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 Wins 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.

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

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? 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? 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 STAT  CALC  8: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 r 2. (More on r 2 later.)

On AP Exam 1. Interpret the slope  ERA is the number of runs given up per game by the pitcher  For 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

AP Statistics, Section 3.2, Part 1 21 Assignment Exercises 3.19, 3.20, 3.27, 3.31, 3.36, 3.37, The Practice of Statistics.