DATA621 Assignment 1
Irene Jacob
9/18/2021
Assignment 1
1. Data Exploration
train <- read.csv("https://raw.githubusercontent.com/irene908/DATA621/main/moneyball-training-data.csv") %>%select(-INDEX)
test <- read.csv("https://raw.githubusercontent.com/irene908/DATA621/main/moneyball-evaluation-data.csv") %>%select(-INDEX)dim(train)## [1] 2276 16summary(train)## 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 :286train %>% gather() %>% ggplot(aes(x= value)) + geom_density(fill='light blue') + facet_wrap(~key, scales = 'free')## Warning: Removed 3478 rows containing non-finite values (stat_density).
train_new <- train %>% gather(key = 'key', value = 'value')
ggplot(train_new,aes(x = key, y = value)) +geom_boxplot()+coord_cartesian(ylim = c(0, 1000))+ theme(axis.text.x=element_text(angle=45, hjust=1))## Warning: Removed 3478 rows containing non-finite values (stat_boxplot).
train %>% cor(., use = "complete.obs") %>% corrplot(., type = "upper", diag = FALSE)
train %>% gather(key, value, -TARGET_WINS) %>% ggplot(., aes(value, TARGET_WINS)) + geom_point( color="purple") + geom_smooth(method = "lm", se = FALSE, color = "black") + facet_wrap(~key, scales ="free", ncol = 3) ## `geom_smooth()` using formula 'y ~ x'## Warning: Removed 3478 rows containing non-finite values (stat_smooth).## Warning: Removed 3478 rows containing missing values (geom_point).
train %>% gather(key, value) %>% filter(is.na(value)) %>% group_by(key) %>% tally() %>% mutate(p = n / nrow(train) * 100) %>% mutate(p = paste0(round(p, ifelse(p < 10, 1, 0)), "%")) %>% arrange(desc(n)) %>% rename(`Variable` = key, `Count` = n, `Percentage` = p) 2. Data Preparation
Handling missing data
# Drop the BATTING_HBP field
train <- train %>% select(-TEAM_BATTING_HBP)
train_new <- train
train_new$TEAM_PITCHING_SO <- ifelse(train_new$TEAM_PITCHING_SO > 4000, NA, train_new$TEAM_PITCHING_SO)
train_new$TEAM_PITCHING_H <- ifelse(train_new$TEAM_PITCHING_H > 5000, NA, train_new$TEAM_PITCHING_H)
train_new$TEAM_PITCHING_BB <- ifelse(train_new$TEAM_PITCHING_BB > 2000, NA, train_new$TEAM_PITCHING_BB)
train_new$TEAM_FIELDING_E <- ifelse(train_new$TEAM_FIELDING_E > 480, NA, train_new$TEAM_FIELDING_E)for(i in 1:ncol(train_new)){
train_new[is.na(train_new[,i]), i] <- mean(train_new[,i], na.rm = TRUE)
}
train_new <- train_new %>%
filter(TARGET_WINS != 0)summary(train_new)## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## Min. : 12.00 Min. : 992 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 : 80.83 Mean :1470 Mean :241.3 Mean : 55.27
