Adjusted R Squared Calculator for Simple Regression

Instructions: Use this calculator to compute the adjusted R-Squared coefficient for a simple linear regression. Please input the data for the independent variable \((X)\) and the dependent variable (\(Y\)), in the form below:

Independent variable \(X\) sample data (comma or space separated) =
Dependent variable \(Y\) sample data (comma or space separated) =
Independent variable Name (optional) =
Dependent variable Name (optional) =

How is the adjusted R Squared calculated?

The Adjusted R Squared coefficient is a correction to the common R-Squared coefficient (also know as coefficient of determination), which is particularly useful in the case of multiple regression with many predictors, because in that case, the estimated explained variation is overstated by R-Squared. The Adjusted R Squared coefficient is computed as:

\[\text{Adj. } R^2 = \displaystyle 1 - \frac{(1-R^2)(n-1)}{n-k-1}\]

where \(n\) is the sample size, \(k\) is the number of predictors (excluding the constant).

How to Compute the Adjusted R-Squared coefficient?

The first thing you need to do if you want to compute the Adjusted R^2 coefficient is to use first the r square formula. As you can see in the formula above, you will need \(R^\) to perform the calculation.

Which one do I use, R square or the Adjusted R squared coefficient?

The answer is depends: when you are working with a simple regression model (where there is only one independent variable), you should use R squared, but when you have a multiple regression model (with many independent variables), you should use the Adjusted R squared coefficient, especially if you have a large number of predictors

What to do if I need to use multiple regression instead of simple regression?

This solver is for a simple linear regression. If you want to compute the Adjusted R Squared coefficient for a multiple regression model, please use this adjusted R-Squared calculator for multiple regression models. calculator instead. Or, if you already know the value of the coefficient of determination \(R^2\), the use this R Squared to Adjusted R Squared calculator.

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