Data Dive 9
Serena Hawkins
2026-03-17
Data Dive Week 9 - Regression Diagnostic
Start by setting up the packages to manipulate data.
suppressPackageStartupMessages({
library(tidyverse)
library(rio)
library(boot)
library(broom)
library(car)
library(GGally)
library(ggrepel)
library(lindia)
source("aptheme.R") #Code that helps format graphs
})Import data
data <- import("plays.csv") %>%
filter(!is.na(dropbackDistance) &
!is.na(timeInTackleBox))Start with the same model from last week:
model <- lm(yardsGained ~ dropbackDistance, data)
summary(model)##
## Call:
## lm(formula = yardsGained ~ dropbackDistance, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -75.097 -6.682 -2.348 3.664 91.016
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.93356 0.20744 28.603 < 2e-16 ***
## dropbackDistance 0.24535 0.05326 4.607 4.15e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.788 on 8915 degrees of freedom
## Multiple R-squared: 0.002375, Adjusted R-squared: 0.002263
## F-statistic: 21.22 on 1 and 8915 DF, p-value: 4.147e-06Adding in a binary variable for pass completion:
data <- data %>%
mutate(completed_pass = passResult == "C")
model <- lm(yardsGained ~ dropbackDistance + completed_pass, data)
summary(model)##
## Call:
## lm(formula = yardsGained ~ dropbackDistance + completed_pass,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -70.949 -4.252 -0.005 1.423 86.438
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.42266 0.21204 -11.43 <2e-16 ***
## dropbackDistance 0.53940 0.04389 12.29 <2e-16 ***
## completed_passTRUE 11.67598 0.17698 65.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.024 on 8914 degrees of freedom
## Multiple R-squared: 0.3297, Adjusted R-squared: 0.3295
## F-statistic: 2192 on 2 and 8914 DF, p-value: < 2.2e-16Here we can see that adding completion percentages drastically increases the share of the variance in yardsGained that is explained by the model. We also now need to check that the dropback distance variable is actually explaining anything, so we run the model below with that term removed.
model <- lm(yardsGained ~ completed_pass, data)
summary(model)##
## Call:
## lm(formula = yardsGained ~ completed_pass, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71.992 -3.992 0.463 0.463 87.008
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4634 0.1410 -3.287 0.00102 **
## completed_passTRUE 11.4551 0.1775 64.521 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.091 on 8915 degrees of freedom
## Multiple R-squared: 0.3183, Adjusted R-squared: 0.3182
## F-statistic: 4163 on 1 and 8915 DF, p-value: < 2.2e-16Here we can see that without the dropback distance variable, the model only explains 21% of the variance in yards gained, rather than 31%, so it does make sense to keep both variables. Next letâs look at the model with the down of a given play added in.
model <- lm(yardsGained ~ dropbackDistance + completed_pass + down, data)
summary(model)##
## Call:
## lm(formula = yardsGained ~ dropbackDistance + completed_pass +
## down, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -70.958 -4.251 -0.023 1.447 86.281
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.71105 0.29963 -9.048 <2e-16 ***
## dropbackDistance 0.54285 0.04396 12.350 <2e-16 ***
## completed_passTRUE 11.69431 0.17748 65.890 <2e-16 ***
## down 0.13731 0.10080 1.362 0.173
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.023 on 8913 degrees of freedom
## Multiple R-squared: 0.3298, Adjusted R-squared: 0.3296
## F-statistic: 1462 on 3 and 8913 DF, p-value: < 2.2e-16Here we can see that the adjusted R squared does not increase, meaning that the down does not help to explain the number of yards gained, and there does not appear to be a significant effect either. The coefficents for dropback distance and completed pass aldo do not change much. For these reasons we will leave it out.