## 3rd Qu.: 92.00 3rd Qu.:1538 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. : 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 : 735.6 Median :106.0
## Mean : 99.66 Mean :501.8 Mean : 735.9 Mean :124.8
## 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_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## Min. : 7.00 Min. :1137 Min. : 0.0 Min. : 119.0
## 1st Qu.: 44.00 1st Qu.:1419 1st Qu.: 50.0 1st Qu.: 476.0
## Median : 52.80 Median :1518 Median :107.0 Median : 537.0
## Mean : 52.83 Mean :1626 Mean :105.7 Mean : 548.3
## 3rd Qu.: 54.50 3rd Qu.:1664 3rd Qu.:150.0 3rd Qu.: 610.0
## Max. :201.00 Max. :4969 Max. :343.0 Max. :1750.0
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP
## Min. : 0.0 Min. : 65.0 Min. : 52.0
## 1st Qu.: 626.0 1st Qu.:127.0 1st Qu.:134.0
## Median : 800.0 Median :159.0 Median :146.4
## Mean : 800.4 Mean :175.6 Mean :146.4
## 3rd Qu.: 956.0 3rd Qu.:191.0 3rd Qu.:161.5
## Max. :3450.0 Max. :479.0 Max. :228.0Feature Engineering
single_Feature <- function(df){ df %>% mutate(TEAM_BATTING_1B = TEAM_BATTING_H - TEAM_BATTING_2B - TEAM_BATTING_3B - TEAM_BATTING_HR) }
train_new <- single_Feature(train_new)
test <- single_Feature(test)View the final prepared data
train_new %>% gather(key, value) %>% ggplot(., aes(value)) + geom_density(fill='blue') + facet_wrap(~key, scales ="free")
#summary of the prepared train data
summary(train_new)## TARGET_WINS TEAM_BATTING_H TEAM_BATTING_2B TEAM_BATTING_3B
## Min. : 12.00 Min. : 992 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 : 80.83 Mean :1470 Mean :241.3 Mean : 55.27
## 3rd Qu.: 92.00 3rd Qu.:1538 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. : 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 : 735.6 Median :106.0
## Mean : 99.66 Mean :501.8 Mean : 735.9 Mean :124.8
## 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_PITCHING_H TEAM_PITCHING_HR TEAM_PITCHING_BB
## Min. : 7.00 Min. :1137 Min. : 0.0 Min. : 119.0
## 1st Qu.: 44.00 1st Qu.:1419 1st Qu.: 50.0 1st Qu.: 476.0
## Median : 52.80 Median :1518 Median :107.0 Median : 537.0
## Mean : 52.83 Mean :1626 Mean :105.7 Mean : 548.3
## 3rd Qu.: 54.50 3rd Qu.:1664 3rd Qu.:150.0 3rd Qu.: 610.0
## Max. :201.00 Max. :4969 Max. :343.0 Max. :1750.0
## TEAM_PITCHING_SO TEAM_FIELDING_E TEAM_FIELDING_DP TEAM_BATTING_1B
## Min. : 0.0 Min. : 65.0 Min. : 52.0 Min. : 709
## 1st Qu.: 626.0 1st Qu.:127.0 1st Qu.:134.0 1st Qu.: 991
## Median : 800.0 Median :159.0 Median :146.4 Median :1050
## Mean : 800.4 Mean :175.6 Mean :146.4 Mean :1073
## 3rd Qu.: 956.0 3rd Qu.:191.0 3rd Qu.:161.5 3rd Qu.:1129
## Max. :3450.0 Max. :479.0 Max. :228.0 Max. :2112Transformation
Finalizing the dataset for model building
# Build clean dataframe with transformation
train_new <- data.frame(cbind(train_new, BATTING_3B = train_temp$BATTING_3B, BATTING_HR = train_temp$BATTING_HR,BASERUN_SB = train_temp$BASERUN_SB, PITCHING_BB = train_temp$PITCHING_BB, PITCHING_SO = train_temp$PITCHING_SO, FIELDING_E = train_temp$FIELDING_E))
