Statistics: Calculate a Pearson's r
posted by Joy Chapman .
In a study on caffeine and stress, college students indicated how many cups of coffee they drink per day and their stress level on a scale of 1 to 10. The data are provided in the following table.
Number of Cups of Coffee
3, 2, 4, 6, 5, 1, 7, 3, 2, 4
Stress Level
5, 3, 3, 9, 4, 2, 10, 5, 3, 8
Calculate a Pearson's r to determine the type and strength of the relationship between caffeine and stress level. How much of the variability in stress scores is accounted for by the number of cups of coffee consumed per day?

Once you determine the correlation coefficient from a Pearson's r, square the correlation coefficient to find the Coefficient of Determination. The Coefficient of Determination shows the strength of the relationship between two variables. The ratio of explained variance to total variance represents the proportion of variability that is shared by the two variables. The Coefficient of Determination can be used to examine the usefulness of a regression line because it looks at the strength of the linear relationship.
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