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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 1 7 1265.531011 12.5101151923 1.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.

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