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 |