove the most collinear variables based on the cross correlation and variance inflation factors shown below:
- TEAM_BATTING_HR: 0.969 correlation with TEAM_PITCHING_HR
- FIELDING_OUTLIER_YN & TEAM_H_Ratio: both are highly correlated to TEAM_FIELDING_E and to each other
- TEAM_BATTING_HR: 0.969 correlation with TEAM_PITCHING_HR
- Although the RMSE increases slightly, the model is simpler and more stable without the collinear variables, so we will use Model3 as the final model
- Coefficient discussion - in this final model, below is a brief discussion of the coefficients for the selected variables:
- TEAM_FIELDING_DP: The negative coefficient suggests that more double plays is associated with fewer wins. While this differs from the suggested impact as per the homework assignment, it could be possible as teams that have more double play opportunities likely have more opposing runners on base at a given time which should have a negative effect. Further research is needed to isolate the impact of double plays.
- TEAM_BATTING_HBP_YN & PITCHER_OUTLIER_YN: Both are flags created to deal with either missing data or outliers; there coefficients may not have intuitive interpretations
- Remaining variables: The remaining variables have signs that are consistent with their expected impact on the number of wins.
- TEAM_FIELDING_DP: The negative coefficient suggests that more double plays is associated with fewer wins. While this differs from the suggested impact as per the homework assignment, it could be possible as teams that have more double play opportunities likely have more opposing runners on base at a given time which should have a negative effect. Further research is needed to isolate the impact of double plays.
cor(train_model1)## TARGET_WINS TEAM_BATTING_2B TEAM_BATTING_3B
## TARGET_WINS 1.00000000 0.28596458 0.1390738
## TEAM_BATTING_2B 0.28596458 1.00000000 -0.1094983
## TEAM_BATTING_3B 0.13907383 -0.10949828 1.0000000
## TEAM_BATTING_HR 0.17355199 0.43450589 -0.6379259
## TEAM_BATTING_BB 0.22547152 0.25286114 -0.2921176
## TEAM_BASERUN_SB 0.12111001 -0.18514149 0.4851236
## TEAM_PITCHING_HR 0.18632661 0.45364008 -0.5701993
## TEAM_FIELDING_E -0.16302210 -0.23086449 0.5225142
## TEAM_FIELDING_DP -0.03005075 0.25735317 -0.2278874
## TEAM_BATTING_1B 0.21340204 0.08476283 0.5995733
## TEAM_BATTING_HBP_YN 0.00193944 0.36203847 -0.2660418
## PITCHER_OUTLIER_YN 0.04663179 0.02967777 0.3225772
## FIELDING_OUTLIER_YN -0.05323680 -0.16160694 0.4759790
## TEAM_H_Ratio 0.08369613 0.11531561 -0.4122639
## TEAM_BATTING_HR TEAM_BATTING_BB TEAM_BASERUN_SB
## TARGET_WINS 0.1735520 0.22547152 0.12111001
## TEAM_BATTING_2B 0.4345059 0.25286114 -0.18514149
## TEAM_BATTING_3B -0.6379259 -0.29211757 0.48512355
## TEAM_BATTING_HR 1.0000000 0.51296999 -0.40836484
## TEAM_BATTING_BB 0.5129700 1.00000000 -0.04547002
## TEAM_BASERUN_SB -0.4083648 -0.04547002 1.00000000
## TEAM_PITCHING_HR 0.9693345 0.45843864 -0.38157640
## TEAM_FIELDING_E -0.5892503 -0.65289124 0.33474354
## TEAM_FIELDING_DP 0.3919539 0.33102671 -0.27029947
## TEAM_BATTING_1B -0.5000378 -0.35934482 0.27225401
## TEAM_BATTING_HBP_YN 0.3922217 0.10289528 -0.11540717
## PITCHER_OUTLIER_YN -0.2831195 -0.48896379 0.13759716
## FIELDING_OUTLIER_YN -0.4389749 -0.47985250 0.42852241
## TEAM_H_Ratio 0.4794442 0.62376581 -0.18395997
## TEAM_PITCHING_HR TEAM_FIELDING_E TEAM_FIELDING_DP
## TARGET_WINS 0.1863266 -0.1630221 -0.03005075
## TEAM_BATTING_2B 0.4536401 -0.2308645 0.25735317
## TEAM_BATTING_3B -0.5701993 0.5225142 -0.22788742
## TEAM_BATTING_HR 0.9693345 -0.5892503 0.39195386
## TEAM_BATTING_BB 0.4584386 -0.6528912 0.33102671
## TEAM_BASERUN_SB -0.3815764 0.3347435 -0.27029947
## TEAM_PITCHING_HR 1.0000000 -0.4936765 0.38992182
## TEAM_FIELDING_E -0.4936765 1.0000000 -0.23034283
## TEAM_FIELDING_DP 0.3899218 -0.2303428 1.00000000
## TEAM_BATTING_1B -0.4181906 0.5628440 -0.08789672
## TEAM_BATTING_HBP_YN 0.3579617 -0.1865065 0.06933660
## PITCHER_OUTLIER_YN -0.1455180 0.6774971 -0.12675890
## FIELDING_OUTLIER_YN -0.3523016 0.8472196 -0.10923311
## TEAM_H_Ratio 0.3222699 -0.8694651 0.18631621
## TEAM_BATTING_1B TEAM_BATTING_HBP_YN PITCHER_OUTLIER_YN
## TARGET_WINS 0.21340204 0.00193944 0.04663179
## TEAM_BATTING_2B 0.08476283 0.36203847 0.02967777
## TEAM_BATTING_3B 0.59957334 -0.26604179 0.32257722
## TEAM_BATTING_HR -0.50003777 0.39222167 -0.28311953
## TEAM_BATTING_BB -0.35934482 0.10289528 -0.48896379
## TEAM_BASERUN_SB 0.27225401 -0.11540717 0.13759716
## TEAM_PITCHING_HR -0.41819055 0.35796169 -0.14551795
## TEAM_FIELDING_E 0.56284404 -0.18650650 0.67749711
## TEAM_FIELDING_DP -0.08789672 0.06933660 -0.12675890
## TEAM_BATTING_1B 1.00000000 -0.23669901 0.47124119
## TEAM_BATTING_HBP_YN -0.23669901 1.00000000 -0.09730010
## PITCHER_OUTLIER_YN 0.47124119 -0.09730010 1.00000000
## FIELDING_OUTLIER_YN 0.43438136 -0.11844255 0.62582226
## TEAM_H_Ratio -0.52640742 0.17224454 -0.80830086
## FIELDING_OUTLIER_YN TEAM_H_Ratio
## TARGET_WINS -0.0532368 0.08369613
## TEAM_BATTING_2B -0.1616069 0.11531561
## TEAM_BATTING_3B 0.4759790 -0.41226395
## TEAM_BATTING_HR -0.4389749 0.47944418
## TEAM_BATTING_BB -0.4798525 0.62376581
## TEAM_BASERUN_SB 0.4285224 -0.18395997
## TEAM_PITCHING_HR -0.3523016 0.32226994
## TEAM_FIELDING_E 0.8472196 -0.86946508
## TEAM_FIELDING_DP -0.1092331 0.18631621
## TEAM_BATTING_1B 0.4343814 -0.52640742
## TEAM_BATTING_HBP_YN -0.1184426 0.17224454
## PITCHER_OUTLIER_YN 0.6258223 -0.80830086
## FIELDING_OUTLIER_YN 1.0000000 -0.73987516
## TEAM_H_Ratio -0.7398752 1.00000000vif(model1$finalModel)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_HR
## 1.715161 2.499062 47.876589
## TEAM_BATTING_BB TEAM_BASERUN_SB TEAM_PITCHING_HR
## 2.282792 1.813637 39.399739
## TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## 9.904034 1.384859 2.258869
## TEAM_BATTING_HBP_YN PITCHER_OUTLIER_YN FIELDING_OUTLIER_YN
## 1.376493 3.233135 4.542274
## TEAM_H_Ratio
## 10.788789train_model3 = train_model1 %>% select(-TEAM_BATTING_HR, -FIELDING_OUTLIER_YN, -TEAM_H_Ratio)
model3 = train(TARGET_WINS ~ ., data = train_model3, method = 'lm')
