In such cases, the coefficient of determination ranges from 0 to 1.

In particular the value of the coefficient of determination 'shrinks'.

The fraction of variance explained is called the coefficient of determination.

In particular, the value of the coefficient of determination will shrink relative to the original training data.

What is the correlation if the coefficient of determination is .64?

The coefficient of determination R is a measure of the global fit of the model.

The reliability of the statistical estimates can be measured by a coefficient of determination, Rs.

R-squared is the coefficient of determination indicating goodness-of-fit of the regression.

The coefficient of determination (R (adjusted)) was used to measure the proportion of variation explained by individual factors.

The coefficient of determination generalizes the correlation coefficient for relationships beyond simple linear regression.

Examples are the coefficient of determination and Goodman and Kruskal's lambda.

Nagelkerke (1991) generalizes the definition of the coefficient of determination:

In regression, the R coefficient of determination is a statistical measure of how well the regression line approximates the real data points.

The paradox pertains to a possible paradoxical relationship between the magnitude of the r (i.e., coefficient of determination) effect size and its practical meaning.

The coefficient of determination for all data () , that is to be maximised under the conditions set by the significance tests, is found from:

This method is therefore most suitable when the model response is in fact linear; linearity can be confirmed, for instance, if the coefficient of determination is large.

Step 3: The test statistic is the result of the coefficient of determination of the auxiliary regression in Step 2 and sample size with:

According to Everitt (2002, p. 78), this usage is specifically the definition of the term "coefficient of determination": the square of the correlation between two (general) variables.

In statistics, the coefficient of determination, denoted R and pronounced R squared, is the proportion of total variation of outcomes explained by a statistical model.

One important way that correlation arises in regression analysis is through the 'coefficient of determination', which is used to explain how well a regression model fits a particular data set.

The simplest version of the test statistic from this auxiliary regression is TR, where T is the sample size and R is the coefficient of determination.

For the case of a linear model with a single independent variable, the coefficient of determination (R squared) is the square of r, Pearson's product-moment coefficient .

"Similarity of EEG spatial configuration of each prototype map with each of the 10 maps is computed using the coefficient of determination to omit the maps' polarities.

Regression analysis quantifies a relationship between a predictor variable and a criterion variable by the coefficient of correlation r, coefficient of determination r2, and the standard regression coefficient β.

Some authors have suggested a formal detection-tolerance or the variance inflation factor (VIF) for multicollinearity:where is the coefficient of determination of a regression of explanator j on all the other explanators.