Description

Q1EDA

After using boxplots for continuous variables and table for categorical variable, we can tell that the higher the number of total points scored in the game(TeamPoints), the higher the number of field goals made in the game(FieldGoals.), the higher the total number of assists(Assists), the higher the total number of steals (balls stolen from the opposing team while the opposing team has possession) in the game(Steals), the higher the total number of blocks (direct prevention of a made field goal after the ball has been shot by an opposing player) in the game (Blocks) and the higher total number of rebounds grabbed in the game(TotalRebounds), the more likely the tean will win the game, since the median is higher. For the Turnovers( Total number of times the ball was lost back to the opposing team while the team had possession), there seems to have no obvious difference between win and loss. While the lower the number of total points scored by the opposing
Away Home Away
77 L 0.6260163
46 W 0.3739837
Home
L0.4227642
W0.5772358
team in the game(OpponentPoints) and the lower the total number of times the ball was lost back to the opposing team, the more likely the team will lose the game.
The probability of wining changes for the location of the game. When the game is a home game, the team is more likely to win, while when it’s a away game, the team is more likely to lose.
Q2
1. We shouldn’t include both FieldGoals. and FieldGoals as predictors in the logistic model, since FieldGoadls. contains the information of both FieldGoals and FieldGoalsAttempted.
2. We shouldn’t include both FieldGoals. and X3PointShots as predictors in the logistic model, since FieldGoadls. includes 3 point shots, it contains the whole information of X3PointShots.
Q3
Estimate Std. Error z value Pr(>|z|)
(Intercept) -29.80 3.94 -7.56 0.00
HomeHome 1.11 0.40 2.75 0.01
TeamPoints -0.01 0.03 -0.34 0.74
FieldGoals. 0.44 0.08 5.78 0.00
Assists -0.11 0.05 -2.23 0.03
Steals 0.39 0.08 4.74 0.00
Blocks 0.04 0.07 0.60 0.55
TotalRebounds 0.28 0.04 6.22 0.00
Turnovers -0.17 0.06 -3.03 0.00
Fitted Model
log(p_win/1-p_win) =β0 + β1Home_Home + β2TeamPoints +β3 FieldGoals+β4Assists+ β5Steals + β6Blocks + β7TotalRecounds + β8Turnovers + ϵ
log(p_win/1-p_win) = -29.80 + 1.11Home_Home – 0.01TeamPoints + 0.44 FieldGoals. –
0.11Assists + 0.39Steals + 0.04Blocks + 0.28TotalRecounds – 0.17Turnovers + ϵ β1: The odds of wining a NBA game when the game is at home are 3.03 times higher than the game is away from home.
β2: As we increase TeamPoints by 1 unit, we increase the log-odds of wining an NBA game by -0.01 (increase the odds for wining an NBA game by a multiplicative effect of 0.99/ the odds of winning an NBA game increase 0.99 times). — not significant
β3: As we increase FieldGoals. by 1 percent, we increase the log-odds of wining an NBA game by 0.44 (increase the odds for wining an NBA game by a multiplicative effect of 1.55/ the odds of winning an NBA game increase 1.55 times).
β4: As we increase Assists by 1 unit, we increase the log-odds of wining an NBA game by -0.11 (increase the odds for wining an NBA game by a multiplicative effect of 0.90/ the odds of winning an NBA game increase 0.90 times).
β5: As we increase Steals by 1 unit, we increase the log-odds of wining an NBA game by 0.39 (increase the odds for wining an NBA game by a multiplicative effect of 1.48/ the odds of winning an NBA game increase 1.48 times).
β6: As we increase Blocks by 1 unit, we increase the log-odds of wining an NBA game by 0.04 (increase the odds for wining an NBA game by a multiplicative effect of 1.04/ the odds of winning an NBA game increase
1.04 times). — not significant
β7: As we increase TotalRebounds by 1 unit, we increase the log-odds of wining an NBA game by 0.28 (increase the odds for wining an NBA game by a multiplicative effect of 1.32/ the odds of winning an NBA game increase 1.32 times).
β8: As we increase TurnOverss by 1 unit, we increase the log-odds of wining an NBA game by -0.17 (increase the odds for wining an NBA game by a multiplicative effect of 0.84/ the odds of winning an NBA game increase 0.84 times).
Q4
x
HomeHome 1.27
TeamPoints 2.03
FieldGoals. 3.44
Assists 1.53
Steals 1.53
Blocks 1.16
TotalRebounds 2.27
Turnovers 1.29
Since all VIFs are between 1 and 5(<10), which means they are moderately correlated, we don’t need to worry about multicollinearity.
Q5

