In Statistical Analysis, the coefficient of determination method is used to predict and explain the future outcomes of a model. This method is also known as R squared. This method also acts like a guideline which helps in measuring the modelâ€™s accuracy. In this article, let us discuss the definition, formula, and properties of the coefficient of determination in detail.

## Coefficient of Determination Definition

The **coefficient of determination** or R squared method is the proportion of the variance in the dependent variable that is predicted from the independent variable. It indicates the level of variation in the given data set.

- The coefficient of determination is the square of the correlation(r), thus it ranges from 0 to 1.
- With linear regression, the correlation of determination is equal to the square of the correlation between the x and y variables.
- If R
^{2}is equal to 0, then the dependent variable should not be predicted from the independent variable. - IfÂ R
^{2}is equal to 1, then the dependent variable should be predicted from the independent variable without any error. - IfÂ R
^{2}is between 0 and 1, then it indicates the extent that the dependent variable can be predictable. IfÂ R^{2Â }of 0.10 means, it is 10 per cent of the variance in y variable is predicted from the x variable. If 0.20 means, it is 20 per cent of the variance is y variable is predicted from the x variable, and so on.

The value of R^{2} shows whether the model would be a good fit for the given data set. On the context of analysis, for any given per cent of the variation, it(good fit) would be different. For instance, in a few fields like rocket science, R^{2} is expected to be nearer to 100 %. But R^{2} = 0(minimum theoretical value), which might not be true as R^{2 } is always greater than 0( by Linear Regression).

The value of R^{2} increases after adding a new variable predictor. Note that it might not be associated with the result or outcome. The R^{2 } which was adjusted will include the same information as the original one. The number of predictor variables in the model gets penalized. When in a multiple linear regression model, new predictors are added, it would increase R^{2}. Only an increase in R^{2} which is greater than the expected(chance alone), will increase the adjusted R^{2}.

** Try Out**: Coefficient of Determination Calculator

Following is the Regression line equation

**pâ€™ = aq + r**

Where ‘p’ is the predicted function value of q. So, the method of checking how good the least-squares equation pÌ‚ = aq + r will make a prediction of how p will be made.

## Coefficient of Determination Formula

### Properties of Coefficient of Determination

- It helps to get the ratio of how a variable which can be predicted from the other one, varies.
- If we want to check how clear it is to make predictions from the data given, we can determine the same by this measurement.
- It helps to find Explained variation / Total Variation
- It also lets us know the strength of the association(linear) between the variables.
- If the value of r
^{2}gets close to 1, The values of y become close to the regression line and similarly if it goes close to 0, the values get away from the regression line. - It helps in determining the strength of association between different variables.

### Steps to Find the Coefficient of Determination

- Find r, Correlation Coefficient
- Square â€˜râ€™.
- Change r to percentage.