Correlation
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Correlation. Correlation Coefficient (r). 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.

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Correlation

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Correlation

Correlation


Correlation coefficient r

Correlation Coefficient (r)

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 r

Correlation (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.

Strong Negative

No Correlation

Strong Positive

-1

1

0


Let s explore

Let’s explore….

  • www.whfreeman.com/tps4e


Pearson s correlation coefficient

Pearson’s Correlation Coefficient

Think about z-scores of the x & y


Pearson s correlation coefficient1

Pearson’s Correlation Coefficient

Think about z-scores of the x & y


Pearson s correlation coefficient2

Pearson’s Correlation Coefficient

Think about z-scores of the x & y


Correlation coefficient

Correlation Coefficient

r


Find the correlation coefficient

Find the correlation coefficient.


Find correlation coefficient

Find correlation coefficient.


Ap exam tip

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.


Properties of r

Properties of “r”

  • 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


Correlation

Scatterplots show relationships – not cause and effect.


Try one

Try One!

  • Create scatterplot

  • Find the correlation

  • Describe the association


Homework

Homework

  • Page 160 (14-18, 21, 26)


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