1 − Specificity

0 1
0 106 23
1 23 94

x
Accuracy 0.8130081

x
Sensitivity 0.8034188
Specificity 0.8217054

The accuracy of this model is 0.813.
AUC:0.897
Q6
Estimate Std. Error z value Pr(>|z|)
(Intercept) 9.19 11.61 0.79 0.43
HomeHome 1.53 0.68 2.25 0.02
TeamPoints 0.14 0.06 2.26 0.02
FieldGoals. 0.40 0.16 2.56 0.01
Assists -0.01 0.08 -0.12 0.91
Steals 0.35 0.18 1.96 0.05
Blocks -0.09 0.10 -0.91 0.36
TotalRebounds 0.17 0.09 1.83 0.07
Turnovers -0.55 0.13 -4.27 0.00
Opp.FieldGoals. -0.86 0.17 -5.08 0.00
Opp.TotalRebounds -0.36 0.09 -3.94 0.00
Opp.TotalFouls 0.10 0.10 0.96 0.34
Opp.Turnovers 0.61 0.16 3.73 0.00
log(p_win/1-p_win) = 9.19 + 1.53Home_Home + 0.14TeamPoints + 0.40 FieldGoals – 0.01Assists + 0.35Steals – 0.09Blocks + 0.17TotalRebounds – 0.55Turnovers 0.86Opp.FieldGoals. – 0.36Opp.TotalRebounds + 0.10Opp.TotalFouls + 0.61Opp.Turnovers
+ ϵ
Significant coefficients includes β1, β2, β3, β8, β9, β10, and β12
β1: The odds of wining a NBA game when the game is at home are 4.62 times higher than the game is away from home.
β2: As we increase TeamPoints by 1 unit, we increase the log-odds of wining an NBA game by 0.14 (increase the odds for wining an NBA game by a multiplicative effect of 1.15/ the odds of winning an NBA game increase 1.15 times).
β3: As we increase FieldGoals. by 1 percent, we increase the log-odds of wining an NBA game by 0.40 (increase the odds for wining an NBA game by a multiplicative effect of 1.49/ the odds of winning an NBA game increase 1.49 times).
β8: As we increase TurnOvers by 1 unit, we increase the log-odds of wining an NBA game by -0.55 (increase the odds for wining an NBA game by a multiplicative effect of 0.58/ the odds of winning an NBA game increase 0.58 times).
β9: As we increase Opp.FieldGoals. by 1 percent, we increase the log-odds of wining an NBA game by -0.86 (increase the odds for wining an NBA game by a multiplicative effect of 0.42/ the odds of winning an NBA game increase 0.42 times).
β10: As we increase Opp.TotalRebounds by 1 unit, we increase the log-odds of wining an NBA game by -0.36 (increase the odds for wining an NBA game by a multiplicative effect of 0.70/ the odds of winning an NBA game increase 0.70 times).
β12: As we increase Opp.Turnovers by 1 unit, we increase the log-odds of wining an NBA game by 0.61 (increase the odds for wining an NBA game by a multiplicative effect of 1.84/ the odds of winning an NBA game increase 1.84 times).
Q7

0 1
0 120 9
1 9 108

x
Accuracy 0.9268293

x
Sensitivity 0.9230769
Specificity 0.9302326

1 − Specificity
The accuracy of this model is 0.927.
AUC for model that includes Opp.FieldGoals., Opp.TotalRebounds, Opp.TotalFouls, and Opp.Turnovers as predictors is higher(0.983 > 0.897), the accuracy is also higher(0.927>0.813). Therefore, this new model is better.
Q8

0 1
0 37 2
1 9 34

x
Accuracy 0.8658537

x
Sensitivity 0.9444444
Specificity 0.8043478

Q9
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
233 82.32 NA NA NA
231 80.78 2 1.54 0.46

0 1
0 39 2
1 7 34

x
Accuracy 0.8902439

x
Sensitivity 0.9444444
Specificity 0.8478261

Resid. Df Resid. Dev Df Deviance Pr(>Chi)
233 82.32 NA NA NA
232 79.60 1 2.72 0.1

