This presentation uses fictional game data.
- Predictor: completed passes
- Response: passing yards
- Each row represents one game
Football Passing Data
The Data
| Completions | Yards |
|---|---|
| 12 | 118 |
| 15 | 146 |
| 17 | 165 |
| 19 | 190 |
| 21 | 201 |
| 23 | 232 |
| 25 | 249 |
| 27 | 268 |
| 29 | 287 |
| 31 | 310 |
| 34 | 341 |
Scatterplot
Simple Linear Regression
\[Y_i=\beta_0+\beta_1X_i+\varepsilon_i\]
\(Y_i\) represents passing yards.
\(X_i\) represents completions.
\(\beta_1\) is the expected change in passing yards for +1 completion.
R Code
model=lm(Yards~Completions,data=football) ggplot(football,aes(Completions,Yards))+geom_point()+geom_smooth(method="lm",se=FALSE)
Interactive Plotly Graph
Regression Line
## `geom_smooth()` using formula = 'y ~ x'
Model Interpretation
\[\widehat{Y}=b_0+b_1X\]
The estimated slope is 10.2.
One completion predicts about 10.2 more passing yards.
The model has an \(R^2\) value of 0.998.
Residual Plot
Conclusion
This example shows a positive relationship between completions and passing yards.
Simple linear regression estimates passing yards from completed passes.
Real analysis might include more games and other variables.