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    | q | 
    For a 2-predictor case: r1y
    = r2y = r12 =
    0.50 
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         If only include one predictor
    (x1) (r2y = r12
    =0) è R2=025 
     | 
   
   
     | 
   
   
         By adding x2
    in the regression (r2y = r12
    =0.25) è R2=033 
     | 
   
   
     | 
   
   
         In this case, the 2nd
    predictor improve the regression. 
     | 
     | 
   
   
     | 
   
   
    | q | 
    For a 2-predictor case: r1y
    = r12 = 0.50 but r2y
    = 0.25 
     | 
     | 
   
   
     | 
     | 
   
   
     | 
   
   
         If with only x1
    è R2=025 
     | 
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     | 
   
   
         Adding x2        è
    R2=025 (still the same!!) 
     | 
     | 
   
   
     | 
   
   
         In this case, the 2nd
    predictor is not useful.  It is
    because 
     | 
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     | 
   
   
         r2y £ r1y
    * r12 = 0.50*0.50 = 0.25 
     | 
     |