Let's look at some of the ways the coefficient of determination (or the correlation coefficient) could be misleading as a measure of “strength of correlation between X and Y.” (a) Show that r2 can be radically influenced by the number of observations, being relatively meaningless when n is small. Take an extreme case-suppose n = 2. (b) What does part (a) say about the coefficient of determination? (c) If you have a large number of observations and r2 is quite close to one, you can conclude that X and Y seem correlated. Then it's a question of seeing which variable is actually causing the other. Comment. (d) Plot a scatter diagram for the following data and compute r2. Then for each X, replace the Y's observed at that level of X by their averages and plot that scatter diagram. Then compute r2. Comment on the results.(e) Plot the scatter diagram for the data in part (d) where instead of the Y's, you record for each X the “proportion above two.” Calculate r2. Comment. (f) For the following data, sketch a scatter diagram and then calculate and interpret r2.
Let’s look at some of the ways the coefficient of determination (or the correlation coefficient)…
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