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Data for question 4
Data for question 5
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. Compare the R-squared in parts (b) and (d). What do you conclude? e. 1 Place 21 3 Tied 2 4 Tied 2 5 Tied 2 6 Tied S 7. Tied 5 Tied 5 9 Tied 5 10 Tied 9 11 Tied 9 12 Tied 9 13 Tied 12 14 Tied 12 15 Tied 12 16 Tied 12 17 Tied 12 18 17 19 Tied 18 20 Tied 28 21 Tied 18 22 Tied 21 23 Tied 21 24 Tied 21 3 TH 21 Km Kin Name Tiger Woods Dustin Johnson Xander Schauffele. Brooks Koepka Jason Day Webb Simpson Tony Finau Francesco Molinari Jon Rahm Patrick Cantlay Rickie Fowler Bubbe Watson Justin Thomas Justin Harding Matt Kuchar lan Poulter Aaron Wise Patton Kizzire Phil Mickelson Adam Scott Woo Kim Kyle Stanley Matthew Fitzpatrick Score Price 275 $2,070,000 log Prize) 6.31597 276 $858,667 5.933825 276 $858,667 5933825 276 $858,667 5933825 277 $403,938 5606315 277 5403,938 5606315 277 $403,938 5606315 277 $403,938 5.006315 278 $310,500 5.492062 278 $310,500 $ 492062 278 $310,500 $.492062 280 $225,400 5352954 280 $225,400 5.352954 280 $225,400 5352954 280 $225.400 $352954 280 5225,400 5312954 201 5184,000 $264818 282 5161,900 5.209247 282 $161 900 5209247 282 $161.900 5.209247 283 5107.956 $038247 283 5107,956 5035247 283 $107,956 $033247 283 $107,956 5053247 SUMMARY OUTPUT (e) n Regression Statistics Multiple R 0.62745 R Square 0.39369 Adjusted R Squ 0.38341 Standard Error 246000 Observations 61 ANOVA F Regression Residual Total 4 33 MS gnificance 12-12 236+12 383090 6.36-08 39 346-32 8.1E-10 60 5.96-12 Coefficient nord for Stat intercept Score 1E-07 1601753 8.30559 548083502395619947 0 mean of logorize) 495958 di SUMMARY OUTPUT M first rsquared rsquared (loggedj0.906 togging the variable provides a better fit of the data 0 0.394 Fluewer 95% per 95 %ower 95.07pper 95 0 45-08 6891495 138-97 6891695 13-07 630 08-4606223555 B6062#-255558 22 Tied 21 23 Tied 21 24 Tied 21 25 Theo 21 26 Tied 21 27 Tied 21 28 Tied 21 29 Tied 21 30 Tied 29 31 Tied 29 32 Tied 29 33 Tied 32 34 Tied 32 35 Tied 32 36 Tied 36 37 Tied 36 38 Tied 36 39 Tied 36 40 Tied 36 41 Tied 36 42 Tied 43 43 Tied 43 44 Tied 43 45 Tied 46 46 Tied 46 Kevin Na x 283 Si Woo Kim Kyle Stanley Matthew Fitzpatrick Kevin Kisner $107,956 5033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.093247 Rory McIlroy Jordan Spieth Lucas Bjerregaard Thorbjorn Olesen Charley Hoffman Bryson DeChambeau 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 $78,200 4 893207 284 284 284 $78,200 4.893207 $78,200 4.893207 $68,042 4.832777 Louis Oosthuizen - Hideki Matsuyama 285 Gary Woodland Charles Howell 1 Kevin Tway Henrik Stenson 568,042 4832777 285 285 $68,042 4832777 $55,488 4744199 286 286 286 $55,488 4.744199 555,488 4.744199 Tommy Fleetwood $55,488 4.744199 Jimmy Walker Patrick Reed Rafael Cabrera Bello 286 286 555,488 4.744199 286 555,488 4744199 $43,700 4640481 