# Coefficient Of Determination Formula

## Coefficient of Determination Formula

R2 or r2 represents the Coefficient of Determination Formula, also known as the r-squared formula. This number indicates the variance in the dependent variable that can be predicted from the independent variable. Future outcomes and predictions can be made using this statistical model. The Coefficient of Determination Formula can also be viewed as a test of the hypothesis. In addition, it aids in determining the linear relationship between the dependent and independent variables. The Coefficient of Determination Formula has been explained in greater detail in the following section.

## What is Coefficient of Determination Formula?

In the Coefficient of Determination Formula, R 2 is calculated to analyse how differences in one variable can be explained by differences in another. We calculate the square of the coefficient of correlation, R, using the coefficient of correlation formula.

### Examples Using Coefficient of Determination

According to statistics, the Coefficient of Determination Formula (denoted R 2 or r 2) is the proportion of variation in the dependent variable that is predictable from the independent variables.

The statistic is used in statistical models to predict future outcomes or test hypotheses based on other relevant information. Based on the proportion of variation explained by the model, the Coefficient of Determination Formula determines how well-observed outcomes are replicated by the model.

It is only sometimes possible to define the Coefficient of Determination Formula in the same way, according to several definitions. The use of r 2 instead of R 2 is one such example of simple linear regression. A sample correlation coefficient (i.e., r) between observed outcomes and observed predictor values is simply r 2 when only an intercept is included. If additional regressors are included, R 2 equals the square of the multiple correlation coefficient. In both cases, the Coefficient of Determination Formula is normally between 0 and 1.

It is possible for the Coefficient of Determination Formula to yield negative values in some cases. The problem may arise when the predictions compared to the outcomes were not derived from a model-fitting procedure. Even when a model-fitting procedure has been used, R 2 may still be negative, for example, when linear regression is conducted without an intercept, or when a non-linear function is used. Based on this particular criterion, the mean of the data provides a better fit to the outcomes than the fitted function values.

The Coefficient of Determination Formula is more (intuitively) informative in regression analysis evaluation than MAE, MAPE, MSE, and RMSE since the former can be expressed as a percentage, while the latter have arbitrary ranges. On the test datasets in the article, it also proved more robust to poor fits than SMAPE.

Goodness-of-fit should not be based on the R 2 of linear regression (i.e., Y obs = m · Y pred + b). In order to evaluate goodness-of-fit, only one linear correlation should be taken into account: Y obs = 1· Y pred + 0 (i.e., the 1:1 line).

A model’s goodness of fit is measured by R 2. A regression prediction’s R 2 Coefficient of Determination Formula is a statistical measure of how well it approximates the real data points. Data fitted perfectly by a regression prediction with an R2 of 1.

A value of R 2 outside the range 0 to 1 indicates that the model fits the data worse than the worst possible least-square predictor (equivalent to a horizontal hyperplane at the same height as the mean of the observed data). By choosing the wrong model or applying nonsensical constraints, this occurs. R 2 can be less than zero when using equation 1 of Kvlseth (the equation used most often). It is possible to have R 2 greater than 1 if equation 2 of Kvlseth is used.

Whenever R 2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SS res. This model’s R 2 increases monotonically with the number of variables included (it will never decrease as the number of variables increases). It illustrates a drawback of one possible use of R 2, in which one might keep adding variables (kitchen sink regression) to increase the R 2 value.