assign10

Load Libraries

library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(readr)
library(car)  # For VIF analysis

## Loading required package: carData

## 
## Attaching package: 'car'

## The following object is masked from 'package:dplyr':
## 
##     recode

#library(caret)  # For ROC curve analysis

Load Dataset

nba_data <- read_csv("C:/Statistics/nba.csv")

## Rows: 1703 Columns: 19
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (4): bbrID, Tm, Opp, Season
## dbl  (12): TRB, AST, STL, BLK, PTS, GmSc, Year, GameIndex, GmScMovingZ, GmSc...
## lgl   (1): Playoffs
## date  (2): Date, Date2
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

str(nba_data)

## spc_tbl_ [1,703 × 19] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ bbrID               : chr [1:1703] "abdelal01" "abdulma02" "abdulta01" "abdursh01" ...
##  $ Date                : Date[1:1703], format: "1993-03-16" "1991-04-02" ...
##  $ Tm                  : chr [1:1703] "BOS" "DEN" "SAC" "ATL" ...
##  $ Opp                 : chr [1:1703] "GSW" "DAL" "VAN" "DET" ...
##  $ TRB                 : num [1:1703] 10 2 2 12 2 13 10 14 2 10 ...
##  $ AST                 : num [1:1703] 2 6 3 5 0 3 1 1 8 3 ...
##  $ STL                 : num [1:1703] 0 4 1 2 0 0 0 1 5 1 ...
##  $ BLK                 : num [1:1703] 0 0 0 1 0 1 0 0 0 3 ...
##  $ PTS                 : num [1:1703] 25 30 31 50 25 17 18 19 31 17 ...
##  $ GmSc                : num [1:1703] 22.7 29.7 26.4 46 17.1 16.9 19.2 20.7 33.2 20.6 ...
##  $ Season              : chr [1:1703] "1992-93" "1990-91" "1997-98" "2001-02" ...
##  $ Playoffs            : logi [1:1703] FALSE FALSE FALSE FALSE FALSE FALSE ...
##  $ Year                : num [1:1703] 1993 1991 1998 2002 2019 ...
##  $ GameIndex           : num [1:1703] 181 64 58 386 160 8 236 124 100 4 ...
##  $ GmScMovingZ         : num [1:1703] 4.13 3.82 4.11 4.06 3.37 2.58 4.27 4.15 3.16 4.68 ...
##  $ GmScMovingZTop2Delta: num [1:1703] 0.24 0.64 1.67 0.84 0.18 0.05 0.02 0.93 0.22 1.16 ...
##  $ Date2               : Date[1:1703], format: "1991-12-04" "1995-12-07" ...
##  $ GmSc2               : num [1:1703] 18.6 40.1 16.9 34.3 16.6 16.8 19.6 18.5 42.3 29.5 ...
##  $ GmScMovingZ2        : num [1:1703] 3.89 3.18 2.44 3.22 3.19 2.53 4.25 3.22 2.94 3.52 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   bbrID = col_character(),
##   ..   Date = col_date(format = ""),
##   ..   Tm = col_character(),
##   ..   Opp = col_character(),
##   ..   TRB = col_double(),
##   ..   AST = col_double(),
##   ..   STL = col_double(),
##   ..   BLK = col_double(),
##   ..   PTS = col_double(),
##   ..   GmSc = col_double(),
##   ..   Season = col_character(),
##   ..   Playoffs = col_logical(),
##   ..   Year = col_double(),
##   ..   GameIndex = col_double(),
##   ..   GmScMovingZ = col_double(),
##   ..   GmScMovingZTop2Delta = col_double(),
##   ..   Date2 = col_date(format = ""),
##   ..   GmSc2 = col_double(),
##   ..   GmScMovingZ2 = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>

summary(nba_data)

