Mini Project 2
Gianna LaFrance
3-10-2023
1 Description of the Data Set
This is a data set of the results of all NFL regular season field goal attempts for the 2008 season. There are 1039 observations with 23 variables The variables are:
GameDate
AwayTeam
HomeTeam
qtr (quarter, 5=overtime)
min (minutes remaining)
sec (seconds remaining, added to minutes)
kickteam (team kicking field goal)
def (defending team)
down
togo (yards to go for 1st down)
kicker (ID #)
ydline (yardline of kicking team)
name (kicker’s name)
distance (yards)
homekick (1 if kicker at Home, 0 if Away)
kickdiff (kicking team lead +, or deficit -, prior to kick)
timerem (Time remaining in seconds, negative = overtime)
offscore (kicking team’s score prior to kick)
defscore (defense team’s score prior to kick)
season (2008)
GOOD (1 is Success, 0 is Miss)
Missed (Missed, not blocked = -1, 0 ow)
Blocked (1 if Blocked, 0 ow)
The variables Missed, Blocked, season, and GameDate are removed from the data set because they do not affect the success of a field goal.
1.1 Question
The objective of this data is to identify what makes a field goal successful.
1.2 Exploratory Analysis
First, the following pairwise scatter plots are made to inspect the potential issues with predictor variables and colinearity.
## Warning: package 'psych' was built under R version 4.2.2
The variables that were removed due to colinearity or violating the normality assumption were: yardline, defscore, offscore, kickteam, quater, timerem, homekick and down.
1.3 Building the Logistic Regression Models
Based on the above exploratory analysis, we first build the full model and the smallest model.
## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 5.535457e+00 | 2.275154e+00 | 2.433004e+00 | 0.0149741 |
| AwayTeamATL | -1.556454e+00 | 2.387268e+00 | -6.519810e-01 | 0.5144134 |
| AwayTeamBAL | -3.971946e+00 | 5.036447e+00 | -7.886405e-01 | 0.4303222 |
| AwayTeamBUF | -7.125008e+00 | 7.561394e+00 | -9.422876e-01 | 0.3460454 |
| AwayTeamCAR | -9.890033e+00 | 9.549332e+00 | -1.035678e+00 | 0.3003524 |
| AwayTeamCHI | -8.926903e+00 | 1.159639e+01 | -7.698005e-01 | 0.4414182 |
| AwayTeamCIN | -1.363555e+01 | 1.334355e+01 | -1.021883e+00 | 0.3068361 |
| AwayTeamCLE | -1.485387e+01 | 1.520253e+01 | -9.770658e-01 | 0.3285366 |
| AwayTeamDAL | -1.731829e+01 | 1.710124e+01 | -1.012692e+00 | 0.3112073 |
| AwayTeamDEN | -1.986115e+01 | 1.898034e+01 | -1.046406e+00 | 0.2953735 |
| AwayTeamDET | -7.840539e+00 | 1.359663e+02 | -5.766530e-02 | 0.9540152 |
| AwayTeamGB | -2.242242e+01 | 2.275244e+01 | -9.854950e-01 | 0.3243810 |
| AwayTeamHOU | -2.341128e+01 | 2.467544e+01 | -9.487687e-01 | 0.3427383 |
| AwayTeamIND | -2.702596e+01 | 2.656083e+01 | -1.017512e+00 | 0.3089099 |
| AwayTeamJAC | -2.866608e+01 | 2.843761e+01 | -1.008034e+00 | 0.3134381 |
| AwayTeamKC | -3.231267e+01 | 3.031489e+01 | -1.065901e+00 | 0.2864684 |
