OVERVIEW: The correlation coefficient, r, is a number that "measures the strength and direction of the linear relationship between two quantitative variables. r assumes values between -1 and 1, inclusive. The formula for r is shown below.
r = [1/(n-1)]sum[(x- x)(y- y)/(sxsy)]
where n is the number of pairs (x,y),
xis the mean of the x values, sx is the standard deviation of the x values, etc.
It should be noted that the formula for r uses standardized
x)/sx and (y-
y)/sy, and that these standardized values
have no units.
Using the TI-83, this can be done very easily with a histogram or a boxplot. For two variable data, a scatterplot should be shown.
Here are some Algebra II scholars illustrating the concept of correlation with their textbooks. What are they demonstrating?
(A) Correlation r close to 1.
(B) Correlation r close to -1.
(C) Correlation r close to 0.