R-squared Calculator

Use our R-squared calculator to determine the coefficient of determination for statistical analysis.

Data Source and Methodology

All calculations are based on standard statistical formulas for computing the coefficient of determination. Visit this source for more details. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]

Glossary of Variables

  • X values: Independent variable data points.
  • Y values: Dependent variable data points.
  • R-squared: The proportion of variance in the dependent variable predictable from the independent variable(s).

How It Works: A Step-by-Step Example

To calculate the R-squared value, input your independent (X) and dependent (Y) variables. The calculator applies the formula to determine the coefficient of determination, which reflects how well the data fits a statistical model.

Frequently Asked Questions (FAQ)

What does an R-squared value indicate?

R-squared indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Can R-squared be negative?

R-squared values usually range from 0 to 1. A negative value would indicate that the model is worse than a horizontal line model.

Is a higher R-squared always better?

A higher R-squared indicates a better fit, but it does not necessarily indicate a correct model. Model selection should involve additional criteria.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}\]
R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}
Formula (extracted text)
The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Full original guide (expanded)

Data Source and Methodology

All calculations are based on standard statistical formulas for computing the coefficient of determination. Visit this source for more details. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]

Glossary of Variables

  • X values: Independent variable data points.
  • Y values: Dependent variable data points.
  • R-squared: The proportion of variance in the dependent variable predictable from the independent variable(s).

How It Works: A Step-by-Step Example

To calculate the R-squared value, input your independent (X) and dependent (Y) variables. The calculator applies the formula to determine the coefficient of determination, which reflects how well the data fits a statistical model.

Frequently Asked Questions (FAQ)

What does an R-squared value indicate?

R-squared indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Can R-squared be negative?

R-squared values usually range from 0 to 1. A negative value would indicate that the model is worse than a horizontal line model.

Is a higher R-squared always better?

A higher R-squared indicates a better fit, but it does not necessarily indicate a correct model. Model selection should involve additional criteria.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}\]
R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}
Formula (extracted text)
The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Data Source and Methodology

All calculations are based on standard statistical formulas for computing the coefficient of determination. Visit this source for more details. All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]

Glossary of Variables

  • X values: Independent variable data points.
  • Y values: Dependent variable data points.
  • R-squared: The proportion of variance in the dependent variable predictable from the independent variable(s).

How It Works: A Step-by-Step Example

To calculate the R-squared value, input your independent (X) and dependent (Y) variables. The calculator applies the formula to determine the coefficient of determination, which reflects how well the data fits a statistical model.

Frequently Asked Questions (FAQ)

What does an R-squared value indicate?

R-squared indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Can R-squared be negative?

R-squared values usually range from 0 to 1. A negative value would indicate that the model is worse than a horizontal line model.

Is a higher R-squared always better?

A higher R-squared indicates a better fit, but it does not necessarily indicate a correct model. Model selection should involve additional criteria.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}\]
R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}}
Formula (extracted text)
The R-squared value is calculated as follows: \[ R^2 = 1 - \frac{\sum{(y_i - f_i)^2}}{\sum{(y_i - \bar{y})^2}} \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).