The Farr-Kroger Classic is a women’s professional golf tournament played each ye

Question

The Farr-Kroger Classic is a women’s professional golf tournament played each year in Ohio. Listed below are the total purse winnings (the amount of money that is distributed to the top golfers) and the prize for the winner for the 15 years from 1991 through 2005. The operators of this golf tournament believe that there is a relationship between the purse winnings and the prize and the prize is related to the purse winnings. In addition to the data provided, some of the possible linear regression relationships are provided.   These might be of help in your analysis.

Using linear regression relationships, answer the questions a) through c) below and on the following page.

a) Develop a projection for the amount of the prize for the winner for the year 2008 if the purse winnings for that year are projected to be $996,430. As part of your answer, include the independent and dependent variables and the accompanying linear regression relationship.

b) Now let’s suppose that we believe the prize for the winner is a function of time (dependent on time). Given this belief, develop a projection for the amount of the prize for the winner for the year 2008 and discuss your results compared to what you found in part a)

c) Would you recommend using the forecasts you found in parts a) and b) based on the strengths of the relationship? Why?

Year Purse Winnings Prize Ind Var Year SUMMARY OUTPUT 1991 $225,000 $33,750 Dep var Purse Winnings 1992 $275,000 $41,250 Regression Statistics 1993 $325,000 $41,250 Multiple R 0.969387633 1994 $325,000 $48,750 R Square 0.939712382 1995 $350,000 $52,500 Adjusted R Square 0.935074873 1996 $400,000 $60,000 Standard Error 65072.5152 1997 $450,000 $67,500 Observations 15 1998 $500,000 $75,000 1999 $500,000 $75,000 ANOVA 2000 $575,000 $86,250 df SS MS F Significance F 2001 $700,000 $105,000 Regression 1 8.58036E+11 8.58036E+11 202.6330017 2.62887E-09 2002 $800,000 $120,000 Residual 13 55047619048 4234432234 2003 $800,000 $120,000 Total 14 9.13083E+11 2004 $1,000,000 $150,000 2005 $1,000,000 $150,000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -110055238.1 7769893.698 -14.16431709 2.79418E-09 -126841072.9 -93269403.32 -126841072.9 -93269403.32 Regression Relationship Independent Variable Dependent Variable Value of b Value of a Coefficent of Determination, r2 Year 55357.14286 3888.826592 14.23492191 2.62887E-09 46955.84379 63758.44192 46955.84379 63758.44192 Regression 1 Year Purse Winnings 55,357.14 -110,055,238.10 0.94 Regression 2 Purse Winnings Prize 0.15 -1,505.89 1.00 Regression 3 Prize Purse Winnings 6.57 11,179.24 1.00 Regression 4 Prize Year 0.00 1,988.85 0.94 Ind Var Purse Winnings SUMMARY OUTPUT Regression 5 Year Prize 8,437.50 -16,776,375.00 0.94 Dep var Prize Regression Statistics a)      x = $996,430 Multiple R 0.998828015 y = -1505.89 + 0.15x = $149,786.51 R Square 0.997657404 Adjusted R Square 0.997477205 b)     x = 2006 Standard Error 1949.897566 y = -110055238.10 + 55357.14x = $991,190.48 Observations 15 ANOVA df SS MS F Significance F Regression 1 21049947693 21049947693 5536.399574 1.7382E-18 Residual 13 49427306.74 3802100.519 Total 14 21099375000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1505.886648 1226.975151 -1.227316337 0.241465598 -4156.605301 1144.832005 -4156.605301 1144.832005 Purse Winnings 0.151834444 0.002040594 74.40698606 1.7382E-18 0.147426009 0.156242879 0.147426009 0.156242879 Ind Var Prize SUMMARY OUTPUT Dep var Purse Winnings Regression Statistics Multiple R 0.998828015 R Square 0.997657404 Adjusted R Square 0.997477205 Standard Error 12827.21014 Observations 15 ANOVA df SS MS F Significance F Regression 1 9.10944E+11 9.10944E+11 5536.399574 1.7382E-18 Residual 13 2138985160 164537320 Total 14 9.13083E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 11179.24109 7942.610888 1.407502048 0.182737687 -5979.726488 28338.20867 -5979.726488 28338.20867 Prize 6.57069226 0.088307464 74.40698606 1.7382E-18 6.379915582 6.761468937 6.379915582 6.761468937 Ind Var Prize SUMMARY OUTPUT Dep var Year Regression Statistics Multiple R 0.971981516 R Square 0.944748067 Adjusted R Square 0.940497919 Standard Error 1.090890292 Observations 15 ANOVA df SS MS F Significance F Regression 1 264.5294588 264.5294588 222.2858866 1.48781E-09 Residual 13 15.47054119 1.19004163 Total 14 280 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1988.846441 0.675479471 2944.347723 3.02269E-39 1987.387156 1990.305726 1987.387156 1990.305726 Prize 0.00011197 7.51011E-06 14.90925507 1.48781E-09 9.57455E-05 0.000128195 9.57455E-05 0.000128195 Ind Var Year SUMMARY OUTPUT Dep var Prize Regression Statistics Multiple R 0.971981516 R Square 0.944748067 Adjusted R Square 0.940497919 Standard Error 9469.713869 Observations 15 ANOVA df SS MS F Significance F Regression 1 19933593750 19933593750 222.2858866 1.48781E-09 Residual 13 1165781250 89675480.77 Total 14 21099375000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -16776375 1130718.09 -14.83692102 1.57972E-09 -19219142.92 -14333607.08 -19219142.92 -14333607.08 Year 8437.5 565.9236469 14.90925507 1.48781E-09 7214.896294 9660.103706 7214.896294 9660.103706

Explanation / Answer

A.

Prize as dependent variable for independent variable as Purse winning (value = 996430)

So using:

So Prize = a+b*Purse winnings

B.

Similarly

Prize as dependent variable for independent variable as time(year) (value = 2008)

So using :

So Prize = a+b*Year

Year =2008

Y =

C.

As per the forecast in a and b,

we see coefficient of determiniation is better in a as compared to b (at value of 1 vs 0.94)

Hence we can say a is a better predictor than b (as the strength of th relationships is better)

Regression Relationship Independent Variable Dependent Variable Value of b Value of a Coefficent of Determination, r2 Regression 2 Purse Winnings Prize 0.15 -1,505.89 1

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