Correlation

Quantitative assessment of the strength of the relationship between x & y.

It is the measure of the extent to which x & y are linearly related.

*It is strong if the points lie close to a straight lint and is weak if they are widely scattered about a line.

Correlation Coefficient (r)

It’s a number between -1 and 1.

The closer it is to the ends, the stronger the positive or negative relationship.

It gives the strength and direction.

Correlation (r)

0 1-1

Strong Positive

No Correlation

Strong Negative

www.whfreeman.com/tps4e

Let’s explore….

Pearson’s Correlation Coefficient

Think about z-scores of the x & y

Pearson’s Correlation Coefficient

Think about z-scores of the x & y

Pearson’s Correlation Coefficient

Think about z-scores of the x & y

Correlation Coefficient

r

Find the correlation coefficient.

x y

6 5

10 3

14 7

19 8

21 12

Find correlation coefficient.

x y

15 219

27 189

31 195

42 173

88 121

92 138

66 152

51 140

AP Exam Tip

If you are asked to interpret a correlation start by looking at a scatterplot of the data. Then be sure to address direction, form, strength, and outliers and put your answer in context.

It does not depend on the unit of measurement.

It doesn’t depend upon which of the 2 variables is “x”

It’s between -1 and 1 It equals -1 or 1 if all points lie on a straight

line It is strongly affected by a few outliers

Properties of “r”

Scatterplots show relationships – not cause and effect.

Try One! Create scatterplot

Find the correlation

Describe the association

Fat (g) Sodium

29 920

31 1150

34 1200

35 1095

39 1180

39 1120

43 1260

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