| AwayTeamMIA | -3.318976e+01 | 3.412020e+01 | -9.727303e-01 | 0.3306873 |
| AwayTeamMIN | -3.459917e+01 | 3.597854e+01 | -9.616612e-01 | 0.3362198 |
| AwayTeamNE | -3.910455e+01 | 3.787649e+01 | -1.032423e+00 | 0.3018742 |
| AwayTeamNO | -4.409573e+01 | 4.170996e+01 | -1.057199e+00 | 0.2904208 |
| AwayTeamNYG | 1.700967e+13 | 3.445357e+14 | 4.936980e-02 | 0.9606246 |
| AwayTeamNYJ | -4.446868e+14 | 4.341656e+14 | -1.024233e+00 | 0.3057252 |
| AwayTeamOAK | -5.163533e+01 | 5.109699e+01 | -1.010536e+00 | 0.3122388 |
| AwayTeamPHI | -5.236801e+01 | 5.298997e+01 | -9.882627e-01 | 0.3230240 |
| AwayTeamPIT | -5.600648e+01 | 5.677777e+01 | -9.864158e-01 | 0.3239291 |
| AwayTeamSD | -5.858989e+01 | 5.867164e+01 | -9.986067e-01 | 0.3179853 |
| AwayTeamSEA | -6.021790e+01 | 6.056500e+01 | -9.942690e-01 | 0.3200919 |
| AwayTeamSF | -6.241997e+01 | 6.244749e+01 | -9.995592e-01 | 0.3175239 |
| AwayTeamSTL | -6.260563e+01 | 6.430006e+01 | -9.736481e-01 | 0.3302313 |
| AwayTeamTB | -6.611665e+01 | 6.623164e+01 | -9.982639e-01 | 0.3181514 |
| AwayTeamTEN | -6.772260e+01 | 6.814420e+01 | -9.938132e-01 | 0.3203138 |
| AwayTeamWAS | -5.607026e+01 | 5.485902e+01 | -1.022079e+00 | 0.3067434 |
| HomeTeamATL | -8.457193e-01 | 2.320184e+00 | -3.645052e-01 | 0.7154808 |
| HomeTeamBAL | -5.237059e+00 | 5.185105e+00 | -1.010020e+00 | 0.3124857 |
| HomeTeamBUF | -8.549868e+00 | 7.711028e+00 | -1.108784e+00 | 0.2675232 |
| HomeTeamCAR | -8.321023e+00 | 9.554322e+00 | -8.709172e-01 | 0.3837994 |
| HomeTeamCHI | -9.240068e+00 | 1.147406e+01 | -8.053008e-01 | 0.4206461 |
| HomeTeamCIN | -1.269760e+01 | 1.330980e+01 | -9.540041e-01 | 0.3400816 |
| HomeTeamCLE | -1.548193e+01 | 1.521054e+01 | -1.017842e+00 | 0.3087528 |
| HomeTeamDAL | -1.480517e+01 | 1.705416e+01 | -8.681268e-01 | 0.3853249 |
| HomeTeamDEN | -1.963814e+01 | 1.902365e+01 | -1.032301e+00 | 0.3019310 |
| HomeTeamDET | -3.856699e+00 | 1.359755e+02 | -2.836320e-02 | 0.9773725 |
| HomeTeamGB | -2.087110e+01 | 2.272722e+01 | -9.183307e-01 | 0.3584457 |
| HomeTeamHOU | -2.340382e+01 | 2.463167e+01 | -9.501519e-01 | 0.3420351 |
| HomeTeamIND | -2.374972e+01 | 2.656899e+01 | -8.938885e-01 | 0.3713815 |
| HomeTeamJAC | -2.801876e+01 | 2.846929e+01 | -9.841750e-01 | 0.3250295 |
| HomeTeamKC | -3.087148e+01 | 3.034373e+01 | -1.017393e+00 | 0.3089667 |
| HomeTeamMIA | -3.394577e+01 | 3.417018e+01 | -9.934324e-01 | 0.3204993 |
| HomeTeamMIN | -3.327315e+01 | 3.598718e+01 | -9.245835e-01 | 0.3551826 |
| HomeTeamNE | -3.760994e+01 | 3.791022e+01 | -9.920792e-01 | 0.3211589 |
| HomeTeamNO | -4.219991e+01 | 4.171806e+01 | -1.011550e+00 | 0.3117532 |
| HomeTeamNYG | 1.700967e+13 | 3.445357e+14 | 4.936980e-02 | 0.9606246 |
| HomeTeamNYJ | -4.446868e+14 | 4.341656e+14 | -1.024233e+00 | 0.3057252 |
| HomeTeamOAK | -5.023005e+01 | 5.114142e+01 | -9.821792e-01 | 0.3260115 |
