Correlation and Strength of a Linear Fit
Concept

Correlation Coefficient

The correlation coefficient, usually denoted by measures the direction and strength of a linear relationship between two variables. It can take on values between and Values near mean that the correlation is strong and negative, while values close to are strong and positive. Values close to represent a weak or very weak correlation, but represents no correlation.
r=1: perfect positive correlation; r in [0.75,1): strong positive correlation; r in [0.3,0.75): moderate positive correlation; r in [0.15,0.3): weak positive correlation; r in [0,0.15):no correlation; equivalently for the negative values
When there is a linear model that describes the relationship between two variables well, the correlation coefficient indicates how close the points are to the line of best fit. The closer the value is to or the closer the points to the line of best fit.
Group of points moving as the correlation coefficient changes
Keep in mind that the correlation coefficient is useful only when a linear model describes the data well. In addition to understanding the meaning of the correlation coefficient, while a graphing calculator is able to find the line of best fit, it is beneficial to learn how to calculate it by hand. Consider the following formula.

Extra

Formula for Finding the Pearson Correlation Coefficient
Given a data set with points the Pearson correlation coefficient can be found by dividing the covariance of and by the product of their standard deviations.
Alternatively, the formula can be rewritten as follows.
Formula for finding the Pearson correlation coefficient

Although there are different types of correlation coefficients, the most commonly used is the Pearson correlation coefficient.

Exercises