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# E let x represent the average number of putts and y

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(e) Let x represent the average number of putts and y represent the average number of strokes. Use the definition of the correlation coefficient above to determine the measurement units of the correlation coefficient r in terms of putts and strokes. x y I II III I II IV III IV

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Chance/Rossman, 2015 ISCAM III Investigation 5.7 360 (f) If the correlation coefficient between two variables equals zero, what do you think the scatterplot will look like? (g) Suppose we find the correlation coefficient of a variable with itself. Substitute x i in for y i (and so x for y and s x for s y ) in the above equation. Simplify. What is the correlation coefficient equal to? (h) Do you think the correlation coefficient will be a resistant measure of association? Explain. (i) The following scatterplots display 7 pairs of variables for these golfers. Rank these graphs in order from strongest negative correlation to strongest positive correlation. A: B: C: D:
Chance/Rossman, 2015 ISCAM III Investigation 5.7 361 E: F: G: (j) Use technology to determine the correlation coefficient for each of the above scatterplots x In R: > cor(x, y) x In Minitab: Choose Stat > Basic Statistics > Correlation and enter the pair of variables. You can unselect the “Show p - values” box for now. Alternatively, type MTB> corr cx cy. Record the values of these correlation coefficients below: Strongest negative birdie conversion and average putts Medium negative money and average score Weak negative money and average putts No association driving distance and average putts Weak positive money and driving distance Medium positive money and birdie average Strongest positive birdie average and birdie conversion (k) Based on these correlation coefficient values and/or the definition/formula, what do you think is the largest value that r can assume? What is the smallest value? [ Hint : It’s not zero.] Largest: Smallest: (l) If the association is negative, what values will r have? What if the association is positive? Strongest negative: Medium negative: Weak negative: No association: Weak positive Medium positive: Strongest positive:

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Chance/Rossman, 2015 ISCAM III Investigation 5.7 362 (m) What does a correlation coefficient equal to zero signify? (n) What does a correlation coefficient close to 1 or ± 1 signify? (o) Which has a stronger correlation coefficient with scoring average: driving distance or average putts? Does this support the cliché? Explain. Study Conclusions The correlation coefficient for scoring average and average putts indicates a moderately strong positive linear association ( r = 0.444) whereas the correlation coefficient for scoring average and driving indicates a weaker negative association ( r = ˗0 .265). This appears to support that putting performance is more strongly related to a PGA golfer’s overall scoring average than the golfer’s driving distance, as the cliché would suggest. We must keep in mind that these data are only for only the first 2.5 months of the season (when most golfers have played only around 6 8 events) and may not be representative of the scores and money earnings later in the year.
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