| HomeTeamPHI | -5.038272e+01 | 5.293466e+01 | -9.517907e-01 | 0.3412031 |
| HomeTeamPIT | -5.586343e+01 | 5.679272e+01 | -9.836372e-01 | 0.3252939 |
| HomeTeamSD | -5.625791e+01 | 5.869768e+01 | -9.584351e-01 | 0.3378434 |
| HomeTeamSEA | -5.876997e+01 | 6.054782e+01 | -9.706372e-01 | 0.3317290 |
| HomeTeamSF | -6.102912e+01 | 6.241582e+01 | -9.777829e-01 | 0.3281817 |
| HomeTeamSTL | -6.291857e+01 | 6.411716e+01 | -9.813062e-01 | 0.3264418 |
| HomeTeamTB | -6.481341e+01 | 6.624534e+01 | -9.783844e-01 | 0.3278842 |
| HomeTeamTEN | -6.644168e+01 | 6.815422e+01 | -9.748726e-01 | 0.3296235 |
| HomeTeamWAS | -5.492697e+01 | 5.485732e+01 | -1.001270e+00 | 0.3166964 |
| min | 1.169800e-03 | 7.131400e-03 | 1.640312e-01 | 0.8697066 |
| sec | 8.748500e-03 | 6.537400e-03 | 1.338232e+00 | 0.1808210 |
| defATL | 2.845128e-01 | 2.403261e+00 | 1.183862e-01 | 0.9057617 |
| defBAL | 6.111634e+00 | 5.209426e+00 | 1.173188e+00 | 0.2407205 |
| defBUF | 8.766517e+00 | 7.794142e+00 | 1.124757e+00 | 0.2606920 |
| defCAR | 9.058731e+00 | 9.574430e+00 | 9.461379e-01 | 0.3440783 |
| defCHI | 8.444654e+00 | 1.151458e+01 | 7.333881e-01 | 0.4633217 |
| defCIN | 1.482772e+01 | 1.338027e+01 | 1.108179e+00 | 0.2677847 |
| defCLE | 1.481924e+01 | 1.524541e+01 | 9.720463e-01 | 0.3310275 |
| defDAL | 1.653002e+01 | 1.704775e+01 | 9.696308e-01 | 0.3322306 |
| defDEN | 2.101824e+01 | 1.903944e+01 | 1.103932e+00 | 0.2696227 |
| defDET | 6.827769e+00 | 1.359700e+02 | 5.021530e-02 | 0.9599509 |
| defGB | 2.128853e+01 | 2.278216e+01 | 9.344387e-01 | 0.3500776 |
| defHOU | 2.381394e+01 | 2.475499e+01 | 9.619858e-01 | 0.3360567 |
| defIND | 2.587322e+01 | 2.659784e+01 | 9.727562e-01 | 0.3306745 |
| defJAC | 2.916836e+01 | 2.849628e+01 | 1.023585e+00 | 0.3060314 |
| defKC | 3.288330e+01 | 3.036123e+01 | 1.083069e+00 | 0.2787780 |
| defMIA | 3.500721e+01 | 3.415395e+01 | 1.024983e+00 | 0.3053713 |
| defMIN | 3.379215e+01 | 3.600769e+01 | 9.384705e-01 | 0.3480027 |
| defNE | 3.728241e+01 | 3.791662e+01 | 9.832734e-01 | 0.3254729 |
| defNO | 4.361795e+01 | 4.172730e+01 | 1.045309e+00 | 0.2958800 |
| defNYG | -1.700967e+13 | 3.445357e+14 | -4.936980e-02 | 0.9606246 |
| defNYJ | 4.446868e+14 | 4.341656e+14 | 1.024233e+00 | 0.3057252 |
| defOAK | 5.142767e+01 | 5.116452e+01 | 1.005143e+00 | 0.3148279 |
| defPHI | 5.255102e+01 | 5.291160e+01 | 9.931853e-01 | 0.3206197 |
| defPIT | 5.624705e+01 | 5.681264e+01 | 9.900447e-01 | 0.3221523 |
| defSD | 5.856069e+01 | 5.873291e+01 | 9.970677e-01 | 0.3187317 |
| defSEA | 6.084801e+01 | 6.055589e+01 | 1.004824e+00 | 0.3149817 |
| defSF | 6.211009e+01 | 6.242307e+01 | 9.949861e-01 | 0.3197430 |
| defSTL | 6.542996e+01 | 6.423115e+01 | 1.018664e+00 | 0.3083625 |
| defTB | 6.673347e+01 | 6.628931e+01 | 1.006700e+00 | 0.3140788 |
| defTEN | 6.549158e+01 | 6.817038e+01 | 9.607044e-01 | 0.3367008 |
| defWAS | 5.572992e+01 | 5.485211e+01 | 1.016003e+00 | 0.3096279 |
