Correlation

Correlation is a measure of strength of the relationship of input (x) and output (y) of a process. An "r" value is used to measure the correlation and it will always range from -1.0 to +1.0.

Correlation is the degree or extent of the relationship between two variables.

If the value of one variable increases when the value of the other increases, they are said to be positively correlated.

If the value of one variable decreases when the value of the other decreases, they are said to be negatively correlated. The degree of linear association between two variables is quantified by the coefficient of correlation.

This value is known as the:

Pearson Product Moment Correlation, also referred to as the Coefficient of Correlation.

It represents a unitless translation of covariance, meaning the closer the value is to +1, the closer the relationship is between the x and y random variables.

As the value of R approaches zero from either side, the correlation is weaker. That is the input, x, has a lower correlation on the output, y.

This is normally shown by a x-y plot referred to as a Scatter Graph. This graph shows all the data points where the input, x, is varied systematically and the output, or the effect, of y is measured.

"X" is considered the independent variable or predictor variable.

"Y" is the dependent variable or predicted variable.

A r-value of +1.0 indicates a perfect and strong POSITIVE correlation.

A r-value of -1.0 indicates a perfect and strong NEGATIVE correlation.

This value squared, r-squared, is the Coefficient of Determination used in regression analysis.

What is the difference between the Coefficient of Correlation (COC) and Coefficient of Determination (COD)?

The COD ranges from 0-1 (0%-100%) and is the proportion of variability of the dependent variable (Y) accounted for or explained by the independent variable (x) equal to the coefficient of correlation value squared. In other words, it is the percentage of variation in Y explained by the linear relationship with X.

The COC is a value from -1 to +1 that describes the linear correlation of the dependent and independent variable. A value near zero indicates no linear relationship.

The sign is necessary to see if relationship is positive or negative so solving for COR by taking the square root of COD may not give the correct correlation since the sign can be positive or negative.