0 1
0 39 2
1 7 34

x
Accuracy 0.8902439

x
Sensitivity 0.9444444
Specificity 0.8478261

Q10
• Although during exploratory data analysis, for the Turnovers( Total number of times the ball was lost back to the opposing team while the team had possession), there seems to have no obvious difference between win and loss. In each model, the coefficient of Turnovers is statistically significant.
• In order to have a higher chance of wining, team should try to get higher FieldGoals/FieldGoalsAttempted and lower the total number of times the ball was lost back to the opposing team while the team had possession(Turnovers). In the meantime, if Opp.FieldGoals/Opp.FieldGoalsAttempted is lower, the number of offensive rebounds grabbed by the opposing team in the game is lower, and the higher the total number of times the ball was won back from the opposing team while the opposing team had possession, the higher the possibility the team will win.
Appendix: All code for this report
knitr::opts_chunk$set(echo = TRUE)
library(ISLR2) library(knitr) library(ggplot2) library(kableExtra) library(lattice) library(dplyr) library(stargazer) library(gt) library(janitor) library(flextable) library(magrittr) library(Hmisc) library(caret) library(patchwork) library(leaps) library(rms) library(arm) library(pROC) library(e1071) library(caret) require(gridExtra)
nba <- read.csv(“nba_games_stats.csv”)
# Set factor variables nba$Home <- factor(nba$Home) nba$Team <- factor(nba$Team)
# This is not always necessary but can be useful
#particularly for R functions that prefer numeric binary variables
#to the original factor variables nba$Win <- rep(0,nrow(nba)) nba$Win[nba$WINorLOSS==”W”] <- 1 # Charlotte hornets subset
nba_reduced <- nba[nba$Team == “CHO”, ] #100*FieldGoals., Opp.FieldGoals.
nba_reduced$FieldGoals. <- (nba_reduced$FieldGoals.)*100
nba_reduced$Opp.FieldGoals.<-(nba_reduced$Opp.FieldGoals.)*100
#boxplot for numerical variables(TeamPoints, FieldGoals.,Assists, Steals, Blocks, OpponentPoints, TotalR
p1 <- ggplot(nba_reduced_train,aes(x=TeamPoints, y=WINorLOSS, fill=TeamPoints)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”TeamPoints vs Win/Loss”, x=”TeamPoints”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
axis.title = eleme
p2 <- ggplot(nba_reduced_train,aes(x=FieldGoals., y=WINorLOSS, fill=FieldGoals.)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”FieldGoals. vs Win/Loss”, x=”FieldGoals.”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p3 <- ggplot(nba_reduced_train,aes(x=Assists, y=WINorLOSS, fill=Assists)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”Assists vs Win/Loss”, x=”Assists”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p4 <- ggplot(nba_reduced_train,aes(x=Steals, y=WINorLOSS, fill=Steals)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”Steals vs Win/Loss”, x=”Steals”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p5 <- ggplot(nba_reduced_train,aes(x=Blocks, y=WINorLOSS, fill=Blocks)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”Blocks vs Win/Loss”, x=”Blocks”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p6 <- ggplot(nba_reduced_train,aes(x=OpponentPoints, y=WINorLOSS, fill=OpponentPoints)) + geom_boxplot() +
scale_fill_brewer(palette=”Blues”) + labs(title=”OpponentPoints vs Win/Loss”, x=”OpponentPoints”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p7 <- ggplot(nba_reduced_train,aes(x=TotalRebounds, y=WINorLOSS, fill=TotalRebounds)) + geom_boxplot() +
scale_fill_brewer(palette=”Reds”) + labs(title=”TotalRebounds vs Win/Loss”, x=”TotalRebounds”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p8 <- ggplot(nba_reduced_train,aes(x=Turnovers, y=WINorLOSS, fill=Turnovers)) + geom_boxplot() +
scale_fill_brewer(palette=”Blues”) + labs(title=”Turnovers vs Win/Loss”, x=”Turnovers”,y=”Win or Loss”) +
theme_classic() + theme(legend.position=”none”,plot.title = element_text(size = 9),
