"Data, data everywhere, but not a thought to think."" -- Computer scientist Jesse Shera

3.2 CORRELATION (Pages 129 - 135)

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), x is 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 observations (x- x)/sx and (y- y)/sy, and that these standardized values have no units.

Extremely important for success of the Advanced Placement Statistics Examination:
If you are given a numerical data set, always (I repeat, always) display the shape of the distribution.

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.


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