Special Topics Correlation Correlation n Correlation is a

Correlation n Correlation is a numerical summary. It measures the strength and direction of

Facts About Correlation Standardizing removes the units and allows us to calculate “r” while

How to Interpret Correlation A positive “r” indicates a positive association between variables. n

How to Interpret Correlation only measures the strength of a linear relationship. It does

Important Note! Correlation does not exist on a linear scale. n Thus, a correlation

Classroom Practice n Enter “Correct Calories” into L 1 and “Guessed Calories” into L

Classroom Practice Run a 2 -Var. Stat to get the mean and standard deviation

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Special Topics Correlation

Correlation n Correlation is a numerical summary. It measures the strength and direction of a linear relationship between two variables (x, y) – denoted as “r” Formula: The correlation “r” is the average of the products of the standardized x’s and standardized y’s.

Facts About Correlation Standardizing removes the units and allows us to calculate “r” while combining unrelated variables. n It does not matter which variable you call x or y – r calculates the same either way. n Both variables must be quantitative to calculate correlation. n

How to Interpret Correlation A positive “r” indicates a positive association between variables. n A negative “r” indicates a negative association. n Correlation falls between -1 and 1. n Correlation values near zero indicate a very weak linear relationship. n Because “r” uses a standardized values of the observations, “r” does not change when we change units. n

How to Interpret Correlation only measures the strength of a linear relationship. It does not describe curved relationships. n Like the mean and standard deviation, correlation is strongly affected by outliers (it is non-resistant). n “r” is not a complete description of twovariable data. n

Connecting “r” to Scatterplots

Important Note! Correlation does not exist on a linear scale. n Thus, a correlation of. 8 is not twice the linear strength of a correlation of. 4! n You can’t use proportional reasoning with this numerical summary. n A moderately strong to strong correlation begins at r =. 8. n

Classroom Practice n Enter “Correct Calories” into L 1 and “Guessed Calories” into L 2.

Classroom Practice Run a 2 -Var. Stat to get the mean and standard deviation of the variables. n Plot the scatterplot on calculator. n *Turn diagnostics on. n Run a Lin. Reg to see diagnostics. n Remove 394 and 419 (outliers) and run the diagnostics again. n What did you notice about the r-value? Do outliers affect the correlation? n

Homework n Worksheet