Here we also add the variable timeInTackelBox to the model:
model <- lm(yardsGained ~ dropbackDistance + completed_pass + timeInTackleBox, data)
summary(model)##
## Call:
## lm(formula = yardsGained ~ dropbackDistance + completed_pass +
## timeInTackleBox, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.996 -4.150 -0.277 1.932 85.646
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.05962 0.33364 -18.162 < 2e-16 ***
## dropbackDistance 0.20720 0.04946 4.189 2.83e-05 ***
## completed_passTRUE 12.18528 0.17880 68.150 < 2e-16 ***
## timeInTackleBox 1.68515 0.12022 14.018 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.937 on 8913 degrees of freedom
## Multiple R-squared: 0.3441, Adjusted R-squared: 0.3439
## F-statistic: 1559 on 3 and 8913 DF, p-value: < 2.2e-16Here we can see an increase in the Adjsted R squared, telling us that time spent in the tackle box helps to further explain the yards gained. Itâs a pretty small increasee, so there is an argument for leaving it out, however the longer a quarterback has in the tackle box, the longer a play has to develop, the more likely the pass will be completed. Since there is a theoretical reason to include it in the model, Iâm going to leave it alone.
Finally we check for multicolinearity:
vif(model)## dropbackDistance completed_pass timeInTackleBox
## 1.311538 1.053942 1.367888Here we can see a little bit of correlation between model terms, but itâs well below 5 and pretty close to 1, suggesting there is only weak correlation and multicolinearity isnât teribly worysome here. At this point, we can begin model evaluation
Evaluation of Model
We start evaluation with the residual vs fitted values:
gg_resfitted(model) +
geom_smooth(se=FALSE) +
theme_ap(family = "sans")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## âı Please use `linewidth` instead.
## âı The deprecated feature was likely used in the lindia package.
## Please report the issue at <https://github.com/yeukyul/lindia/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
Here weâve got a little concern about the variance of residuals. Instead of a constant random scatter of points, we see two clumps of data, the second larger clump that is funnel shaped. This means there could be an issue with heteroscedasticity, since the eror is higher for cases where yards gained is more than 10.
Next we look at the residuals vs x values
plots <- gg_resX(model, plot.all = FALSE)## Warning: `fortify(<lm>)` was deprecated in ggplot2 4.0.0.
## âı Please use `broom::augment(<lm>)` instead.
## âı The deprecated feature was likely used in the lindia package.
## Please report the issue at <https://github.com/yeukyul/lindia/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.plots$dropbackDistance +
geom_smooth(se = FALSE)## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
plots$completed_pass +
geom_smooth(se = FALSE)## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
plots$timeInTackleBox +
geom_smooth(se = FALSE)## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
Here there is nothing overly concerning. For the most part, the points look plotted randomly. There are definitely some outliers to contend with, and the timeInTackleBox graph is showing a bit of a hump in the middle, but thereâs nothing heinous here.
Now we check correlations between explanatory variables
ggcorr(select(data,
dropbackDistance,
timeInTackleBox), label = TRUE) +
labs(title='Correlation Heatmap') 
This is reflective of what we saw from VIF. There is some slight correlation between dropbackDistance and timeInTackleBox, but not enough to be terribly problematic.
gg_reshist(model)## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
Here we can see a roughly normal distribution. Thereâs a little concern with the longer right hand tail, but nothing too worrisome. Next we look at the QQ plot:
gg_qqplot(model)
This is showing what looks like some pretty strong deviation from the theoretical normal distribution. The QQ plot is incredibly sensitive, so itâs maybe to sensitive to completely throw out the model, but it does give caution for values at the more extreme values.
Last we look at Cooks d:
gg_cooksd(model, threshold = 'matlab')
This is potentially the most concerning plot. It is showing more than just a handful of observations that have significant influence on the model.
Model Conclusions
From the model we can see the effect that a quarterbackâs drop back distance, and time in the tackle box influence yards gained on a given play when controlling for whether a pass is completed or not. Every foot more a quarterback drops back is associated with a .20 yard pickup and for ever second the quarterback can stay in the tackle box, it is associated with an additional 1.69 yards. This highlights the importance of the offensive line players. The better blocking they provide, the longer the play has to develop, and the longer a play can develop, the more yards get picked up.
However, there is a big caveat with the model we have built here. It appears that the model has problems with values that are further away from the mean. There appear to be a lot of outliers in the data, but so many outliers that we cannot simply remove them. These will be a trick to handle.