AP Statistics Section 3.1B Correlation

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: Put data into 2 lists STAT CALC 8:LinReg(a+bx) *If r does not appear: 2nd 0 (Catalog) Scroll to “Diagnostic On” Press ENTER twice

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

Important facts to remember when interpreting correlation: 1 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 ___ 4. The correlation r is always between ___ and ___. Values of r near 0 indicate a very _____ relationship. weak

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.

4. Correlation is not a complete summary of two-variable data 4. Correlation is not a complete summary of two-variable data. Give the mean and standard deviations of both x and y along with the correlation.