Free online Sxx Syy Sxy calculator for linear regression – Calculate the Sxx, Syy, and Sxy values in statistics with our efficient and user-friendly calculator. Get accurate results for your statistical analysis.

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## Formula of Sxx, Syy and Sxy in linear regression

In linear regression, the formulas for Sxx, Syy and Sxy for data set in statistics

**Sum of squares of the dependent variable (Syy):**

Syy = Σ(y – ȳ)² where:

- Σ denotes the sum over all data points.
- y represents the observed values of the dependent variable.
- ȳ is the mean (average) of the dependent variable.

**Sum of squares of the independent variable (Sxx):**

Sxx = Σ(x – x̄)² where:

- Σ denotes the sum over all data points.
- x represents the observed values of the independent variable.
- x̄ is the mean (average) of the independent variable.

**Sum of cross-products (Sxy):**

Sxy = Σ(x – x̄)(y – ȳ) where:

- Σ denotes the sum over all data points.
- x represents the observed values of the independent variable.
- y represents the observed values of the dependent variable.
- x̄ is the mean (average) of the independent variable.
- ȳ is the mean (average) of the dependent variable.

## What is Sxx, Sxy and Syy Equations?

In Linear regressions, Sxx, Sxy, and Syy equations are:-

- Sxx = Σ(x – x̄)²
- Sxy = Σ(x – x̄)(y – ȳ)
- Syy = Σ(y – ȳ)²

## Examples of Sxx, Sxy and Syy equations

Calculate | X-values | Y-values |
---|---|---|

Example- | 1,2,3,4,5,7,7,8 | 2,2,4,5,5,6,6,6,9 |

Sum of Square (Sxx,Syy) | 45.88 | 38.00 |

Sum of cross products (Sxy) | 28.50 | 28.50 |

Mean | X: 4.63 | Y: 5.00 |

Mode | X: 7 | Y: 6 |

Median | X: 4.50 | Y: 5.00 |