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