Keegan Bradley Keith Mitchell 287 287 287 543,700 4640481 Li Haotong 543,700 4640481 Corey Conners 288 $37.950 4579212 288 537,950 4579212 () d) G M of $$ MS F gnificance 1 12.5068 12.5068 566.512 614-32 50 130254 0.02208 60 11.8094 K mean of logiprize) 4.95958 SUMMARY OUTPUT Regression Statistics Multiple 0.95167 R Square 0.90568 Adjusted 0.90408 Standard 0.14858 Observat 61 ANOVA Regressi Residual Toral Coefficientandard ft Stor Intercept 27.982 0.96745 28 9233 Score -008085 00034 -239015 L N O P-value ower 95%Jpper 95%ower 95 Oroper 95 ON 156-36 26.0481 29 9178 28 0461 29 9178 616-12 -0.08765 007405-008765 -0.07405 N8 43 Tied 43 Keith Mitchell 44 Tied 43 45 Tied 46 46 Tied 46 47 Tied 46 48 Tied 49 49 Tied 49 50 Tied 51 51 Tied 51 52 Tied 51 53 Tied 51 -54 Tied 56 55 Tied 56 56 Tied 58 57 Tied 58 58 61 59 Tied 62 60 Tied 62 61 Tied 62 62 Tied 62 63 64 65 56 67 S Li Haotong Corey Conners Kevin Na Andrew Landry Marc Leishman. Kiradech Aphibarnre Cameron Smith Eddie Pepperell Martin Kaymer Trevor Immelman Tyrrell Hatton Billy Horschel Branden Grace Zach Johnson Satoshi Kodaira 18. Holmes Bernhard Langer Emiliano Grillo Alexander Noren Sx C D $43,700 4.640481 287 287 $43,700 4640481 288 $37,950 4579212 288 $37,950 4.579212 288 $37,950 4.579212 289 532,430 4.510947 289 $32,430 4.510947 $28,693 4.457776 290 290 $28,693 4.457776 $28,693 4.457776 290 290 292 $26,565 $28,693 4.457776 4.42431 292 $26,565 4.42431 293 $25,185 4.401142 $25,185 4401142 $24,150 4382917 293 294 296 296 $22,425 4350732 $22,425 4.350732 296 $22.425 4350732 296 $22,425 4.350732 G H Number K M N Styles O P Q Ce Store Size Sales 1 (thousands of square feet) (millions $) 2 3.7 9.18 3 2.0 4.58 4 5.0 8.22 5 0,7 1.45 6 2.6 6.51 7 2.9 2.82 8 5.2 10.45 9 5.9 9.94 10 3.0 4.43 11 24 4.75 12 2.4 7.30 13 0.5 3.33 14 5.0 6.76 0.4 0.55 7.56 2.25 4.49 9.90 8.93 7.60 371 5.47 15 16 17 18 285201 19 23 1006 42 31 26 5.2 3.3 3.2 4.9 5.5 10% UWA G D G H SUMMARY OUTPUT Regression Statistics Multiple R 0.65808 R Square 0.43306 Adjusted R S 0.40841 Standard Erre 1.19591 Observations 25 ANOVA Regression Residual Total Intercept Sales (millions) 0.36714 0.08759 419153 0.00055 018595 of M $$ MS F 1 25.1271 25.1271 onificonce F 17.569 0.00035 1.4302 23 32.8945 24 58 0216 Coefficientandard Eret Stot P-value ower 95% Jpper 95%ower 95 0fpper 95.0% 104261 05771 1.80664 0.08392 015121 2.23643 -0.15121 225643 0.54834 018595 054834 N O P 4 3 14 15 16 17 18 19 20 21 22 23 24 103132222212 25 26 27 29 34 35 0.5 5.0 0.4 4.2 31 2.6 5.2 3.3 3.2 4.9 5.5 2.9 2.2 23 5973 B 3.33 6.76 0.55 7.56 2.23 4.49 9.90 8.93 7.60 3.71 5.47 8.22 7.17 4.35 D H K L M 1 25.1271 25.1271 17.569 0.00035 Regression Residual 1.4302 23 32.8945 24 58 0216 Total Coefficientandard Et Stat P-value ower 95%/pper 95%ower 95 0fpper 95.0% 0.08392 015121 2.23643 015121 2.25645 Intercept 104261 0.5771 1.80664 Sales (millions$) 0.36714 008759 4.19153 0.00035 