##     bbrID                Date                 Tm                Opp           
##  Length:1703        Min.   :1984-12-11   Length:1703        Length:1703       
##  Class :character   1st Qu.:1998-03-22   Class :character   Class :character  
##  Mode  :character   Median :2008-04-02   Mode  :character   Mode  :character  
##                     Mean   :2007-04-20                                        
##                     3rd Qu.:2016-12-27                                        
##                     Max.   :2022-05-20                                        
##       TRB             AST             STL              BLK        
##  Min.   : 0.00   Min.   : 0.00   Min.   : 0.000   Min.   :0.0000  
##  1st Qu.: 4.00   1st Qu.: 1.00   1st Qu.: 1.000   1st Qu.:0.0000  
##  Median : 7.00   Median : 3.00   Median : 1.000   Median :0.0000  
##  Mean   : 7.37   Mean   : 3.74   Mean   : 1.669   Mean   :0.8949  
##  3rd Qu.:10.00   3rd Qu.: 5.00   3rd Qu.: 2.000   3rd Qu.:1.0000  
##  Max.   :29.00   Max.   :22.00   Max.   :10.000   Max.   :9.0000  
##       PTS             GmSc          Season           Playoffs      
##  Min.   : 4.00   Min.   : 6.40   Length:1703        Mode :logical  
##  1st Qu.:19.00   1st Qu.:18.90   Class :character   FALSE:1655     
##  Median :24.00   Median :24.10   Mode  :character   TRUE :48       
##  Mean   :26.06   Mean   :25.14                                     
##  3rd Qu.:32.00   3rd Qu.:30.10                                     
##  Max.   :81.00   Max.   :64.60                                     
##       Year        GameIndex       GmScMovingZ    GmScMovingZTop2Delta
##  Min.   :1985   Min.   :   0.0   Min.   :2.170   Min.   :0.0000      
##  1st Qu.:1998   1st Qu.:  70.0   1st Qu.:3.240   1st Qu.:0.1500      
##  Median :2008   Median : 148.0   Median :3.630   Median :0.3500      
##  Mean   :2007   Mean   : 251.1   Mean   :3.691   Mean   :0.5057      
##  3rd Qu.:2017   3rd Qu.: 369.0   3rd Qu.:4.050   3rd Qu.:0.7050      
##  Max.   :2022   Max.   :1592.0   Max.   :6.750   Max.   :3.7300      
##      Date2                GmSc2        GmScMovingZ2  
##  Min.   :1984-11-21   Min.   : 5.30   Min.   :1.840  
##  1st Qu.:1998-02-14   1st Qu.:16.90   1st Qu.:2.860  
##  Median :2008-02-27   Median :21.60   Median :3.170  
##  Mean   :2007-03-14   Mean   :22.68   Mean   :3.185  
##  3rd Qu.:2016-04-10   3rd Qu.:27.40   3rd Qu.:3.485  
##  Max.   :2022-05-03   Max.   :53.80   Max.   :5.110

Data Cleaning

# Convert necessary columns to factors
nba_data$Playoffs <- as.factor(nba_data$Playoffs)
nba_data$Season <- as.factor(nba_data$Season)

Logistic Regression Model for Playoff Qualification

# Build a logistic regression model to predict Playoff status
logit_model <- glm(Playoffs ~ PTS + AST + TRB + STL, data = nba_data, family = binomial)
summary(logit_model)

## 
## Call:
## glm(formula = Playoffs ~ PTS + AST + TRB + STL, family = binomial, 
##     data = nba_data)
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -4.968063   0.497939  -9.977  < 2e-16 ***
## PTS          0.054249   0.011948   4.540 5.61e-06 ***
## AST         -0.008144   0.047783  -0.170    0.865    
## TRB         -0.003548   0.033113  -0.107    0.915    
## STL         -0.057788   0.105194  -0.549    0.583    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 437.25  on 1702  degrees of freedom
## Residual deviance: 418.06  on 1698  degrees of freedom
## AIC: 428.06
## 
## Number of Fisher Scoring iterations: 6

Model Evaluation: McFadden’s Pseudo R²

# McFadden's Pseudo R²
pseudo_r2 <- 1 - (logLik(logit_model) / logLik(glm(Playoffs ~ 1, data = nba_data, family = binomial)))
pseudo_r2

## 'log Lik.' 0.04389706 (df=5)

Interpretation of Coefficients

Each coefficient represents the log-odds change in the probability of making the playoffs for a one-unit increase in the predictor:

PTS (Points per game): A positive coefficient means that higher points increase the probability of making the playoffs.
AST (Assists per game): Indicates how passing contributes to playoff qualification.
TRB (Total rebounds per game): A strong rebound presence may positively or negatively affect playoff chances.
STL (Steals per game): Defensive contributions through steals may influence playoff qualification.

Confidence Interval for a Coefficient

# Confidence Interval for AST coefficient
coef_estimate <- coef(summary(logit_model))["AST", "Estimate"]
std_error <- coef(summary(logit_model))["AST", "Std. Error"]
confidence_interval <- coef_estimate + c(-1.96, 1.96) * std_error
confidence_interval

## [1] -0.10179873  0.08551149

Interpretation

The 95% confidence interval for the AST coefficient represents the range in which we are confident the true effect of assists on playoff qualification lies. If the interval does not include zero, the effect is statistically significant.

Conclusion

This logistic regression model helps understand the key predictors of playoff qualification.

Significance: The p-values in the model summary indicate which variables have a statistically significant effect.
Multicollinearity: VIF values help check if any predictor variables are highly correlated.
Model Performance: McFadden’s Pseudo R² and the ROC curve provide insights into how well the model classifies teams.
Confidence Intervals: These help confirm the reliability of the coefficient estimates.
Future Investigation: Additional variables or interaction terms could further refine predictions.

Further improvements could include testing for interaction effects or using alternative model evaluation techniques like precision-recall analysis.