APOLLO GROUP                
                                   QUADRATIC REGRESSION EQUATION FITTED TO AVERAGE NET INCOME AS A % OF REVENUE    
    Annual Net Income and Annual Revenue, Net Income Ave. Net Income Forecast Forecast Error
Year X X^2 $ million as a % of Revenue as a % of Revenue (%) (%)
Year X X^2 Net Income Revenue as a % of Revenue as a % of Revenue Forecast (%)
2000 0 0 $71,191 $609,997 11.7% 40% 41% -0.56%
2001 1 1 $107,817 $769,474 14.0% 35% 35% 0.61%
2002 2 4 $161,150 $1,009,455 16.0% 30% 30% 0.49%
2003 3 9 $247,010 $1,339,517 18.4% 26% 25% 0.09%
2004 4 16 $277,774 $1,798,423 15.4% 21% 22% -0.97%
2005 5 25 $427,933 $2,251,472 19.0% 19% 19% -0.01%
2006 6 36 $414,833 $2,477,533 16.7% 17% 16% 0.35%
2007 7 49 15%  
2008 8 64         14%  
Text Box: The average net income 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 Net Income as a % of revenue is expected to be 15% for 2007 and 14% 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  
  0.003 -0.061 0.406
  0.001 0.005 0.006
  0.9957 0.007 #N/A
  461.8634 4 #N/A
  0.0463 0.0002 #N/A
   
                    Model Specification:  
Y= .406 + -.061*X+.003*X^2    
where Y = annual revenue, $ thousand average net income 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 = .007%