0.18595 054834 018595 0.54854 N O P q 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. Compare the R-squared in parts (b) and (d). What do you conclude? e. 1 Place 21 3 Tied 2 4 Tied 2 5 Tied 2 6 Tied S 7. Tied 5 Tied 5 9 Tied 5 10 Tied 9 11 Tied 9 12 Tied 9 13 Tied 12 14 Tied 12 15 Tied 12 16 Tied 12 17 Tied 12 18 17 19 Tied 18 20 Tied 28 21 Tied 18 22 Tied 21 23 Tied 21 24 Tied 21 3 TH 21 Km Kin Name Tiger Woods Dustin Johnson Xander Schauffele. Brooks Koepka Jason Day Webb Simpson Tony Finau Francesco Molinari Jon Rahm Patrick Cantlay Rickie Fowler Bubbe Watson Justin Thomas Justin Harding Matt Kuchar lan Poulter Aaron Wise Patton Kizzire Phil Mickelson Adam Scott Woo Kim Kyle Stanley Matthew Fitzpatrick Score Price 275 $2,070,000 log Prize) 6.31597 276 $858,667 5.933825 276 $858,667 5933825 276 $858,667 5933825 277 $403,938 5606315 277 5403,938 5606315 277 $403,938 5606315 277 $403,938 5.006315 278 $310,500 5.492062 278 $310,500 $ 492062 278 $310,500 $.492062 280 $225,400 5352954 280 $225,400 5.352954 280 $225,400 5352954 280 $225.400 $352954 280 5225,400 5312954 201 5184,000 $264818 282 5161,900 5.209247 282 $161 900 5209247 282 $161.900 5.209247 283 5107.956 $038247 283 5107,956 5035247 283 $107,956 $033247 283 $107,956 5053247 SUMMARY OUTPUT (e) n Regression Statistics Multiple R 0.62745 R Square 0.39369 Adjusted R Squ 0.38341 Standard Error 246000 Observations 61 ANOVA F Regression Residual Total 4 33 MS gnificance 12-12 236+12 383090 6.36-08 39 346-32 8.1E-10 60 5.96-12 Coefficient nord for Stat intercept Score 1E-07 1601753 8.30559 548083502395619947 0 mean of logorize) 495958 di SUMMARY OUTPUT M first rsquared rsquared (loggedj0.906 togging the variable provides a better fit of the data 0 0.394 Fluewer 95% per 95 %ower 95.07pper 95 0 45-08 6891495 138-97 6891695 13-07 630 08-4606223555 B6062#-255558 22 Tied 21 23 Tied 21 24 Tied 21 25 Theo 21 26 Tied 21 27 Tied 21 28 Tied 21 29 Tied 21 30 Tied 29 31 Tied 29 32 Tied 29 33 Tied 32 34 Tied 32 35 Tied 32 36 Tied 36 37 Tied 36 38 Tied 36 39 Tied 36 40 Tied 36 41 Tied 36 42 Tied 43 43 Tied 43 44 Tied 43 45 Tied 46 46 Tied 46 Kevin Na x 283 Si Woo Kim Kyle Stanley Matthew Fitzpatrick Kevin Kisner $107,956 5033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.093247 Rory McIlroy Jordan Spieth Lucas Bjerregaard Thorbjorn Olesen Charley Hoffman Bryson DeChambeau 283 $107,956 5.033247 283 $107,956 5.033247 283 $107,956 5.033247 $78,200 4 893207 284 284 284 $78,200 4.893207 $78,200 4.893207 $68,042 4.832777 Louis Oosthuizen - Hideki Matsuyama 285 Gary Woodland Charles Howell 1 Kevin Tway Henrik Stenson 568,042 4832777 285 285 $68,042 4832777 $55,488 4744199 286 286 286 $55,488 4.744199 555,488 4.744199 Tommy Fleetwood $55,488 4.744199 Jimmy Walker Patrick Reed Rafael Cabrera Bello 286 286 555,488 4.744199 286 555,488 4744199 $43,700 4640481 Keegan Bradley Keith Mitchell 287 287 287 