NUMB3RS: Season 3 - "Hardball"
Least Squares Regression & MLB Statistical Anomalies
Difficulty: StatisticsTI Activity PDF
Step 1 of 6
Bivariate Data and Informal Fits
When analyzing baseball statistics, fans and managers notice that power hitters who hit many home runs () also tend to strike out () with higher frequency. To model this positive correlation, we look for a linear relationship:
Before calculators automate this, mathematicians used a trial-and-error approach to manually place a line through a scatter plot so that it passes through the 'middle' of the data.
MLB Regression Simulator
Explore Sum of Squared Residuals (SSR) dynamically.
Interactive Formula
y = 2.00x + 55.00
Sum of Squared Residuals (SSR)
61.00
Slope (m): 2.00Range: 1.0 - 3.5
Y-Intercept (b): 55.00Range: 30 - 80
Geometric Breakdown Table
| Player | HR (x) | Actual SO (y) | Predicted (ŷ) | Residual (e) | e² (Area of Square) |
|---|---|---|---|---|---|
| Player A | 12 | 80 | 79.00 | +1.00 | 1.00 |
| Player B | 22 | 96 | 99.00 | -3.00 | 9.00 |
| Player C | 32 | 124 | 119.00 | +5.00 | 25.00 |
| Player D | 42 | 138 | 139.00 | -1.00 | 1.00 |
| Player E | 48 | 156 | 151.00 | +5.00 | 25.00 |
| Sum of Squared Residuals (SSR) | 61.00 | ||||