R-Squared Calculator

R-Squared Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: textarea, number
Output type: json
Sample coverage: 4
API ready: Yes

Overview

The R-Squared Calculator is a specialized tool designed to measure the goodness of fit for regression models by calculating the coefficient of determination. By comparing actual observed data against predicted values, it quantifies how much of the variance in the dependent variable is explained by the model, providing essential metrics like R², explained variance percentage, and sum of squared errors.

When to use

Evaluating the accuracy of a linear or non-linear regression model after training.
Comparing different statistical models to determine which one better fits a specific dataset.
Validating forecasting results against historical data to assess predictive performance.

How it works

1Input your set of actual observed values and the corresponding predicted values from your model into the respective text areas.
2Specify the desired number of decimal places to control the precision of the calculated results.
3The tool computes the Sum of Squared Errors (SSE) and the Total Sum of Squares (SST) based on your data points.
4The final R-squared value is derived using the formula 1 - (SSE/SST) and returned as a JSON object containing the variance percentage.

Use cases

Data scientists verifying the performance of machine learning algorithms on test datasets.
Financial analysts assessing the reliability of stock price prediction models against historical trends.
Researchers measuring the strength of the relationship between variables in experimental studies.

Examples

1. Regression Model Validation

Data Analyst

Background

A data analyst has developed a linear regression model to predict housing prices and needs to quantify its accuracy.

Problem

Determine the percentage of variance in prices explained by the model to justify its use to stakeholders.

How to use

Enter the actual sale prices in the 'Actual Values' field and the model's estimates in the 'Predicted Values' field.

decimalPlaces: 4

Outcome

The tool returns an R-squared of 0.60, indicating that 60% of the price variance is captured by the model.

2. Sales Forecast Accuracy Check

Business Intelligence Specialist

Background

A retail company wants to evaluate how well their monthly sales forecasts matched the actual revenue generated over the last quarter.

Problem

Quantify the goodness of fit for the forecasting algorithm used by the inventory team.

How to use

Paste the actual monthly revenue figures and the corresponding forecasted values into the calculator.

FAQ

What does an R-squared value of 1.0 indicate?

It indicates a perfect fit where the model explains 100% of the variance in the data.

Can R-squared be negative?

Yes, if the chosen model fits the data worse than a horizontal line representing the mean of the actual values.

What is the difference between SSE and SST?

SSE measures the deviation of predicted values from actual values, while SST measures the deviation of actual values from their mean.

How many data points do I need?

You need at least two pairs of actual and predicted values, though more points provide a more reliable metric.

Is R-squared the same as the Correlation Coefficient?

In simple linear regression, R-squared is the square of the Pearson correlation coefficient (r).

decimalPlaces: 2

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Regression Model Validation

2. Sales Forecast Accuracy Check

FAQ

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