543,700 4640481 Li Haotong 543,700 4640481 Corey Conners 288 $37.950 4579212 288 537,950 4579212 () d) G M of $$ MS F gnificance 1 12.5068 12.5068 566.512 614-32 50 130254 0.02208 60 11.8094 K mean of logiprize) 4.95958 SUMMARY OUTPUT Regression Statistics Multiple 0.95167 R Square 0.90568 Adjusted 0.90408 Standard 0.14858 Observat 61 ANOVA Regressi Residual Toral Coefficientandard ft Stor Intercept 27.982 0.96745 28 9233 Score -008085 00034 -239015 L N O P-value ower 95%Jpper 95%ower 95 Oroper 95 ON 156-36 26.0481 29 9178 28 0461 29 9178 616-12 -0.08765 007405-008765 -0.07405 N8 43 Tied 43 Keith Mitchell 44 Tied 43 45 Tied 46 46 Tied 46 47 Tied 46 48 Tied 49 49 Tied 49 50 Tied 51 51 Tied 51 52 Tied 51 53 Tied 51 -54 Tied 56 55 Tied 56 56 Tied 58 57 Tied 58 58 61 59 Tied 62 60 Tied 62 61 Tied 62 62 Tied 62 63 64 65 56 67 S Li Haotong Corey Conners Kevin Na Andrew Landry Marc Leishman. Kiradech Aphibarnre Cameron Smith Eddie Pepperell Martin Kaymer Trevor Immelman Tyrrell Hatton Billy Horschel Branden Grace Zach Johnson Satoshi Kodaira 18. Holmes Bernhard Langer Emiliano Grillo Alexander Noren Sx C D $43,700 4.640481 287 287 $43,700 4640481 288 $37,950 4579212 288 $37,950 4.579212 288 $37,950 4.579212 289 532,430 4.510947 289 $32,430 4.510947 $28,693 4.457776 290 290 $28,693 4.457776 $28,693 4.457776 290 290 292 $26,565 $28,693 4.457776 4.42431 292 $26,565 4.42431 293 $25,185 4.401142 $25,185 4401142 $24,150 4382917 293 294 296 296 $22,425 4350732 $22,425 4.350732 296 $22.425 4350732 296 $22,425 4.350732 G H Number K M N Styles O P Q Ce Store Size Sales 1 (thousands of square feet) (millions $) 2 3.7 9.18 3 2.0 4.58 4 5.0 8.22 5 0,7 1.45 6 2.6 6.51 7 2.9 2.82 8 5.2 10.45 9 5.9 9.94 10 3.0 4.43 11 24 4.75 12 2.4 7.30 13 0.5 3.33 14 5.0 6.76 0.4 0.55 7.56 2.25 4.49 9.90 8.93 7.60 371 5.47 15 16 17 18 285201 19 23 1006 42 31 26 5.2 3.3 3.2 4.9 5.5 10% UWA G D G H SUMMARY OUTPUT Regression Statistics Multiple R 0.65808 R Square 0.43306 Adjusted R S 0.40841 Standard Erre 1.19591 Observations 25 ANOVA Regression Residual Total Intercept Sales (millions) 0.36714 0.08759 419153 0.00055 018595 of M $$ MS F 1 25.1271 25.1271 onificonce F 17.569 0.00035 1.4302 23 32.8945 24 58 0216 Coefficientandard Eret Stot P-value ower 95% Jpper 95%ower 95 0fpper 95.0% 104261 05771 1.80664 0.08392 015121 2.23643 -0.15121 225643 0.54834 018595 054834 N O P 4 3 14 15 16 17 18 19 20 21 22 23 24 103132222212 25 26 27 29 34 35 0.5 5.0 0.4 4.2 31 2.6 5.2 3.3 3.2 4.9 5.5 2.9 2.2 23 5973 B 3.33 6.76 0.55 7.56 2.23 4.49 9.90 8.93 7.60 3.71 5.47 8.22 7.17 4.35 D H K L M 1 25.1271 25.1271 17.569 0.00035 Regression Residual 1.4302 23 32.8945 24 58 0216 Total Coefficientandard Et Stat P-value ower 95%/pper 95%ower 95 0fpper 95.0% 0.08392 015121 2.23643 015121 2.25645 Intercept 104261 0.5771 1.80664 Sales (millions$) 0.36714 008759 4.19153 0.00035 0.18595 054834 018595 0.54854 N O P
