3.2 Correlation

Correlation Measures direction and strength of the linear relationship in the scatterplot. Measures direction and strength of the linear relationship in the scatterplot. Correlation coefficient is r. Correlation coefficient is r. In words, r is the sum of the product of the standardized values of the observations divided by the degrees of freedom.

Calculating the Correlation Coefficient Exercise 3.24 Find the correlation coefficient, r, step – by – step. Femur: Humerus: Can’t we do this on the calculator?!

Facts about correlation coefficient No distinction between explanatory and response variables. No distinction between explanatory and response variables. Both variables must be quantitative. Both variables must be quantitative. r has no unit of measure. Changing units will not change the value for r. r has no unit of measure. Changing units will not change the value for r. +r = positive linear association; -r = negative linear association. +r = positive linear association; -r = negative linear association. -1 < r < 1. The closer the values are to -1 or 1 indicate how close the points lie to a straight line. -1 < r < 1. The closer the values are to -1 or 1 indicate how close the points lie to a straight line.

Correlation facts continued … r = -1 or r = 1 shows a perfect linear relationship. r = -1 or r = 1 shows a perfect linear relationship. Correlation measures the strength of linear relationships between two variables. For curved relationships we will use another determiner. Correlation measures the strength of linear relationships between two variables. For curved relationships we will use another determiner. The correlation is NOT RESISTANT. The correlation is NOT RESISTANT. Correlation is not an end all solve all. We use it in part to help describe the data along with the means and standard deviations of two variables. Correlation is not an end all solve all. We use it in part to help describe the data along with the means and standard deviations of two variables.

r: Paper/Pencil vs. Calculator almighty! At this point, we should have an appreciation of what our handy-dandy calculator can do … At this point, we should have an appreciation of what our handy-dandy calculator can do … The most efficient way to obtain the correlation coefficient, r, is to ensure the calculator’s diagnostics is turned on and run a linear regression on the scatterplot. The most efficient way to obtain the correlation coefficient, r, is to ensure the calculator’s diagnostics is turned on and run a linear regression on the scatterplot. Complete exercises 3.26 – 3.28, 3.32, 3.35 – 3.37 (Quiz 3.2: Monday, 10/4). Complete exercises 3.26 – 3.28, 3.32, 3.35 – 3.37 (Quiz 3.2: Monday, 10/4).

Correlation Activity UNIVERSITY OF ILLINOIS AT URBANA- CHAMPAIGN (UIUC) UNIVERSITY OF ILLINOIS AT URBANA- CHAMPAIGN (UIUC)