Definition:
" A measure that determine the degree to which two variables movments are associated"
Explanation:
The quantity r, called the linear correlation coefficient, measures the strength and
the direction of a linear relationship between two variables. The linear correlation
coefficient is sometimes referred to as the Pearson product moment correlation coefficient in
honor of its developer Karl Pearson.
The mathematical formula for computing r is:
 |
| r Farmula |
where n is the number of pairs of data.
(Aren't you glad you have a graphing calculator that computes this formula?)
- The value of r is such that -1 <r <+1. The + and - signs are used for positive linear correlations and negative linear correlations, respectively.
- Positive correlation: If x and y have a strong positive linear correlation, r is close to +1. An r value of exactly +1 indicates a perfect positive fit. Positive values indicate a relationship between x and y variables such that as values for x increases,values for y also increase.
- Negative correlation: If x and y have a strong negative linear correlation, r is close to -1. An r value of exactly -1 indicates a perfect negative fit. Negative values indicate a relationship between x and y such that as values for x increase, values for y decrease.
- No correlation: If there is no linear correlation or a weak linear correlation, r is close to 0. A value near zero means that there is a random, nonlinear relationship between the two variables
- Note that r is a dimensionless quantity; that is, it does not depend on the units employed.
- A perfect correlation of ± 1 occurs only when the data points all lie exactly on a straight line. If r = +1, the slope of this line is positive. If r = -1, the slope of this line is negative.
- A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak. These values can vary based upon the
- "Type" of data being examined. A study utilizing scientific data may require a stronger correlation than a study using social science data.
