A regression residual is the difference between the actual value of a dependent variable and the value predicted by a regression model. The formula for calculating the residual is:
Residual = Observed Value - Predicted Value
Enter or paste values for the independent and dependent variable in the spreadsheet below and then click on the 'Calculate' button to calculate the residuals for each row.
| Independent Variable (X) | Dependent Variable (Y) | |
| 1 | 14 | 49 |
| 2 | 7 | 27 |
| 3 | 12 | 40 |
| 4 | 10 | 33 |
| 5 | 19 | 60 |
| 6 | 11 | 36 |
| 7 | 16 | 52 |
| 8 | 17 | 56 |
| 9 | 13 | 44 |
| 10 | 12 | 39 |
The linear regression equation is :
ŷ = 4.9150 + (2.9531)*x
The predicted value and residuals are shown in the table below:
| X | Y | Predicted Y (ŷ) | Residuals (y-ŷ) | |
| 1 | 14 | 49 | 46.258 | 2.742 |
| 2 | 7 | 27 | 25.586 | 1.414 |
| 3 | 12 | 40 | 40.352 | -0.352 |
| 4 | 10 | 33 | 34.446 | -1.446 |
| 5 | 19 | 60 | 61.023 | -1.023 |
| 6 | 11 | 36 | 37.399 | -1.399 |
| 7 | 16 | 52 | 52.164 | -0.164 |
| 8 | 17 | 56 | 55.117 | 0.883 |
| 9 | 13 | 44 | 43.305 | 0.695 |
| 10 | 12 | 39 | 40.352 | -1.352 |
Share Share Tweet