AP Statistics Section 3.1BCorrelation

A scatterplot displays the direction, form and the strength of the

relationship between two quantitative variables.

Linear relations are particularly important because a straight line is

a simple pattern that is quite common.

We say a linear relation is strong if

and weak if

the points lie close to a straight line

they are widely scattered about the line.

Relying on our eyes to try to judge the strength of a linear relationship

is very subjective. We will be determining a numerical summary

called the __________.correlation

The correlation ( r ) measures the direction and the strength of the linear relationship between two

quantitative variables.

The formula for correlation of variables x and y for n individuals is:

Y

in

i X

i

s

YY

s

XX

nr

11

1

etc.

,individual second theY and

X ,individualfirst for the

valuesare Y and X where

2

2

ii

TI 83/84: Put data into 2 lists, say STAT CALC 8:LinReg(a+bx) ENTER

Note: If r does not appear,2nd 0 (Catalog) Scroll down to “Diagnostic On”Press ENTER twice

21,LL21 and LL

Find r for the data on sparrowhawk colonies from section 3.1 A

7485.r

Important facts to remember when interpreting correlation:

1. Correlation makes no distinction between __________ and

________ variables.explanatory

response

2. r does not change when we change the unit of measurement

of x or y or both.

3. Positive r indicates a ________ association between the variables

and negative r indicates a ________ association.

positive

negative

4. The correlation r is always between ___ and ___. Values of r

near 0 indicate a very _____ relationship.

1 1weak

Example 1: Match the scatterplots below with their corresponding

correlation r

6 4 2 1 3 5

Cautions to keep in mind:

1. Correlation requires both variables be quantitative.

2. Correlation does not describe curved relationships between

variables, no matter how strong.

3. Like the mean and standard deviation, the correlation is NOT

resistant to outliers.

What effect does adding an outlier have on r and why?

outlier. he without twould

they as linestraight a toclose as lienot do points the

outlier with thebecause zero, closer to move r will

4. Correlation is not a complete summary of two-variable data.

Ideally , give the mean and standard deviations of both x and y

along with the correlation.