Correlations

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The Basics

Correlation coefficient - the correlation coefficient shows the strength of the relationship between two variables; attempts to find a line of best fit through the data of 2 variables; denoted by r; r is calculated by a formula and the resulting r from the calculation stands for how far the data points are from this line of best fit; can range from a value of -1 to +1; a +1 denotes a perfect positive relationship, that is, when one variable goes up the other goes up and vice versa; -1 denotes a perfectly negative relationship, that is, when one variable goes up, the other goes down; 0 is undefined and indicates no correlation between the two variables

Computing r

There are several formulas to calculate Pearson's r, including:



When computing r, the variables must be 2 quantitative variables as the interval or ratio level.

Interpreting r

There are guidelines to interpreting r positive or negative .1-.3 equals to a small strength of association; positive or negative .3-.5 is a medium association; positive or negative .5-1.0 is a large association.

r squared

A r score of .8 does not equate to explaining 80% of the variance between the two variables, it actually accounts for 64% of the variance and we know this due to r squared.

r squared ranges from 0 to 1 (or 0% to 100%) and tells you the proportion of the total variance that is "explained" by your linear regression model.

.8 * .8 = .64 or 64%

The remained, 36%, is the amount of the unexplained variance.

The total variance is the sum of the explained variance and the unexplained variance.

More Information

13 Ways to look at the correlation coefficient: http://www.stat.berkeley.edu/~rabbee/correlation.pdf

Understanding the Correlation Coefficient https://www.hawaii.edu/powerkills/UC.HTM#S4.3