# Correlation Coefficient R

Tools

ANOVA

Models

Regression by Backwards Elimination

Data Transforms

Transformations used in Regression

This correlation coefficient calculation is a measure of how much linear relationship exists between the values for the two variables.

The correlation coefficient can range between +1 and -1.

Positive values indicate a relationship between X and Y variables so that as X increases so does Y.

Negative values mean the relationship between X and Y is such that as values for X increase, values for Y decrease.

A value near zero means that there is a random, nonlinear relationship between the two variables. Use the correlation coefficient calculation shown below.

where N is the total number of observations, and are the averages of x and y, respectively, and Ïƒx and Ïƒy are the sample sigma of the x and y values, respectively.

The square of the Correlation Coefficient R, referred to as the Coefficient of Determination (or sometimes just â€œR Squaredâ€), provides an estimate of the percentage of variation in the dependent variable accounted for by the regression function.

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