Section 3.2 Part 1 Statistics

Correlation r The correlation measures the direction and the strength of the linear relationship between two quantitative variables.  Correlation is usually written as r. AP Statistics, Section 3.2, Part 1 2

3 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?

AP Statistics, Section 3.2, Part 1 4 Calculating Correlation The calculation of correlation is based on mean and standard deviation. Remember that both mean and standard deviation are not resistant measures.

AP Statistics, Section 3.2, Part 1 5 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 6 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.

Computing Correlation AP Statistics, Section 3.2, Part Calculate the mean for both sets of data 2. Find the standard deviation for both sets of data To use your calculator: 1.Enter data into L1 and L2 2.Run a 2-Var Stat Now calculate the correlation.

AP Statistics, Section 3.2, Part 1 8

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

AP Statistics, Section 3.2, Part 1 11 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.)

AP Statistics, Section 3.2, Part 1 12 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 13 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 14 Interpreting r If the -1<r<-.75, the association is called “strong negative” If the -.75<r<-.25, the association is called “moderate negative” If the -.25<r<0, the association is called “weak negative” And r=0, no correlation!

AP Statistics, Section 3.2, Part 1 15 Interpreting r If the 0<r<.25, the association is called “weak positive” If the.25<r<.75, the association is called “moderate positive” If the.75<r<1, the association is called “strong positive”

AP Statistics, Section 3.2, Part 1 16 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 17

AP Statistics, Section 3.2, Part 1 18 Assignment Exercises 3.19, 3.20, 3.27, 3.31, 3.36, 3.37, The Practice of Statistics.