Multiple Correlation Coefficient Calculator

Instructions: Use this Multiple Correlation Coefficient Calculator for a multiple linear regression. Please input the data for the independent variables \((X_i's)\) and the dependent variable (\(Y\)), in form below, and the step-by-step calculations will be shown:

Dependent variable sample data (\(Y\), comma or space separated) =
X values (comma or space separated, press '\' for a new variable)
Independent variable Names (Comma separated. Optional) =
Dependent variable Name (optional) =

Multiple Correlation Coefficient

The multiple correlation coefficient is a numerical measure of how well a linear regression model fits a set of data \(Y_i\).

Technically speaking, it is the simple correlation coefficient for dependent variable values \(Y_i\) and the predicted values \(\hat Y_i\) that are obtained with the least squares multiple linear regression


\[R_{mult} =\frac{n \sum_{i=1}^n hat Y_i Y_i - \left(\sum_{i=1}^n \hat Y_i \right) \left(\sum_{i=1}^n Y_i \right) }{\sqrt{n \sum_{i=1}^n \hat Y_i^2 - \left( \sum_{i=1}^n \hat Y_i \right)^2} \sqrt{n \sum_{i=1}^n Y_i^2 - \left( \sum_{i=1}^n Y_i \right)^2} }\]

but it can also be computed \(\sqrt{\frac{SSR}{SST}}\), where \(SSR\) is the sum of regression squares and \(SST\) is the total sum of squares, because that way is a bit simpler by following some (intensive) matrix calculations .

What are the limits of multiple correlation coefficient?

For the case of a simple linear regression, the correlation coefficient may range from -1 to 1. For the case of the multiple correlation coefficient, it ranges from 0 to 1.

Other associated calculators

If you need to estimate the regression model instead, you can use this multiple linear regression calculator.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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