is.na(train_new) <- sapply(train_new, is.infinite)
# Impute missing value with the mean
train_new$BATTING_3B[is.na(train_new$BATTING_3B)] <- mean(train_new$BATTING_3B, na.rm = TRUE)
train_new$BASERUN_SB[is.na(train_new$BASERUN_SB)] <- mean(train_new$BASERUN_SB, na.rm = TRUE)
train_new$PITCHING_SO[is.na(train_new$PITCHING_SO)] <- mean(train_new$PITCHING_SO, na.rm = TRUE)3. Build models
x<-c(1,17,18,19,20,21,22)
train_df <- train_new[,x]
train_new <- train_new[,1:16]Simple model using the transformed data
selecting a few high correlation variables
colnames(train_df)<- c('TARGET_WINS','TEAM_BATTING_3B','TEAM_BATTING_HR', 'TEAM_BASERUN_SB', 'TEAM_PITCHING_BB', 'TEAM_PITCHING_SO', 'TEAM_FIELDING_E')
train_simple <- lm(TARGET_WINS ~ TEAM_BATTING_HR + TEAM_PITCHING_BB + TEAM_FIELDING_E, data = train_df)
summary(train_simple)##
## Call:
## lm(formula = TARGET_WINS ~ TEAM_BATTING_HR + TEAM_PITCHING_BB +
## TEAM_FIELDING_E, data = train_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -60.556 -9.901 0.616 10.193 79.631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.3652 11.0563 2.023 0.0432 *
## TEAM_BATTING_HR 0.5566 0.1140 4.881 1.13e-06 ***
## TEAM_PITCHING_BB 8.3934 1.4427 5.818 6.80e-09 ***
## TEAM_FIELDING_E -3.7810 34.0849 -0.111 0.9117
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.28 on 2271 degrees of freedom
## Multiple R-squared: 0.04918, Adjusted R-squared: 0.04793
## F-statistic: 39.16 on 3 and 2271 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_simple)
Simple model without the transformed data
train_simple_t <- lm(TARGET_WINS ~ TEAM_BATTING_HR + TEAM_PITCHING_BB + TEAM_FIELDING_E, data = train_new)
summary(train_simple_t)##
## Call:
## lm(formula = TARGET_WINS ~ TEAM_BATTING_HR + TEAM_PITCHING_BB +
## TEAM_FIELDING_E, data = train_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -68.377 -9.930 0.786 10.054 74.808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 66.984768 1.989178 33.675 < 2e-16 ***
## TEAM_BATTING_HR 0.041095 0.007094 5.793 7.88e-09 ***
## TEAM_PITCHING_BB 0.016128 0.002612 6.174 7.87e-10 ***
## TEAM_FIELDING_E 0.005141 0.005715 0.900 0.368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.3 on 2271 degrees of freedom
## Multiple R-squared: 0.0468, Adjusted R-squared: 0.04554
## F-statistic: 37.17 on 3 and 2271 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_simple_t)
Full model without the transformed data
train_full <- lm(TARGET_WINS ~., data = train_new)
summary(train_full)##
## Call:
## lm(formula = TARGET_WINS ~ ., data = train_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -62.212 -8.029 0.171 8.440 65.249
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.073680 5.583949 3.953 7.95e-05 ***
