Reminder

Remember that both mean and standard deviation are not resistant measures so you want to take that into account when calculating the correlation r.

Review practice quiz for 3.2 quiz

AP Statistics, Section 3.2, Part 1 1

Warm Up Select two quantitative variables for the class and

create a scatter plot to see if there is an association.

OR Ladies

Collect the height in inches and shoes size from the ladies and create a scatter plot.

Gentlemen Collect the height in inches and shoes size from the

gentlemen and create a scatter plot.

Section 3.2

AP Statistics

AP Statistics, Section 3.2, Part 1 4

Correlation

Is there a “correlation” between a baseball team’s “earned run average” and the number of wins?

Is the association strong or weak?

Is the association positively associated or negatively associated?

2003 ERA vs Wins

ERA Quality of pitching

AP Statistics, Section 3.2, Part 1 5

Calculating Correlation

The calculation of correlation is based on mean and standard deviation.

Remember that both mean and standard deviation are not resistant measures.

1

1i i

x y

x x y yrn s s

Reminder

Remember that both mean and standard deviation are not resistant measures so you want to take that into account when calculating the correlation r.

AP Statistics, Section 3.2, Part 1 6

AP Statistics, Section 3.2, Part 1 7

Calculating Correlation

What does the contents of the parenthesis look like?

What happens when the values are both from the lower half of the population? From the upper half?

1

1i i

x y

x x y yrn s s

Both z-values are negative. Their product

is positive.

Both z-values are positive. Their product

is positive.

The formula for calculating

z-values.

AP Statistics, Section 3.2, Part 1 8

Calculating Correlation

What happens when one value is from the lower half of the population but other value is from the upper half?

1

1i i

x y

x x y yrn s s

One z-value is positive and the other is

negative. Their product is negative.

AP Statistics, Section 3.2, Part 1 9

Using the TI-83 to calculate r

You must have “DiagnosticOn” from the “Catalog”

AP Statistics, Section 3.2, Part 1 10

Using the TI-83 to calculate r

Run LinReg(ax+b) with the explantory variable as the first list, and the response variable as the second list

Example

shoe size vs. height

STATCALC8:LinReg(a+bx)L1,L2

AP Statistics, Section 3.2, Part 1 11

AP Statistics, Section 3.2, Part 1 12

Using the TI-83 to calculate r

The results are the slope and vertical intercept of the regression equation (more on that later) and values of r and r2. (More on r2 later.)

On AP Exam

1. Interpret the slopeERA is the number of runs given up per

game by the pitcherFor every run my team gives up, the team

losses 15games

2. Interpret the intercept

3. Interpret r

AP Statistics, Section 3.2, Part 1 13

AP Statistics, Section 3.2, Part 1 14

Facts about correlation

Both variables need to be quantitative Because the data values are standardized,

it does not matter what units the variables are in

The value of r is unitless.

AP Statistics, Section 3.2, Part 1 15

Facts about correlation

The value of r will always be between -1 and 1. Values closer to -1 reflect strong negative linear

association. Values closer to +1 reflect strong positive linear

association. Values close to 0 reflect no linear association. Correlation does not measure the strength of

non-linear relationships

AP Statistics, Section 3.2, Part 1 16

Interpreting r

If the -1<r<-.75, the association is called “strong negative” linear association

If the -.75<r<-.25, the association is called “moderate negative” linear association

If the -.25<r<0, the association is called “weak negative” linear association

And r=0, no correlation!

AP Statistics, Section 3.2, Part 1 17

Interpreting r

If the 0<r<.25, the association is called “weak positive” linear association

If the .25<r<.75, the association is called “moderate positive” linear association

If the .75<r<1, the association is called “strong positive” linear association

AP Statistics, Section 3.2, Part 1 18

Facts about correlation

Correlation is blind to the relationship between explanatory and response variables.

Even though you may get a r value close to -1 or 1, you may not say that explanatory variable causes the response variable. We will talk about this in detail in the second semester.

AP Statistics, Section 3.2, Part 1 19

AP Statistics, Section 3.2, Part 1 20

Assignment

Exercises 3.25,3.26, 3.27,3.31,3.36,3.37 Chapter 3.2 practice quiz for quiz on