summary(model3)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.505 -8.475 0.093 8.349 57.846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.232637 3.516409 6.891 7.14e-12 ***
## TEAM_BATTING_2B 0.033594 0.007636 4.400 1.13e-05 ***
## TEAM_BATTING_3B 0.106657 0.014722 7.244 5.92e-13 ***
## TEAM_BATTING_BB 0.015579 0.003362 4.634 3.80e-06 ***
## TEAM_BASERUN_SB 0.024497 0.003988 6.143 9.52e-10 ***
## TEAM_PITCHING_HR 0.077009 0.007130 10.800 < 2e-16 ***
## TEAM_FIELDING_E -0.028218 0.002283 -12.361 < 2e-16 ***
## TEAM_FIELDING_DP -0.111020 0.012815 -8.663 < 2e-16 ***
## TEAM_BATTING_1B 0.043179 0.003135 13.774 < 2e-16 ***
## TEAM_BATTING_HBP_YN -3.046056 1.138163 -2.676 0.0075 **
## PITCHER_OUTLIER_YN 7.929821 1.406515 5.638 1.94e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.05 on 2264 degrees of freedom
## Multiple R-squared: 0.3087, Adjusted R-squared: 0.3057
## F-statistic: 101.1 on 10 and 2264 DF, p-value: < 2.2e-16model3$results## intercept RMSE Rsquared RMSESD RsquaredSD
## 1 TRUE 13.12131 0.2915539 0.3520247 0.03006092vif(model3$finalModel)## TEAM_BATTING_2B TEAM_BATTING_3B TEAM_BATTING_BB
## 1.701453 2.255375 2.254677
## TEAM_BASERUN_SB TEAM_PITCHING_HR TEAM_FIELDING_E
## 1.547392 2.547793 3.527537
## TEAM_FIELDING_DP TEAM_BATTING_1B TEAM_BATTING_HBP_YN
## 1.320439 2.175392 1.330373
## PITCHER_OUTLIER_YN
## 2.241767SELECT MODELS
Model selection rationale
As discussed above, we selected Model3, which was based on backward elimination, followed by removal of any highly collinear variables. Although Model3 did not have the lowest RMSE, it was the most parsimonious (fewest variables) and stable (little collinearity between variables).
Inference and regression diagnostics
For our inferences to be valid, we need to perform some regression diagnostics and validate some assumptions:
- Independence of errors: Based on the residual plot below, the residuals appear random over the index values
- Outliers and leverage: Based on the leverage plots below, there do not appear to be any data points exerting undue leverage on the regression
- Normality: Based on the qq-plot below, the residuals are fairly normally distributed, although there are some outliers in the tails
- Constant variance: Based on the spread-level plot below, variance appears relatively constant, although again with a few outliers
fit = model3$finalModel
plot(fit$residuals)
leveragePlots(fit)
qqPlot(fit)
spreadLevelPlot(fit)
##
## Suggested power transformation: 1.492206Evaluation of regression model
Based on the above regression diagnostics results, we can comfortably make inferences from our model results:
- RMSE: 13.05
- Adjusted R2: 0.3057
- F-statistic: 101.1
- residual plots: see regression diagnostics above
summary(model3)##
