The SSE calculator is a statistical device to estimate the range of the records values throughout the regression line. The sum of squared residuals calculator calculates the dispersion of the points across the imply and what kind of the established variable deviates from anticipated values in the regression analysis.
The sum of rectangular mistakes(SSE) is the difference among the located and the anticipated values. The SEE is likewise represented as RSS (residual sum of squares). The SEE is the unfold of the statistics set values and it's miles an alternative to the same old deviation or absolute deviation.
Recollect the facts sample of the impartial variables 5, 6, 8, 9, 11, 13, 14, 15, 16, and 18, and the dependent variable 10, 12, 13, 14, 15, 15, 14, 12, 11, and 9. Find the sum of squared residuals or SEE values.
Solution:
The records represent the structured and the unbiased variable:
| Obs. | X | Y |
| 1 | 5 | 10 |
| 2 | 6 | 12 |
| 3 | 8 | 13 |
| 4 | 9 | 14 |
| 5 | 11 | 15 |
| 6 | 13 | 15 |
| 7 | 14 | 14 |
| 8 | 15 | 12 |
| 9 | 16 | 11 |
| 10 | 18 | 9 |
Now, by the predicted and the response variable, we assemble the following table:
| Obs. | X | Y | Xᵢ² | Yᵢ² | Xᵢ · Yᵢ |
| 1 | 5 | 10 | 25 | 100 | 50 |
| 2 | 6 | 12 | 36 | 144 | 72 |
| 3 | 8 | 13 | 64 | 169 | 104 |
| 4 | 9 | 14 | 81 | 196 | 126 |
| 5 | 11 | 15 | 121 | 225 | 165 |
| 6 | 13 | 15 | 169 | 225 | 195 |
| 7 | 14 | 14 | 196 | 196 | 196 |
| 8 | 15 | 12 | 225 | 144 | 180 |
| 9 | 16 | 11 | 256 | 121 | 176 |
| 10 | 18 | 9 | 324 | 81 | 162 |
| Sum = | 115 | 125 | 1497 | 1601 | 1426 |
The calculations for the required values are:
\( SS_{XX} = \sum^n_{i=1}X_i^2 - \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right)^2 \)
\( = 1497 - \dfrac{1}{10} (115)^2 = 1497 - 1322.25 = 174.75 \)
\( SS_{YY} = \sum^n_{i=1}Y_i^2 - \dfrac{1}{n} \left(\sum^n_{i=1}Y_i \right)^2 \)
\( = 1601 - \dfrac{1}{10} (125)^2 = 1601 - 1562.5 = 38.5 \)
\( SS_{XY} = \sum^n_{i=1}X_iY_i - \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right)\left(\sum^n_{i=1}Y_i \right) \)
\( = 1426 - \dfrac{1}{10} (115)(125) = 1426 - 1437.5 = -11.5 \)
The slope and intercept are:
\( \hat{\beta}_1 = \dfrac{SS_{XY}}{SS_{XX}} = \dfrac{-11.5}{174.75} = -0.0658 \)
\( \hat{\beta}_0 = \bar{Y} - \hat{\beta}_1 \cdot \bar{X} = 12.5 - (-0.0658)(11.5) = 13.26 \)
Regression equation:
\( \hat{Y} = 13.26 - 0.0658X \)
Now calculate:
\( SS_{Total} = SS_{YY} = 38.5 \)
\( SS_{R} = \hat{\beta}_1 SS_{XY} = -0.0658 \cdot -11.5 = 0.7567 \)
\( SS_{E} = SS_{Total} - SS_{R} = 38.5 - 0.7567 = 37.7433 \)
SSE sum of squared residuals mistakes explains how carefully the impartial variable is associated with the dependent variable.
The better SSE method the variable is deviated from the anticipated fee.
