**Instructions:** Use this Coefficient of Determination Calculator to compute the coefficient of determination (\(R^2\)) associated to the regression model obtained from sample data provided the independent variable \((X)\) and the dependent variable (\(Y\)), in the form below:

## Coefficient of Determination Calculator

The idea of linear regression is to being able to predict a dependent variable from one or more independent variables. For that purpose we are looking for a model that adjusts to the data as good as possible.

A measure of goodness of fit for a linear regression model is represented by the coefficient of determination, or \(R^2\), and it is broadly used to assess the quality of a linear regression model.

### How do you compute the Coefficient of Determination?

Most often, the coefficient of determination is computed using some type of statistical software package. But using the actual Math definition is useful to arrive to an important interpretation for R-Squared.

Mathematically, the coefficient of determination is computed as

\[ R^2 = \frac{SSR}{SST}\]where \(SSR\) stand for the regression sum of squares and \(SST\) stands for the total sum of squares. Let us remember that the total variation (\(SST\)) is divided into explained variation (\(SSR\)) and unexplained variation (\(SSE\)), as it is shown below:

\[SST = SSR + SSE\]### What does the coefficient of determination represent?

*Coefficient of determination interpretation*: Based on the way it is defined, the coefficient of determination is simply the ratio of the explained variation and the total variation. In other words, the coefficient of determination represents the proportion (or percentage) of variation in the dependent variable that is explained by the linear regression model.

For example, if the coefficient of determination is \(R^2 = 0.473\), what does that tell you? It indicates that 47.3% of the variation in the dependent variable is explained by the corresponding linear regression model.

### How do you calculate the coefficient of determination calculator given r

That is a simple task: if you have or are provided with the correlation coefficient \(r\), all you have to do is to square that number, this to compute \(r^2\), to get the coefficient of determination.

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