# Coefficient of Determination Calculator

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Instructions:
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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

There are different ways to assess the strength of a linear association between two variables and this r-squared calculator is one tool that is used to assess that.

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.

Of course you cannot go by R or R^2 alone, you will need to make a scatterplot and see that the data visually follows a straight line pattern.

## Is this r squared calculator?

Yes it is. Indeed, coefficient of determination is another name for *R-Squared*, and they can be used interchangeably, especially
for the case of one dependent variable (Y) and one independent variable (X), this is, in the case of a
simple linear regression.

For the case of a multiple linear regression where this is more than one independent variable (or predictor),
things are a bit more subtle, as the R-squared coefficient is usually called
*coefficient of multiple determination*.

Also, in a multiple linear regression, the R-squared is known to "inflate" the percentage of variation explained, and we prefer to use the Adjusted R-Squared coefficient.

For example, you can use this adjusted R-Squared coefficient calculator to obtain it directly from sample data, or you can get this calculator to get it from R-squared, if you already have that. R-squared.

### 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?

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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.

### R-Squared calculator in Excel

Can you compute R-Squared in Excel? The answer is: of course! You need to compute the correlation coefficient \(r\) by using the command "=CORREL()", and then, using the cell that contains the correlation, say "A1", you create a cell with the formula "=A1^2" to get r squared

### R calculator

Are the r calculator and the r-squared calculator related? Usually they are. Most r squared calculators first compute the correlation coefficient and then they square it to get r squared.

You can use this calculator to calculate r directly using the provided sample data.