Correlation Coefficient

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Purpose

The correlation coefficient is used to estimate the intensity of the relationship between two random variables.



Anatomy

Correlation Coefficient

Reference: Juran's Quality Control Handbook

Terminology

A. Coefficient of Linear Correlation – It is an estimate of the intensity of the linear relation between Variable A and Variable B.

  • When "r" is close to +1, there is a strong positive relationship between the Variables, i.e. when Variable A increases, Variable B increases. When "r" is close to 0, there is very little or no relationship between the Variables.
  • When "r" is close to -1, there is a strong negative relationship between the Variables, i.e. when Variable A increases, Variable B decreases and vice versa.

B. The individual values of the independent variable.
C. The Mean value of the independent variable.
D. The individual values of the dependent variable.
E. The Mean value of the dependent variable.


Major Considerations

A large "r" (i.e. approaches +1 or –1) is an indication of strong relation between two variables, however, it does not necessarily imply that there is a cause and effect relation between them. It should also be noted that data has to be entered in ordered pairs.

Application Cookbook

1. Collect data samples

2. Enter the data corresponding to the variables into two separate columns in Minitab

3. Obtain the matrix using STAT>BASIC STATISTICS>CORRELATION

4. In the Variables field, select columns corresponding to the two variables. Order of the variables does not affect the result.

5. Do not select the box for Store Matrix as this feature is not activated for some Minitab releases.

6. Interpret the value of "r". A large value, i.e. close to +1 or –1 is indicative of strong positive and negative relations respectively.

7. There is no hard and fast rule on how large the coefficient should be. For many cases, value greater than +/- 0.8 is considered to be reasonable. It truly depends on the application and consequence of the interpretation.

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