APOLLO GROUP                
                                 QUADRATIC REGRESSION EQUATION FITTED TO AVERAGE COST OF REVENUE AS A % OF REVENUE                
    Annual Cost of Revenue and Annual Revenue,        
      $ million Cost of Revenue Ave. Cost of Revenue Forecast Forecast Error
Year X X^2 Cost of Revenue Revenue as a % of Revenue as a % of Revenue (%) (%)
2000 0 0 $352,874 $609,997 57.8% 109% 111% -1.5%
2001 1 1 $410,084 $769,474 53.3% 94% 92% 1.5%
2002 2 4 $484,454 $1,009,455 48.0% 77% 76% 1.2%
2003 3 9 $612,940 $1,339,517 45.8% 64% 64% 0.4%
2004 4 16 $765,495 $1,798,423 42.6% 52% 54% -1.6%
2005 5 25 $935,743 $2,251,472 41.6% 45% 47% -1.6%
2006 6 36 $1,112,660 $2,477,533 44.9% 45% 43% 1.5%
2007 7 49 43%  
2008 8 64         45%  
Text Box: The average cost of revenue as a % of revenue has shown a continual decline since 2000. Based upon the above analysis, industry operations, and company operations, forecasted values for Average Cost of Revenue as a % of revenue is expected to be 43% for 2007 and 45% for 2008. No anomolies exist here. As research has indicated, revenues and costs of the company parallel one another historically. They also make effort to expand campuses, programs, and centers, thus, contributing to more revenue and cost offset. The quadratic model is a valid model because the average error of the forecast is zero and forecasted error scatter randomly about zero. The linear regression model was rejected because, when plotted, the forecasted errors did not show randomization about zero and the standard error of estimate and coefficient of determination are greater with the quadratic model than the linear , exponential, and cubic models. The exponential and cubic regression models were initially rejected because initial scatter behavior did not reveal a concave upward curve.
Average Error 0%
   
     LINEST Output for Quadratic Model  
  0.015 -0.203 1.109
  0.002 0.013 0.016
  0.9964 0.02 #N/A
  555.3354 4 #N/A
  0.3741 0.0013 #N/A
   
                    Model Specification:  
Y= 1.109 + -.203*X+.015*X^2    
where Y = annual revenue, $ thousand average cost of revenue as a % of revenue,  
    and X = number of years since 2000 (i.e., X=0  
         for 2000, 1 for 2001, 2 for 2002, etc.)  
Model's standard error of estimate = .02 or 2%