## TEAM_BATTING_H 0.043162 0.003722 11.597 < 2e-16 ***
## TEAM_BATTING_2B -0.018652 0.009097 -2.050 0.04045 *
## TEAM_BATTING_3B 0.090657 0.016626 5.453 5.50e-08 ***
## TEAM_BATTING_HR -0.048907 0.030706 -1.593 0.11135
## TEAM_BATTING_BB 0.066961 0.005095 13.143 < 2e-16 ***
## TEAM_BATTING_SO 0.003144 0.003956 0.795 0.42688
## TEAM_BASERUN_SB 0.023170 0.004193 5.526 3.66e-08 ***
## TEAM_BASERUN_CS 0.005847 0.015797 0.370 0.71131
## TEAM_PITCHING_H 0.003070 0.000935 3.284 0.00104 **
## TEAM_PITCHING_HR 0.086333 0.027145 3.180 0.00149 **
## TEAM_PITCHING_BB -0.034795 0.004370 -7.962 2.67e-15 ***
## TEAM_PITCHING_SO -0.005554 0.002884 -1.926 0.05422 .
## TEAM_FIELDING_E -0.049204 0.005488 -8.966 < 2e-16 ***
## TEAM_FIELDING_DP -0.146089 0.013343 -10.949 < 2e-16 ***
## TEAM_BATTING_1B NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.97 on 2260 degrees of freedom
## Multiple R-squared: 0.3181, Adjusted R-squared: 0.3139
## F-statistic: 75.31 on 14 and 2260 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_full)
Polynomial Regression without the transformed data
train_poly <- "TARGET_WINS ~ TEAM_BATTING_1B + TEAM_BATTING_2B + TEAM_BATTING_3B + TEAM_BATTING_HR + TEAM_BATTING_BB + TEAM_BATTING_SO + TEAM_BASERUN_SB + TEAM_BASERUN_CS + TEAM_PITCHING_H + TEAM_PITCHING_HR + TEAM_PITCHING_BB + TEAM_PITCHING_SO + TEAM_FIELDING_E + TEAM_FIELDING_DP + I(TEAM_BATTING_1B^2)+ I(TEAM_BATTING_2B^2) + I(TEAM_BATTING_3B^2) + I(TEAM_BATTING_HR^2) + I(TEAM_BATTING_BB^2) + I(TEAM_BATTING_SO^2) + I(TEAM_BASERUN_SB^2) + I(TEAM_BASERUN_CS^2) + I(TEAM_PITCHING_H^2) + I(TEAM_PITCHING_HR^2) + I(TEAM_PITCHING_BB^2) + I(TEAM_PITCHING_SO^2) + I(TEAM_FIELDING_E^2) + I(TEAM_FIELDING_DP^2) + I(TEAM_BATTING_1B^3)+ I(TEAM_BATTING_2B^3) + I(TEAM_BATTING_3B^3) + I(TEAM_BATTING_HR^3) + I(TEAM_BATTING_BB^3) + I(TEAM_BATTING_SO^3) + I(TEAM_BASERUN_SB^3) + I(TEAM_BASERUN_CS^3) + I(TEAM_PITCHING_H^3) + I(TEAM_PITCHING_HR^3) + I(TEAM_PITCHING_BB^3) + I(TEAM_PITCHING_SO^3) + I(TEAM_FIELDING_E^3) + I(TEAM_FIELDING_DP^3) +I(TEAM_BATTING_1B^4) + I(TEAM_BATTING_2B^4) + I(TEAM_BATTING_3B^4) + I(TEAM_BATTING_HR^4) + I(TEAM_BATTING_BB^4) + I(TEAM_BATTING_SO^4) + I(TEAM_BASERUN_SB^4) + I(TEAM_BASERUN_CS^4) + I(TEAM_PITCHING_H^4) + I(TEAM_PITCHING_HR^4) + I(TEAM_PITCHING_BB^4) + I(TEAM_PITCHING_SO^4) + I(TEAM_FIELDING_E^4) + I(TEAM_FIELDING_DP^4) "
train_poly_lm <- lm(train_poly, train_new)
train_poly_lm_stepback <- MASS::stepAIC(train_poly_lm, direction="backward", trace = F)
train_poly_lm_call <- summary(train_poly_lm_stepback)$call
train_poly_lm_stepback <- lm(train_poly_lm_call[2], train_new)
summary(train_poly_lm_stepback)##
## Call:
## lm(formula = train_poly_lm_call[2], data = train_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.291 -7.246 0.158 7.658 52.304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.670e+01 2.017e+01 -0.828 0.407654
