What is sum of squares (SS)?

The sum of squared deviations from the mean: SS = Σ(xᵢ - x̄)². It measures total variation in data and is the basis for variance.

What are TSS, ESS, and RSS?

In regression: TSS (Total) = total variation, ESS (Explained) = variation explained by model, RSS (Residual) = unexplained variation. TSS = ESS + RSS.

How is sum of squares related to variance?

Variance = SS/(n-1) for sample variance. SS is the numerator; dividing by degrees of freedom gives variance.

What is R² (R-squared)?

R² = ESS/TSS = 1 - RSS/TSS. It's the proportion of variance explained by the model, ranging from 0 (no fit) to 1 (perfect fit).

Sum of Squares Calculator

Calculate the sum of squares (SS) for statistical analysis. Essential for variance, standard deviation, and ANOVA.

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Calculation Type

Formula: SS = Σx² = x₁² + x₂² + ... + xₙ²

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Understanding Sum of Squares

Simple SS (Σx²)

Sum of all values squared. Used in regression and some formulas.

SS from Mean Σ(x-x̄)²

Measures total variation around the mean. Foundation for variance.

Applications in Statistics

• Variance: σ² = SS / n (population) or s² = SS / (n-1) (sample)
• Standard Deviation: √Variance
• ANOVA: Partitions SS into between-group and within-group components
• Regression: SS measures how well the model fits data

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About Sum of Squares Calculator - SS, TSS, ESS, RSS

Calculate sum of squares for statistics and regression. Find TSS, ESS, RSS, and sum of squared deviations with step-by-step solutions.

Our **Sum of Squares Calculator** computes various sum of squares values essential for statistics and regression analysis. Calculate TSS, ESS, RSS, and sample variance components with detailed breakdowns. For mean calculations, see our Geometric Mean Calculator.

Sum of squares (SS) measures total variation in data. In regression, TSS = ESS + RSS: Total Sum of Squares equals Explained Sum of Squares plus Residual Sum of Squares. Our calculator breaks down each component.

Understand the building blocks of variance, standard deviation, and R² coefficient of determination. Essential for statistics students and data analysts working with regression models.

Key Features

Sum of squared deviations

TSS, ESS, RSS breakdown

Variance calculation

Step-by-step sums

Mean calculation

Individual squared terms

Why Use This Tool?

Regression analysis

Variance understanding

ANOVA preparation

Statistics homework

R² calculation

Common Use Cases

Statistics: Calculate variance and standard deviation.

Regression: Find explained vs residual variation.

ANOVA: Partition variance for group comparisons.

Quality Control: Measure process variation.

Related Tools

Geometric Mean Calculator

Alternative averages.

Poisson Calculator

Probability distributions.

How to Use

Enter your data values (comma-separated)

Optionally enter predicted values for regression SS

Click Calculate

View all sum of squares components