Answer Happy

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4. Use the data found in sheet 4 of Excel entitled "Question 4". Every April, The Masters - one of the most prestigious golf tournaments on the PGA Tour - is played in Augusta, GA. In 2019, 61 players received prize money. The 2019 winner, Tiger Woods, earned a prize of $2.07 million, while Dustin Johnson, Xander Schauffele, and Brooks Koepka shared second place each earning $858,667. Additionally, four amateur players finished in the money", however we're unable to accept due to their amateur status. They are excluded from the data. The dataset in "Question 4" includes variables on finishing position, score, and prize (in $). We are interested in studying 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 your score increases the prize money decreases? (HINT: In golf, a lower score indicates that you are doing better. The higher the score, the more strokes it took to complete the course.) 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), using the Excel command ( =log10( ... )), which is the log to the base of 10 of Prize. What is the mean of this variable? d. Develop a regression equation and compute the Coefficient of Determination ("R- squared") using log(Prize) as the dependent variable, instead of Prize. e. Compare the R-squared in parts (b) and (d). What do you conclude?
SUMMARY OUTPUT Regression Statistics Multiple R 0.627445 R Square 0.393688 Adjusted R Squan 0.383411 Standard Error 245999.5 Observations 61 ANOVA Regression Residual Total d SS MS 1 232E+12 2 32L+12 38.30957 59 3.57E-12 6.05E-10 60 5.89€ 12 Intercept Score Coefficient anderd Er Stat p.value 10096794 1601753 6.303592 403-08 -34809356219516159426 26.08 c mean of fogprije 4.959576 d) SUMMARY OUTPUT Place Name 1 Tiger Woods Tied 2 Dustin Johnson Tied 2 Xander Schauffele Tied 2 Brooks Koepka Tied 5 Jason Day Tied 5 Webb Simpson Tied 5 Tony Finau Tied 5 Francesco Molinari Tied 9 Jon Rahm Tied 9 Patrick Cantay Tied 9 Rickie Fowler Tied 12 Bubba Watson Tied 12 Justin Thomas Tied 12 Justin Harding Tied 12 Matt Kuchar Tied 12 lan Poulter 17 Aaron Wise Tied 18 Patton Kizzire Tied 18 Phil Mickelson Tied 18 Adam Scott Tied 21 Si Woo Kim Tied 21 Kyle Stanley Tied 21 Matthew Fitzpatrick Tied 21 Kevin Kiet Tied 21 Rory McIlroy Tied 21 Jordan Spieth Tied 21 Lucas Bjerregaard Tied 21 Thorbjorn Olesen Tied 29 Charley Hoffman Tied 29 Bryson DeChambeau Tied 29 Louis Oosthuizen Tied 32 Hideki Matsuyama Tied 32 Gary Woodland Tied 32 Charles Howell Tied 36 Kevin Tway Tied 36 Henrik Stenson Tied 36 Tommy Fleetwood Tied 36 Jimmy Walker Tied 36 Patrick Reed Tied 36 Rafael Cabrera Bello Tied 43 Keegan Bradley Tied 43 Keith Mitchell Tied 43 Haotong Tied 46 Corey Conners Tied 46 Kevin Na Tied 46 Andrew Landry Tied 49 Marc Leishman Tied 49 Kiradech Aphibarnrat Tied 51 Cameron Smith Tied 51 Eddie Pepperell Tied 51 Martin Kaymer Tied 51 Trevor Immelman Tied 56 Tyrrell Hatton Tied S6 Billy Horschel Tied 58 Branden Grace Tied 58 Zach Johnson 61 Satoshi Kodaira Tied 62 J.B. Holmes Tied 62 Bernhard Langer Tied 62 Emiliano Grillo Tied 62 Alexander Noren Regression Statistics Multiple F 0.951671 R Square 0905677 Adjusted 0.904079 Standard 0.148583 Observat 61 Score Prire Log Prize) 275 $2,070,000 6.31597 276 $858,667 5.933825 276 $858,667 5.933825 276 $858,667 5.933825 277 $403,938 5.606315 277 S403,938 5.606315 277 $403.938 5.606315 277 $403.938 5.606315 278 $310.500 5.492062 278 $310,500 5.492062 278 $310,500 5.492062 280 $225,400 5352954 280 $225,400 5352954 280 $225,400 5.352954 280 $225,400 5352954 280 $225,400 $ 352954 281 $184,000 5.264818 282 $161,900 5.209247 282 $161,900 5.209247 282 $161,900 5.209247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 S033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 284 $78,200 4.893207 284 $78,200 4893207 284 $78,200 4893207 285 $68,042 4832777 285 $68,042 4832777 285 $68,042 4832777 286 $55,488 4.744199 286 $55,488 4.744199 286 $55.488 4.744199 286 $55,488 4.744199 286 $55.488 4.744199 286 $55.488 4.744199 287 $43,700 4.6404481 287 $43,700 4.640481 287 $43,700 4.640481 288 $37.950 4579212 288 $37,950 4579212 288 $37950 4579212 289 $32,430 4510947 289 $32.430 4.510947 290 $28,693 4.457776 290 $28,693 4.457276 290 $28,693 4.457776 290 $28,693 4.457776 292 $26,565 4.42431 292 $26,565 4.42431 293 $25,185 4.401142 293 $25,185 4 401142 294 $24,150 4382917 296 $22.425 4350732 296 $22,425 4350732 296 $22.425 4.350732 296 $22,425 4350732 ANOVA Regressio Residual Total of 55 MS 1 12.50682 12.50682 59 1.302536 0.022077 60 13 80935 Coefficientandard Er stor Intercept 27.98197 0967453 28.92333 Score 0.0008 0.003397 23.8015
SUMMARY OUTPUT e) first r squared 0.394 r squared (logged) 0.90.6 f) logging the variable provides a better fit of the data Regression Statistics Multiple R 0.62745 R Square 0.39369 Adjusted R Squan 0.38341 Standard Error 246000 Observations 61 ANOVA F ignificance F 38.3096 6.3E-08 Regression Residual Total df 1 59 60 SS 2.3E+12 3.6E+12 5.9E+12 MS 2.3E+12 6.1E+10 Intercept Score Coefficient:andard Err Stat 1E+07 1601753 6.30359 -34809.3 5623.95 -6.18947 P-value Lower 95%Upper 95%ower 95.0/pper 95.0% 4E-08 6891695 1.3E+07 6891695 1.3E+07 6.3E-08 -46062.8 -23555.8 -46062.8 -23555.8 c) mean of log(prize)= 4.95958 d) d) SUMMARY OUTPUT Regression Statistics Multiple F 0.95167 R Square 0.90568 Adjustedi 0.90408 Standard 0.14858 Observati 61 ANOVA Regressio Residual Total df 1 59 60 SS MS gnificance F 12.5068 12.5068 566.512 6.1E-32 1.30254 0.02208 13.8094 Coefficient:andard Err Stat Intercept 27.982 0.96745 28.9233 Score -0.08085 0.0034 -23.8015 P-value Lower 95%Upper 95%ower 95.0Ipper 95.0% 1.5E-36 26.0461 29.9178 26.0461 29.9178 6.1E-32 -0.08765 -0.07405 -0.08765 -0.07405