p1+p2+p3+p4+p5+p6+p7+p8+plot_layout(ncol=3)
#tables for factor variable Home
t1 <- table(nba_reduced_train[,c(“WINorLOSS”,”Home”)])
axis.title = eleme
axis.title = eleme
axis.title = eleme
axis.title = eleme
axis.title = eleme
axis.title = eleme
axis.title = eleme (“WINorLOSS”
t2 <- apply(table(nba_reduced_train[,c(“WINorLOSS”,”Home”)])/sum(table(nba_reduced_train[,c
2,function(x) x/sum(x)) knitr::kable(list(t1, t2))
nba_glm <- glm(Win ~ Home + TeamPoints + FieldGoals. + Assists + Steals + Blocks +
#summary(nba_glm)
knitr::kable(summary(nba_glm)$coefficients,digits = 2)%>% kable_styling(position=”center”,
#vif(nba_glm)
knitr::kable(vif(nba_glm),digits = 2)%>% kable_styling(full_width = FALSE,latex_options = Conf_mat <- confusionMatrix(as.factor(ifelse(fitted(nba_glm) >= 0.5, “1”,”0″)), as.factor(nba_reduced_train$Win),positive = “1”)
t1 <- Conf_mat$table
t2 <- Conf_mat$overall[“Accuracy”];
t3 <- Conf_mat$byClass[c(“Sensitivity”,”Specificity”)]
knitr::kable(list(t1, t2,t3))
roc(nba_reduced_train$Win,fitted(nba_glm),plot=T,print.thres=”best”,legacy.axes=T, print.auc =T,col=”red3″)
nba_glm_new <- glm(Win ~ Home + TeamPoints + FieldGoals. + Assists + Steals + Blocks +
#summary(nba_glm_new)
knitr::kable(summary(nba_glm_new)$coefficients,digits = 2)%>% kable_styling(position= Conf_mat <- confusionMatrix(as.factor(ifelse(fitted(nba_glm_new) >= 0.5, “1”,”0″)), as.factor(nba_reduced_train$Win),positive = “1”)
t1.1 <- Conf_mat$table
t2.1 <- Conf_mat$overall[“Accuracy”];
t3.1 <- Conf_mat$byClass[c(“Sensitivity”,”Specificity”)]
knitr::kable(list(t1.1, t2.1,t3.1))%>% kable_styling(position=”center”,full_width = FALSE, roc(nba_reduced_train$Win,fitted(nba_glm_new),plot=T,print.thres=”best”,legacy.axes=T, print.auc =T,col=”red3″)
pred <- predict(nba_glm_new, nba_reduced_test, type = “response”) pred_new <- as.factor(ifelse(pred >=0.5,’1′,’0′))
Conf_mat <- confusionMatrix(pred_new, as.factor(nba_reduced_test$Win),positive = “1”)
t1<-Conf_mat$table
t2<-Conf_mat$overall[“Accuracy”];
t3<-Conf_mat$byClass[c(“Sensitivity”,”Specificity”)]
knitr::kable(list(t1, t2,t3))%>% kable_styling(position=”center”,full_width = FALSE, nba_glm_new_1 <- glm(Win ~ Home + TeamPoints + FieldGoals. + Assists + Steals + Blocks +
#summary(nba_glm_new_1)
#knitr::kable(summary(nba_glm_new_1)$coefficients,digits = 2)%>% kable_styling(position=”center”,full_wi
#anova(nba_glm_new,nba_glm_new_1, test = ‘Chisq’)
knitr::kable(anova(nba_glm_new,nba_glm_new_1,test = ‘Chisq’),digits = 2)%>% kable_styling( pred1 <- predict(nba_glm_new_1, nba_reduced_test, type = “response”) pred_new_1 <- as.factor(ifelse(pred1 >=0.5,’1′,’0′))
Conf_mat <- confusionMatrix(pred_new_1, as.factor(nba_reduced_test$Win),positive = “1”)
t1<-Conf_mat$table
t2<-Conf_mat$overall[“Accuracy”];
t3<-Conf_mat$byClass[c(“Sensitivity”,”Specificity”)]
TotalRebounds + Turno full_width = c(“hold_positi
TotalRebounds +
“center”,full_width
latex_options latex_options = c(“h TotalRebounds
knitr::kable(list(t1, t2,t3))%>% kable_styling(position=”center”,full_width = FALSE, nba_glm_new_2 <- glm(Win ~ Home + TeamPoints + FieldGoals. + Assists + Steals + Blocks +
#summary(nba_glm_new_2) #vif(nba_glm_new_2)
#knitr::kable(summary(nba_glm_new_2)$coefficients,digits = 2)%>% kable_styling(position=”center”,full_wi
#anova(nba_glm_new,nba_glm_new_2, test = ‘Chisq’)
knitr::kable(anova(nba_glm_new,nba_glm_new_2,test = ‘Chisq’),digits = 2)%>% kable_styling( pred2 <- predict(nba_glm_new_2, nba_reduced_test, type = “response”) pred_new_2 <- as.factor(ifelse(pred1 >=0.5,’1′,’0′))
Conf_mat <- confusionMatrix(pred_new_2, as.factor(nba_reduced_test$Win),positive = “1”)
t1<-Conf_mat$table
t2<-Conf_mat$overall[“Accuracy”];
t3<-Conf_mat$byClass[c(“Sensitivity”,”Specificity”)]
knitr::kable(list(t1, t2,t3))%>% kable_styling(position=”center”,full_width = FALSE,
position=”cent latex_options = c(“h TotalRebounds
position=”cent
latex_options = c(“h