Assignment 6: Los Angeles Sparks

1 Introduction

2 Tables

This is the space where I will describe the data set, my team and the 2025 season.

Table Discussion- Table 1: My team did not make the playoffs, some stat to prove it

summary %>% 
  kbl() %>%
  kable_styling()

team_name	mean_score	sd_score	mean_fgp	sd_fgp	mean_rebounds	sd_rebounds	mean_3ptpct	sd_3ptpct	mean_steals	sd_steals
Aces	85.52174	9.558566	45.26739	5.815881	33.78261	5.879959	35.26957	7.075776	6.804348	2.671825
Dream	76.92857	10.588518	41.27857	6.777565	35.95238	4.405940	30.82857	9.315926	7.142857	2.816081
Fever	84.50000	10.169898	45.56429	5.378404	35.09524	5.494163	34.99524	8.989885	5.880952	2.286785
Liberty	84.98077	9.916298	44.53462	5.609966	36.90385	5.770988	35.37692	10.057611	7.750000	2.186187
Lynx	82.35849	11.386724	45.20755	6.336459	33.15094	5.058870	37.80377	9.428760	8.358491	3.168926
Mercury	81.92857	12.597702	44.28333	7.338070	32.26190	5.392224	32.97143	10.344865	6.547619	2.120773
Mystics	79.30000	8.691876	43.35750	4.824504	31.85000	4.660527	36.64250	8.688746	7.275000	2.241651
Sky	77.40000	9.623156	42.44250	5.219878	36.60000	5.573748	31.73500	11.624191	7.000000	3.297241
Sparks	78.40000	10.567973	42.62750	6.151505	32.67500	5.520997	32.08750	10.995435	7.300000	2.775349
Storm	82.66667	9.654183	43.42619	5.385484	34.66667	6.018940	28.35238	9.027309	9.238095	3.267053
Sun	80.36170	9.893840	44.30000	5.282169	33.42553	4.619169	32.84043	11.666911	7.893617	3.285237
Wings	84.20000	11.469469	44.46750	5.238437	34.75000	4.650613	32.06000	11.754646	7.125000	2.945553

#making a table to show average score in a win versus average score in a loss
my_team_means %>%
  kbl(caption = "2025 Los Angeles Sparks") %>%
  kable_classic(full_width = F, html_font = "Cambria")

2025 Los Angeles Sparks

result	mean
Loss	76.6875
Win	85.2500

3 Histograms

Histogram discussion

#creating a histogram 
p <- my_team %>%
  ggplot( aes(x=team_score, fill=result)) + 
    geom_histogram(color = "purple", alpha = 0.6, position = 'identity') + 
    scale_fill_manual(values=c("purple", "yellow"))
p

## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

#making side by side box plots to compare points scored in a win versus a loss
 boxplot(team_score ~ result, data = my_team, notch = TRUE, 
        col = c("purple", "yellow"),
        main = "Points scored by game result",
        xlab = "Result", ylab = "Points")

## Warning in (function (z, notch = FALSE, width = NULL, varwidth = FALSE, : some
## notches went outside hinges ('box'): maybe set notch=FALSE

Histogram Discussion Winning v Losing, Side by Side, etc.

4 Models

\(~\)

After all models were run and model reduction was completed, my final model is team_score = -50.4334385 + 4.044072 * field_goal_pct + -1.6678826 * total_rebounds + 2.5656832 * three_point_field_goal_pct + -0.0989813 * field_goal_pct:total_rebounds + 0.0609006 * three_point_field_goal_pct:total_rebounds

This model significantly predicts team score, F(rmodel4sum$fstatistic[1], rmodel4sum$fstatistic[2]) = rmodel4sum$fstatistic[1], p, adjusted R^2= radj.r.squared

See table below for results.

	Dependent variable:
	team_score
field_goal_pct	4.044***
	(1.221)
three_point_field_goal_pct	-1.668*
	(0.925)
total_rebounds	2.566**
	(1.097)
field_goal_pct:total_rebounds	-0.099**
	(0.037)
three_point_field_goal_pct:total_rebounds	0.061**
	(0.028)
Constant	-50.433
	(38.164)
Observations	40
R2	0.503
Adjusted R2	0.429
Residual Std. Error	7.983 (df = 34)
F Statistic	6.869*** (df = 5; 34)
Note:	p<0.1; p<0.05; p<0.01

#creating histogram of residuals
ols_plot_resid_hist(model4)

#creating versus fit plot
ols_plot_resid_fit(model4)

#creating studentized residuals plot
ols_plot_resid_stud(model4)

#creating leverage plot
ols_plot_resid_lev(model4, threshold = 3)

#creating cooks distance plot
ols_plot_cooksd_chart(model4)

#to find the median values
summary(cor_data)

##  field_goal_pct  total_rebounds  three_point_field_goal_pct     steals    
##  Min.   :26.00   Min.   :21.00   Min.   :10.50              Min.   : 1.0  
##  1st Qu.:39.05   1st Qu.:29.00   1st Qu.:25.00              1st Qu.: 5.0  
##  Median :40.90   Median :33.00   Median :32.80              Median : 6.5  
##  Mean   :42.63   Mean   :32.67   Mean   :32.09              Mean   : 7.3  
##  3rd Qu.:47.12   3rd Qu.:36.00   3rd Qu.:38.55              3rd Qu.: 9.0  
##  Max.   :60.00   Max.   :49.00   Max.   :60.90              Max.   :13.0

#creating new data frame for the median game
newdata=data.frame(field_goal_pct=40.90, total_rebounds = 33, three_point_field_goal_pct = 32.80, steals = 6.5)

#predicting team score with medians
predict(model4, newdata, interval = "confidence", level = 0.95)

##        fit     lwr      upr
## 1 77.25382 74.3196 80.18804

I built the model to predict my team’s points for a game where they achieved the median value for every variable. The predicted team score is rprediction[1]. With 95% confidence interval, (rprediction[2],rprediction[3])