Every April, The Masters—one of the most prestigious golf tournaments on the PGA golf tour—is played in Augusta, Georgia. In 2019, 61 players received prize money. The 2019 winner, Tiger Woods, earned a prize of $2,070,000. Dustin Johnson, Xander Schauffele, and Brooks Koepka tied for second place, each earning $858,667. Four amateur players finished “in the money” but they could not accept the prize money. They are not included in the data. The data are briefly summarized here. Each player has three corresponding variables: finishing position, score, and prize (in dollars). We want to study the relationship between score and prize.

a. Using Score as the independent variable and Prize as the dependent variable, develop a scatter diagram. Does the relationship appear to be linear? Does it seem reasonable that as Score increases the Prize decreases?

b. What percentage of the variation in the dependent variable, Prize, is accounted for by the independent variable, Score?

c. Calculate a new variable, Log-Prize, computing the log to the base 10 of Prize. Draw a scatter diagram with Log-Prize as the dependent variable and Score as the independent variable.

d. Develop a regression equation and compute the coefficient of determination using Log-Prize as the dependent variable.

e. Compare the coefficient of determination in parts (b) and (d). What do you conclude?

f. Write out the regression equation developed in part (d). If a player shot an even par score of 288 for the four rounds, how much would you expect that player to earn?

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Position Name Score Prize 1 Tiger Woods 275 $2,070,000 $ 858,667 $ 858,667 $ 858,667 $ 403,938 $ 403,938 $ 403,938 $ 403,938 Tied 2 Dustin Johnson 276 Tied 2 Xander Schauffele 276 Tied 2 Brooks Koepka 276 Tied 5 277 Jason Day Webb Simpson Tied 5 277 Tony Finau Francesco Molinari Tied 5 277 Tied 5 277 $ 26,565 $ 26,565 $ 25,185 $ 25,185 $ 24,150 Tied 56 Tyrrell Hatton 292 Tied 56 Billy Horschel 292 Tied 58 Branden Grace 293 Tied 58 Zach Johnson 293 61 Satoshi Kodaira 294 Tied 62 J.B. Holmes 296 22,425 $ 22,425 $ 22,425 $ 22,425 Tied 62 Bernhard Langer 296 Tied 62 Emiliano Grillo 296 Tied 62 Alexander Noren 296