Question
In: Operations Management
The Farr-Kroger Classic is a women’s professional golf tournament played each year in Ohio. Listed below...
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.
| 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 | |||||||||||
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?
Solutions
Expert Solution
A.
Prize as dependent variable for independent variable as Purse winning (value = 996430)
So using:
| 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 |
So Prize = a+b*Purse winnings
| a) x = | 9,96,430 | |
| y = -1505.89 + 0.15x = | 147958.6 | |
B.
Similarly
Prize as dependent variable for independent variable as time(year) (value = 2008)
So using :
| Regression Relationship | Independent Variable | Dependent Variable | Value of b | Value of a | Coefficent of Determination, r2 |
| Regression 5 | Year | Prize | 8,437.50 | -1,67,76,375.00 | 0.94 |
So Prize = a+b*Year
Year =2008
Y =
| 166125 |
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)
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