This scatterplot below is representing the relationship between the free throw p

Question

This scatterplot below is representing the relationship between the free throw percentage and the number of rebounds in a season, for players of the National Basketball Association. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0 200 400 1200 600 Rebounds 800 1000 a) What can we say about a player represented in the top left of the scatterplot and in the bottom right of the scatterplot? b) Is the direction of association appearing to be more positive or negative? What does that mean in this context? c) Which value is the best guess at the correlation (circle one) 20 -2, 1, -0.9, -0.4, 0, 0.4, 0.9,1, 2, 20 d) Which of the values listed in part (e) are impossible values for a correlation? Explain why?

Explanation / Answer

Answer to the question is as follows:

a. Top left is not so scattered, it is dense, meaning points should be arond the line of best fit

The bottom right points are scattered, meaning they are away from the best line of fit. It also means higher variance for higher variable values

b. The direction of association is clearly negative.

In this context it means that if Rebounds increases then FTPct decreases by certain marginal quanitity

c. Correlation' best guess is a negative value between -1 and 1 ( including). Other values

are either invalid values of correlation or they aren't negative

So, the slope doesn't seem to be Y=-X or near to it and hence, -1, -9 are rules out

Answer is -0.4

d. -20, -2, 2, and 20 are impossible values as correlation cannot take values beyond a magnitude of 1

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