## Call:
## lm(formula = .outcome ~ ., data = dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.505 -8.475 0.093 8.349 57.846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.232637 3.516409 6.891 7.14e-12 ***
## TEAM_BATTING_2B 0.033594 0.007636 4.400 1.13e-05 ***
## TEAM_BATTING_3B 0.106657 0.014722 7.244 5.92e-13 ***
## TEAM_BATTING_BB 0.015579 0.003362 4.634 3.80e-06 ***
## TEAM_BASERUN_SB 0.024497 0.003988 6.143 9.52e-10 ***
## TEAM_PITCHING_HR 0.077009 0.007130 10.800 < 2e-16 ***
## TEAM_FIELDING_E -0.028218 0.002283 -12.361 < 2e-16 ***
## TEAM_FIELDING_DP -0.111020 0.012815 -8.663 < 2e-16 ***
## TEAM_BATTING_1B 0.043179 0.003135 13.774 < 2e-16 ***
## TEAM_BATTING_HBP_YN -3.046056 1.138163 -2.676 0.0075 **
## PITCHER_OUTLIER_YN 7.929821 1.406515 5.638 1.94e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.05 on 2264 degrees of freedom
## Multiple R-squared: 0.3087, Adjusted R-squared: 0.3057
## F-statistic: 101.1 on 10 and 2264 DF, p-value: < 2.2e-16Predictions on evaluation set
# prep evaluation data for prediction
test_raw = read.csv("~/Google Drive/CUNY/git/DATA621/HW1/moneyball-evaluation-data.csv")
test_clean = test_raw
# create TEAM_BATTING_1B column
test_clean = test_clean %>% mutate(TEAM_BATTING_1B = TEAM_BATTING_H - TEAM_BATTING_2B - TEAM_BATTING_3B - TEAM_BATTING_HR) %>%
select(-TEAM_BATTING_H)
# fill in missing values
test_clean = test_clean %>% mutate(
TEAM_PITCHING_SO = ifelse(is.na(TEAM_PITCHING_SO), median(TEAM_PITCHING_SO, na.rm = TRUE), TEAM_PITCHING_SO),
TEAM_BATTING_SO = ifelse(is.na(TEAM_BATTING_SO), median(TEAM_BATTING_SO, na.rm = TRUE), TEAM_BATTING_SO),
TEAM_BASERUN_SB = ifelse(is.na(TEAM_BASERUN_SB), median(TEAM_BASERUN_SB, na.rm = TRUE), TEAM_BASERUN_SB),
TEAM_BASERUN_CS = ifelse(is.na(TEAM_BASERUN_CS), median(TEAM_BASERUN_CS, na.rm = TRUE), TEAM_BASERUN_CS),
TEAM_FIELDING_DP = ifelse(is.na(TEAM_FIELDING_DP), median(TEAM_FIELDING_DP, na.rm = TRUE), TEAM_FIELDING_DP))
# add TEAM_BATTING_HBP_YN
test_clean = test_clean %>% mutate(TEAM_BATTING_HBP_YN = ifelse(is.na(TEAM_BATTING_HBP), 0, 1))
# add outlier flags
test_clean = test_clean %>%
mutate('PITCHER_OUTLIER_YN' = ifelse(TEAM_PITCHING_H > quantile(TEAM_PITCHING_H, 0.75) + 1.5 * IQR(TEAM_PITCHING_H) |
TEAM_PITCHING_H < quantile(TEAM_PITCHING_H, 0.25) - 1.5 * IQR(TEAM_PITCHING_H),
1, 0))
test_clean = test_clean %>%
mutate('BATTING_OUTLIER_YN' = ifelse(TEAM_BATTING_1B > quantile(TEAM_BATTING_1B, 0.75) + 1.5 * IQR(TEAM_BATTING_1B) |
TEAM_BATTING_1B < quantile(TEAM_BATTING_1B, 0.25) - 1.5 * IQR(TEAM_BATTING_1B),
1, 0))
test_clean = test_clean %>%
mutate('BATTING_OUTLIER_YN' = ifelse(TEAM_BATTING_1B > quantile(TEAM_BATTING_1B, 0.75) + 1.5 * IQR(TEAM_BATTING_1B) |
TEAM_BATTING_1B < quantile(TEAM_BATTING_1B, 0.25) - 1.5 * IQR(TEAM_BATTING_1B),
1, 0))
test_clean = test_clean %>%
mutate('BASERUN_OUTLIER_YN' = ifelse(TEAM_BASERUN_SB > quantile(TEAM_BASERUN_SB, 0.75) + 1.5 * IQR(TEAM_BASERUN_SB) |
TEAM_BASERUN_SB < quantile(TEAM_BASERUN_SB, 0.25) - 1.5 * IQR(TEAM_BASERUN_SB),
1, 0))
test_clean = test_clean %>%
mutate('FIELDING_OUTLIER_YN' = ifelse(TEAM_FIELDING_E > quantile(TEAM_FIELDING_E, 0.75) + 1.5 * IQR(TEAM_FIELDING_E) |
TEAM_FIELDING_E < quantile(TEAM_FIELDING_E, 0.25) - 1.5 * IQR(TEAM_FIELDING_E),
1, 0))
# make predictions and save as csv file
pred = predict(model3, newdata = test_clean)
write.csv(pred, "~/Google Drive/CUNY/git/DATA621/HW1/moneyball-evaluation-pred.csv")