assignment_11
2025-03-21
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, unionlibrary(readr)
library(car) # For VIF analysis## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodeLoad 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. :5.110Data Cleaning
# Convert necessary columns to factors
nba_data$Playoffs <- as.factor(nba_data$Playoffs)
nba_data$Season <- as.factor(nba_data$Season)Exploratory Data Analysis
# Histogram of Points per Game
ggplot(nba_data, aes(x = PTS)) +
geom_histogram(bins = 30, fill = "blue", alpha = 0.7) +
labs(title = "Distribution of Points per Game", x = "Points", y = "Frequency")
# Boxplot of Points by Playoff Status
ggplot(nba_data, aes(x = Playoffs, y = PTS, fill = Playoffs)) +
geom_boxplot() +
labs(title = "Points by Playoff Status", y = "Points", x = "Playoffs")
Checking for Multicollinearity
# Fit a multiple linear regression model for VIF check
vif_model <- lm(PTS ~ AST + TRB + STL, data = nba_data)
vif(vif_model)## AST TRB STL
## 1.087890 1.024103 1.063847Linear Regression Model
# Build a linear regression model to predict Points per Game
lm_model <- lm(PTS ~ AST + TRB + STL, data = nba_data)
summary(lm_model)##
## Call:
## lm(formula = PTS ~ AST + TRB + STL, data = nba_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.611 -7.066 -1.684 5.606 56.387
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.91659 0.62604 35.008 < 2e-16 ***
## AST 0.58152 0.07798 7.457 1.40e-13 ***
## TRB 0.27694 0.05575 4.968 7.45e-07 ***
## STL -0.04264 0.17259 -0.247 0.805
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.11 on 1699 degrees of freedom
## Multiple R-squared: 0.04118, Adjusted R-squared: 0.03948
## F-statistic: 24.32 on 3 and 1699 DF, p-value: 2.077e-15Model Diagnostics
par(mfrow = c(2,2)) # Arrange plots
plot(lm_model) # Residuals vs Fitted, Q-Q Plot, Scale-Location, Residuals vs Leverage
Interpretation of Coefficients
Each coefficient represents the expected change in points per game (PTS) for a one-unit increase in the predictor:
- AST (Assists per game): A positive coefficient means that higher assists tend to increase points per game.
- TRB (Total rebounds per game): Indicates how rebounding influences scoring.
- STL (Steals per game): Defensive contributions through steals may correlate with higher offensive output.
Confidence Interval for a Coefficient
# Confidence Interval for AST coefficient
confint(lm_model, "AST", level = 0.95)## 2.5 % 97.5 %
## AST 0.4285716 0.734478Interpretation
The 95% confidence interval for the AST coefficient represents the range in which we are confident the true effect of assists on points per game lies. If the interval does not include zero, the effect is statistically significant.
Conclusion
- Significance: The p-values in the model summary indicate which variables significantly impact points per game.
- Multicollinearity: VIF values help check if any predictor variables are highly correlated.
- Model Performance: Residual plots diagnose any issues like heteroscedasticity or outliers.
- Confidence Intervals: These help confirm the reliability of the coefficient estimates.
Further improvements could include testing for interaction effects or using alternative model evaluation techniques like cross-validation.