Sum of Squared Errors Calculator

Calculate SSE, analyze model fit, compare regression models, and visualize residuals for statistical analysis.

Data Input

Input Method:

Data Format:

Observed Values (one per line):

Predicted Values (one per line):

Data Preview

#	Observed	Predicted	Residual	Squared Error
Enter data to see preview

Quick Statistics

Data Points

Mean Residual

Error Analysis Results

SSE

Sum of Squared Errors

MSE

Mean Squared Error

RMSE

Root Mean Squared Error

R²

Coefficient of Determination

Visualizations

Observed vs Predicted

Residual Plot

Statistical Analysis

Residual Statistics:

Mean:

Standard Deviation:

Min Residual:

Max Residual:

Model Quality:

MAE:

MAPE:

Adjusted R²:

Model Fit:

Model Comparison

Model	SSE	MSE	RMSE	R²	Rank

Interpretation & Recommendations

About Sum of Squared Errors (SSE)

What is Sum of Squared Errors?

Sum of Squared Errors (SSE) is a statistical measure that quantifies the total deviation between observed values and predicted values from a model. It's calculated by summing the squares of all residuals (differences between observed and predicted values). SSE is fundamental in regression analysis, model evaluation, and determining the goodness of fit.

Key Error Metrics

SSE

SSE = Σ(yᵢ - ŷᵢ)²

Sum of squared differences between observed and predicted values.

MSE

MSE = SSE / n

Mean Squared Error - average of squared errors.

RMSE

RMSE = √MSE

Root Mean Squared Error - in same units as original data.

Model Evaluation Metrics

R² (R-squared): Proportion of variance explained by the model (0-1, higher is better)
MAE (Mean Absolute Error): Average of absolute differences
MAPE (Mean Absolute Percentage Error): Average percentage error
Adjusted R²: R² adjusted for number of predictors
Residual Analysis: Pattern analysis in prediction errors

How to Use This Calculator

Choose your input method: manual entry, CSV upload, or sample datasets
Select data format: observed vs predicted, X-Y data with model fitting, or direct residuals
Enter your data or upload a CSV file
For X-Y data, choose the appropriate model type for fitting
Click "Calculate SSE Analysis" to generate comprehensive results
Review error metrics, visualizations, and statistical analysis
Use "Compare Models" to evaluate multiple model types
Export charts and results for reports or presentations

Applications

Regression Analysis: Evaluate linear and nonlinear model performance
Machine Learning: Compare different algorithms and hyperparameters
Quality Control: Assess measurement accuracy and process control
Forecasting: Evaluate prediction model accuracy
Research: Statistical analysis and hypothesis testing
Engineering: Model validation and system optimization

Interpretation Guidelines

Lower SSE/MSE/RMSE: Better model fit
R² close to 1: Model explains most variance
Random residual patterns: Good model assumptions
Systematic residual patterns: Model may be inadequate
Outliers: May indicate data quality issues or model limitations

Sample Data Examples

Try These Examples:

Linear Relationship: Perfect linear correlation with minimal error
Quadratic Curve: Nonlinear relationship requiring polynomial fitting
Exponential Growth: Exponential model comparison
Noisy Data: Real-world data with measurement errors
Data with Outliers: Impact of outliers on model performance
Perfect Fit: Zero error baseline for comparison