## TEAM_BATTING_2B 1.263e+00 1.863e-01 6.776 1.57e-11 ***
## TEAM_BATTING_3B -3.581e-01 1.867e-01 -1.918 0.055194 .
## TEAM_BATTING_HR 6.536e-01 2.431e-01 2.688 0.007231 **
## TEAM_BATTING_BB 3.697e-01 7.163e-02 5.161 2.67e-07 ***
## TEAM_BASERUN_SB 5.272e-02 1.111e-02 4.743 2.23e-06 ***
## TEAM_PITCHING_H -3.976e-02 1.674e-02 -2.376 0.017590 *
## TEAM_PITCHING_HR -7.726e-01 2.059e-01 -3.753 0.000179 ***
## TEAM_PITCHING_SO -6.595e-02 1.581e-02 -4.172 3.14e-05 ***
## TEAM_FIELDING_E -1.803e-01 2.364e-02 -7.628 3.51e-14 ***
## I(TEAM_BATTING_2B^2) -4.771e-03 7.432e-04 -6.419 1.67e-10 ***
## I(TEAM_BATTING_3B^2) 1.065e-02 3.682e-03 2.892 0.003866 **
## I(TEAM_BATTING_HR^2) -7.648e-03 2.927e-03 -2.613 0.009042 **
## I(TEAM_BATTING_BB^2) -1.206e-03 2.832e-04 -4.259 2.14e-05 ***
## I(TEAM_BATTING_SO^2) 1.428e-04 3.043e-05 4.694 2.85e-06 ***
## I(TEAM_BASERUN_CS^2) -5.503e-04 3.604e-04 -1.527 0.126919
## I(TEAM_PITCHING_H^2) 2.021e-05 6.340e-06 3.188 0.001452 **
## I(TEAM_PITCHING_HR^2) 9.262e-03 2.272e-03 4.076 4.75e-05 ***
## I(TEAM_PITCHING_SO^2) 5.738e-05 2.259e-05 2.540 0.011160 *
## I(TEAM_FIELDING_E^2) 2.295e-04 4.246e-05 5.405 7.17e-08 ***
## I(TEAM_FIELDING_DP^2) -2.476e-03 3.470e-04 -7.137 1.29e-12 ***
## I(TEAM_BATTING_1B^3) 1.075e-08 7.740e-10 13.888 < 2e-16 ***
## I(TEAM_BATTING_2B^3) 5.920e-06 9.696e-07 6.106 1.20e-09 ***
## I(TEAM_BATTING_3B^3) -7.825e-05 2.806e-05 -2.789 0.005331 **
## I(TEAM_BATTING_HR^3) 3.197e-05 1.467e-05 2.179 0.029458 *
## I(TEAM_BATTING_BB^3) 1.778e-06 4.539e-07 3.918 9.20e-05 ***
## I(TEAM_BATTING_SO^3) -1.834e-07 4.686e-08 -3.915 9.33e-05 ***
## I(TEAM_BASERUN_SB^3) -3.601e-07 1.410e-07 -2.555 0.010698 *
## I(TEAM_BASERUN_CS^3) 3.260e-06 2.113e-06 1.543 0.122946
## I(TEAM_PITCHING_H^3) -2.656e-09 7.386e-10 -3.596 0.000330 ***
## I(TEAM_PITCHING_HR^3) -3.574e-05 1.003e-05 -3.564 0.000373 ***
## I(TEAM_PITCHING_BB^3) -7.060e-08 1.022e-08 -6.908 6.39e-12 ***
## I(TEAM_PITCHING_SO^3) -2.523e-08 1.145e-08 -2.204 0.027640 *
## I(TEAM_FIELDING_DP^3) 8.972e-06 1.495e-06 6.003 2.26e-09 ***
## I(TEAM_BATTING_3B^4) 1.684e-07 7.006e-08 2.404 0.016294 *
## I(TEAM_BATTING_HR^4) -4.607e-08 2.575e-08 -1.789 0.073787 .
## I(TEAM_BATTING_BB^4) -8.716e-10 2.523e-10 -3.455 0.000561 ***
## I(TEAM_BATTING_SO^4) 6.131e-11 2.042e-11 3.003 0.002703 **
## I(TEAM_BASERUN_SB^4) 4.673e-10 2.024e-10 2.309 0.021042 *
## I(TEAM_PITCHING_HR^4) 4.609e-08 1.489e-08 3.095 0.001992 **
## I(TEAM_PITCHING_BB^4) 3.980e-11 6.218e-12 6.401 1.87e-10 ***
## I(TEAM_PITCHING_SO^4) 3.872e-12 1.819e-12 2.129 0.033389 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.19 on 2233 degrees of freedom
## Multiple R-squared: 0.4052, Adjusted R-squared: 0.3943
## F-statistic: 37.1 on 41 and 2233 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_poly_lm_stepback)## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
excluding variables with Multicollinearity
