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Statistics Calculators ▶ SSE Calculator

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**Table of Content**

The SSE calculator is a statistical tool to estimate the variability of the data values across the regression line. The sum of squared residuals calculator calculates the dispersion of the points around the mean and how much the dependent variable deviates from predicted values in the regression analysis.

The sum of Square Error(SSE) is the difference between the observed and the predicted values. The SEE is also represented as RSS (residual sum of squares).

The SEE is the spread of the data set values and it is an alternative to the standard deviation or absolute deviation.

Consider the data sample of the independent variables 6, 7, 7, 8, 12, 14, 15, 16, 16, 19, and the dependent variable 14, 15, 15, 17, 18, 18, 16, 14, 11, and 8. Then find the sum of squared residuals or SEE values:

The data represent the dependent and the independent variable:

Obs. |
X |
Y |

1 | 6 | 14 |

2 | 7 | 15 |

3 | 7 | 15 |

4 | 8 | 17 |

5 | 12 | 18 |

6 | 14 | 18 |

7 | 15 | 16 |

8 | 16 | 14 |

9 | 16 | 11 |

10 | 19 | 8 |

Now by the predicted and the response variable, we construct the following table

Obs. |
X |
Y |
Xᵢ² |
Yᵢ² |
Xᵢ · Yᵢ |

1 | 6 | 14 | 36 | 196 | 84 |

2 | 7 | 15 | 49 | 225 | 105 |

3 | 7 | 15 | 49 | 225 | 105 |

4 | 8 | 17 | 64 | 289 | 136 |

5 | 12 | 18 | 144 | 324 | 216 |

6 | 14 | 18 | 196 | 324 | 252 |

7 | 15 | 16 | 225 | 256 | 240 |

8 | 16 | 14 | 256 | 196 | 224 |

9 | 16 | 11 | 256 | 121 | 176 |

10 | 19 | 8 | 361 | 64 | 152 |

Sum = | 120 | 146 | 1636 | 2220 | 1690 |

The sum of all the squared values from the table is given by:

The sum of squared residuals calculator calculates the deviation of the distances by summing all the mean points.

\(SS_{XX} = \sum^n_{i-1}X_i^2 – \dfrac{1}{n} \left(\sum^n_{i-1}X_i \right)^2\)

\(= 1636 – \dfrac{1}{10} (120)^2\)

\(= 196\)

\(SS_{YY} = \sum^n_{i-1}Y_i^2 – \dfrac{1}{n} \left(\sum^n_{i-1}Y_i \right)^2\)

\(= 2220 – \dfrac{1}{10} (146)^2\)

\(= 88.4\)

\(SS_{XY} = \sum^n_{i-1}X_iY_i – \dfrac{1}{n} \left(\sum^n_{i-1}X_i \right) \left(\sum^n_{i-1}Y_i \right)\)

\(= 1690 – \dfrac{1}{10} (120) (146)\)

\(= -62\)

The slope of the line and the y-intercepts are calculated by the given

Formulas:

\(hat{\beta}_1 = \dfrac{SS_{XY}}{SS_{XX}}\)

\(= \dfrac{-62}{196}\)

\(= -0.31633\)

\(hat{\beta}_0 = \bar{Y} – \hat{\beta}_1 \times \bar{X}\)

\(= 14.6 – -0.31633 \times 12\)

\(= 18.396\)

Then, the regression equation is:

\(hat{Y} = 18.396 -0.31633X\)

Now, The total sum of the square is:

\(SS_{Total} = SS_{YY} = 88.4\)

Also, the regression sum of the square is calculated as:

\(SS_{R} = \hat{B}_1 SS_{XY}\)

\(= -0.31633 \times -62\)

\(= 19.612\)

Now:

\(SS_{E} = SS_{Total} – SS_{R}\)

\(= 88.4 – 19.612\)

\(SS_{E} = 68.788\)

The sum of squares error calculator measures the distance between each point and the mean of all points in a data set or group of statistical data.

For the smooth working of the sum of the squared residuals calculator follow the steps below:

**Input:**

- Enter the data set values for the dependent and independent variable
- Tap Calculate

**Output:**

- SSE values
- Step by step calculations

The SSE sum of squared residuals error explains how closely the independent variable is related to the dependent variable. The SSE calculator identifies the effect of the dependent variable on the independent variable or its correlation.

The higher SSE means the variable is deviated from the **expected value.**

No, the **standard deviation** (SD) will always be larger than the standard error (SE).

No, it can never be negative as the squared residual calculator takes square of the all the data values.

From the source of 365datascience.com: Sum of Squares, What Is SST

From the source of sixsigmastudyguide.com: SSE, Sum of Square formula