Transcript AP Statistics

Special Topics
Correlation
Correlation
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Correlation is a numerical summary. It measures the
strength and direction of a linear relationship between
two variables (x,y) – denoted as “r”
Formula:
 xi  x   yi  y 
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r

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 

n  1  sx   sy 
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The correlation “r” is the average of the products of the
standardized x’s and standardized y’s.
Facts About Correlation
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Standardizing removes the units and allows us to
calculate “r” while combining unrelated
variables.
It does not matter which variable you call x or y
– r calculates the same either way.
Both variables must be quantitative to calculate
correlation.
How to Interpret Correlation
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A positive “r” indicates a positive association
between variables.
A negative “r” indicates a negative association.
Correlation falls between -1 and 1.
Correlation values near zero indicate a very weak
linear relationship.
Because “r” uses a standardized values of the
observations, “r” does not change when we
change units.
How to Interpret Correlation
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Correlation only measures the strength of a
linear relationship. It does not describe curved
relationships.
Like the mean and standard deviation,
correlation is strongly affected by outliers (it is
non-resistant).
“r” is not a complete description of two-variable
data.
Connecting “r” to Scatterplots
Important Note!
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Correlation does not exist on a linear scale.
Thus, a correlation of .8 is not twice the linear
strength of a correlation of .4!
You can’t use proportional reasoning with this
numerical summary.
A moderately strong to strong correlation begins
at r = .8.
Classroom Practice
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Enter “Correct Calories” into L1 and “Guessed
Calories” into L2.
Classroom Practice
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Run a 2-VarStat to get the mean and standard
deviation of the variables.
Plot the scatterplot on calculator.
*Turn diagnostics on.
Run a LinReg to see diagnostics.
Remove 394 and 419 (outliers) and run the
diagnostics again.
What did you notice about the r-value? Do
outliers affect the correlation?
Homework
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Worksheet