| togo | -1.156760e-02 | 2.870510e-02 | -4.029808e-01 | 0.6869623 |
| kicker | 1.861579e+00 | 1.891689e+00 | 9.840831e-01 | 0.3250747 |
| nameC.Barth | -1.816808e+00 | 2.380101e+00 | -7.633322e-01 | 0.4452653 |
| nameD.Rayner | 2.060280e+01 | 4.359682e+05 | 4.730000e-05 | 0.9999623 |
| nameG.Hartley | 4.503600e+15 | 1.862078e+07 | 2.418588e+08 | 0.0000000 |
| nameJ.Carney | -1.700967e+13 | 3.445357e+14 | -4.936980e-02 | 0.9606246 |
| nameJ.Feely | 4.446868e+14 | 4.341656e+14 | 1.024233e+00 | 0.3057252 |
| nameL.Tynes | -1.700967e+13 | 3.445357e+14 | -4.936980e-02 | 0.9606246 |
| nameM.Gramatica | 3.637611e+00 | 2.628972e+00 | 1.383663e+00 | 0.1664617 |
| nameM.Nugent | 4.446868e+14 | 4.341656e+14 | 1.024233e+00 | 0.3057252 |
| nameM.Stover | 8.924217e-01 | 1.922320e+00 | 4.642421e-01 | 0.6424743 |
| distance | -1.445343e-01 | 1.593330e-02 | -9.071209e+00 | 0.0000000 |
| kickdiff | -6.291900e-03 | 1.409080e-02 | -4.465250e-01 | 0.6552181 |
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 6.4956640 | 0.5703859 | 11.388191 | 0.0000000 |
| distance | -0.1192415 | 0.0123408 | -9.662395 | 0.0000000 |
| sec | 0.0080947 | 0.0054667 | 1.480729 | 0.1386788 |
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 6.4956640 | 0.5703859 | 11.388191 | 0.0000000 |
| distance | -0.1192415 | 0.0123408 | -9.662395 | 0.0000000 |
| sec | 0.0080947 | 0.0054667 | 1.480729 | 0.1386788 |
| Deviance.residual | Null.Deviance.Residual | AIC | |
|---|---|---|---|
| full.model | 557.9044 | 809.6515 | 775.9044 |
| reduced.model | 684.7092 | 817.7227 | 690.7092 |
| final.model | 684.7092 | 817.7227 | 690.7092 |
1.4 Final Model
In the exploratory analysis, only the variables distance and second are linearly correlated. After automatic variable selection, all the other variables were dropped out of the model besides distance and second.
| Estimate | Std. Error | z value | Pr(>|z|) | odds.ratio | |
|---|---|---|---|---|---|
| (Intercept) | 6.4956640 | 0.5703859 | 11.388191 | 0.0000000 | 662.2638362 |
| distance | -0.1192415 | 0.0123408 | -9.662395 | 0.0000000 | 0.8875935 |
| sec | 0.0080947 | 0.0054667 | 1.480729 | 0.1386788 | 1.0081276 |
Because the odds ratio for distance in less than 1, so as the distance increases, the odds of having a successful field goal decrease. Because the odds ratio for second is almost 1, it means that it doesn’t affect the success of a field goal.
1.5 Summary and Conclusion
The case study focused on the association analysis between a set of potential factors that might influence a field goal’s success. The initial data set has 18 numerical and 5 categorical variables.
After exploratory analysis, some highly correlated values were removed from the model.
After automatic variable selection, the final model was obtained with 2 factors: distance in yards and seconds. And as this distance increases, the success of a field goal decreases.