Find R² and adjust R² for the following data:
Given: Y = 0.2X + 60
| X | Y |
|---|---|
| 80 | 85 |
| 75 | 70 |
| 85 | 80 |
| 70 | 95 |
| 65 | 70 |
Solution:
Mean of Y = 80
| X | Y | Predicted Y | (Y - Mean of Y)² | (Predicted Y - Actual Y)² | (Predicted Y - Mean of Y)² |
|---|---|---|---|---|---|
| 80 | 85 | 76 | 25 | 81 | 16 |
| 75 | 70 | 75 | 100 | 25 | 25 |
| 85 | 80 | 77 | 0 | 9 | 9 |
| 70 | 95 | 74 | 225 | 441 | 36 |
| 65 | 70 | 73 | 100 | 9 | 49 |
SST = 25 + 100 + 0 + 225 + 100 = 450
SSE = 81 + 25 + 9 + 441 + 9 = 565
SSR = 16 + 25 + 9 + 36 + 49 = 135