train_multi <- lm(TARGET_WINS ~.- TEAM_BATTING_SO- TEAM_PITCHING_BB- TEAM_PITCHING_H- TEAM_PITCHING_HR, data = train_new)
summary(train_multi)##
## Call:
## lm(formula = TARGET_WINS ~ . - TEAM_BATTING_SO - TEAM_PITCHING_BB -
## TEAM_PITCHING_H - TEAM_PITCHING_HR, data = train_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.834 -8.089 0.262 8.451 57.598
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.782093 4.876182 6.313 3.29e-10 ***
## TEAM_BATTING_H 0.039246 0.003284 11.951 < 2e-16 ***
## TEAM_BATTING_2B -0.012053 0.009020 -1.336 0.18158
## TEAM_BATTING_3B 0.089511 0.016668 5.370 8.67e-08 ***
## TEAM_BATTING_HR 0.057120 0.008850 6.454 1.33e-10 ***
## TEAM_BATTING_BB 0.032662 0.002953 11.059 < 2e-16 ***
## TEAM_BASERUN_SB 0.020187 0.004164 4.847 1.34e-06 ***
## TEAM_BASERUN_CS 0.018095 0.015907 1.138 0.25542
## TEAM_PITCHING_SO -0.005450 0.001516 -3.596 0.00033 ***
## TEAM_FIELDING_E -0.045863 0.005517 -8.313 < 2e-16 ***
## TEAM_FIELDING_DP -0.155824 0.013415 -11.615 < 2e-16 ***
## TEAM_BATTING_1B NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.19 on 2264 degrees of freedom
## Multiple R-squared: 0.2942, Adjusted R-squared: 0.2911
## F-statistic: 94.38 on 10 and 2264 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_multi)
Excluding variables having insignificant p values
train_p <- lm(TARGET_WINS ~.- TEAM_BATTING_SO - TEAM_PITCHING_BB - TEAM_PITCHING_H - TEAM_PITCHING_HR - TEAM_BASERUN_CS, data = train_new)
summary(train_p)##
## Call:
## lm(formula = TARGET_WINS ~ . - TEAM_BATTING_SO - TEAM_PITCHING_BB -
## TEAM_PITCHING_H - TEAM_PITCHING_HR - TEAM_BASERUN_CS, data = train_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.994 -8.015 0.249 8.425 57.277
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.044558 4.748519 6.748 1.89e-11 ***
## TEAM_BATTING_H 0.039052 0.003280 11.907 < 2e-16 ***
## TEAM_BATTING_2B -0.011197 0.008989 -1.246 0.213044
## TEAM_BATTING_3B 0.088809 0.016658 5.331 1.07e-07 ***
## TEAM_BATTING_HR 0.055487 0.008734 6.353 2.54e-10 ***
## TEAM_BATTING_BB 0.032743 0.002953 11.089 < 2e-16 ***
## TEAM_BASERUN_SB 0.021076 0.004090 5.153 2.79e-07 ***
## TEAM_PITCHING_SO -0.005558 0.001513 -3.674 0.000244 ***
## TEAM_FIELDING_E -0.046147 0.005511 -8.373 < 2e-16 ***
## TEAM_FIELDING_DP -0.156115 0.013414 -11.639 < 2e-16 ***
## TEAM_BATTING_1B NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.19 on 2265 degrees of freedom
## Multiple R-squared: 0.2938, Adjusted R-squared: 0.291
## F-statistic: 104.7 on 9 and 2265 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(train_p)
4. Select Model
test$TARGET_WINS <- round(predict(train_poly_lm_stepback, test), 0)write.csv(test,"DATA621_Assignment1.csv")