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Write a detailed note on Carl's Correlation Coefficient Algorithm.

Mumbai University > Computer Engineering > Sem 7 > Digital Signal Processing

Marks: 10 Marks

Year: May 2016

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Meaning of the Linear Correlation Coefficient.

Carl Pearson’s Correlation Coefficient is a linear correlation coefficient that returns a value of between -1 and +1. A -1 means there is a strong negative correlation and +1 means that there is a strong positive correlation. A 0 means that there is no correlation (this is also called zero order correlation).

This can initially be a little hard to wrap your head around (who likes to deal with negative numbers?).

The Political Science Department at Quinnipiac University posted this useful list of the meaning of Pearson’s Correlation coefficients.

They note that these are “crude estimates” for interpreting strengths of correlations using Pearson’s Correlation:

|r value| $ \ \ $| |-|-|
|+.70 or higher |Very strong positive relationship| |+.40 to +.69| Strong positive relationship| |+.30 to +.39| Moderate positive relationship| |+.20 to +.29| weak positive relationship| |+.01 to +.19| No or negligible relationship| |0 |No relationship [zero order correlation]| |-.01 to -.19| No or negligible relationship| |-20 to -.29 |weak negative relationship| |-.30 to -.39| Moderate negative relationship| |-.40 to -.69| Strong negative relationship| |-.70 or higher| Very strong negative relationship|

It may be helpful to see graphically what these correlations look like:

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Graphs showing a correlation of -1 (a negative correlation), 0 and +1 (a positive correlation)

The images show that a strong negative correlation means that the graph has a downward slope from left to right: as the x-values increase, the y-values get smaller. A strong positive correlation means that the graph has n upward slope from left to right: as the x-values increase, the y-values get larger.

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