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45-734 PROBABILITY AND STATISTICS II (4th Mini AY1997-98)

Note Set 8 Handouts

PERF.WF1 Examples

LS PERF C X1 X2 
============================================================
LS // Dependent Variable is PERF                                      
Date: 04/09/98   Time: 10:29                                          
Sample: 1 30                                                          
Included observations: 30                                             
============================================================
      Variable      CoefficienStd. Errort-Statistic  Prob.            
============================================================
         C           68.08707   2.235369   30.45898   0.0000          
         X1          10.99481   3.353054   3.279045   0.0029          
         X2          8.424032   3.026705   2.783236   0.0097          
============================================================
R-squared            0.317410    Mean dependent var 74.38863          
Adjusted R-squared   0.266848    S.D. dependent var 8.255667          
S.E. of regression   7.068859    Akaike info criter 4.006038          
Sum squared resid    1349.157    Schwarz criterion  4.146157          
Log likelihood      -99.65872    F-statistic        6.277605          
Durbin-Watson stat   0.942343    Prob(F-statistic)  0.005770          
============================================================
LS PERF (1-X1)*(1-X2) X1 X2 
============================================================
LS // Dependent Variable is PERF                                      
Date: 04/09/98   Time: 10:42                                          
Sample: 1 30                                                          
Included observations: 30                                             
============================================================
      Variable      CoefficienStd. Errort-Statistic  Prob.            
============================================================
   (1-X1)*(1-X2)     68.08707   2.235369   30.45898   0.0000          
         X1          79.08189   2.499219   31.64264   0.0000          
         X2          76.51110   2.040604   37.49435   0.0000          
============================================================
R-squared            0.317410    Mean dependent var 74.38863          
Adjusted R-squared   0.266848    S.D. dependent var 8.255667          
S.E. of regression   7.068859    Akaike info criter 4.006038          
Sum squared resid    1349.157    Schwarz criterion  4.146157          
Log likelihood      -99.65872    F-statistic        6.277605          
Durbin-Watson stat   0.942343    Prob(F-statistic)  0.005770          
============================================================
WALD Test For Centers 2 and 3 
====================================================
Wald Test:                                                    
Equation: Untitled                                            
====================================================
Null HypothesisC(2)=C(3)                                      
====================================================
F-statistic     0.634853    Probability     0.432532          
Chi-square      0.634853    Probability     0.425581          
====================================================
LS PERF C X1+X2 
============================================================
LS // Dependent Variable is PERF                                      
Date: 04/09/98   Time: 14:56                                          
Sample: 1 30                                                          
Included observations: 30                                             
============================================================
      Variable      CoefficienStd. Errort-Statistic  Prob.            
============================================================
         C           68.08707   2.220746   30.65955   0.0000          
       X1+X2         9.452345   2.719847   3.475322   0.0017          
============================================================
R-squared            0.301360    Mean dependent var 74.38863          
Adjusted R-squared   0.276409    S.D. dependent var 8.255667          
S.E. of regression   7.022615    Akaike info criter 3.962612          
Sum squared resid    1380.879    Schwarz criterion  4.056025          
Log likelihood      -100.0073    F-statistic        12.07786          
Durbin-Watson stat   0.960152    Prob(F-statistic)  0.001681          
============================================================
LS PERF C X1 X2 W W*X1 W*X2 
============================================================
LS // Dependent Variable is PERF                                      
Date: 04/09/98   Time: 15:02                                          
Sample: 1 30                                                          
Included observations: 30                                             
============================================================
      Variable      CoefficienStd. Errort-Statistic  Prob.            
============================================================
         C           64.34457   1.264947   50.86742   0.0000          
         X1          13.48746   1.897420   7.108314   0.0000          
         X2          3.016915   1.712746   1.761450   0.0909          
         W           7.484998   1.788905   4.184124   0.0003          
        W*X1        -4.985283   2.683357  -1.857853   0.0755          
        W*X2         10.81423   2.422188   4.464655   0.0002          
============================================================
R-squared            0.902854    Mean dependent var 74.38863          
Adjusted R-squared   0.882616    S.D. dependent var 8.255667          
S.E. of regression   2.828507    Akaike info criter 2.256354          
Sum squared resid    192.0108    Schwarz criterion  2.536594          
Log likelihood      -70.41347    F-statistic        44.61035          
Durbin-Watson stat   2.024369    Prob(F-statistic)  0.000000          
============================================================
WALD Test For Interaction Terms 
====================================================
Wald Test:                                                    
Equation: Untitled                                            
====================================================
Null HypothesisC(5)=0                                         
               C(6)=0                                         
====================================================
F-statistic     20.82484    Probability     0.000006          
Chi-square      41.64968    Probability     0.000000          
====================================================
WALD Test Centers 2 and 3 Equally Effective 
====================================================
Wald Test:                                                    
Equation: Untitled                                            
====================================================
Null HypothesisC(2)+C(5)=C(3)+C(6)                            
====================================================
F-statistic     8.518918    Probability     0.007522          
Chi-square      8.518918    Probability     0.003515          
====================================================
WALD Test Centers 1 and 2 are Equally Effective 
====================================================
Wald Test:                                                    
Equation: Untitled                                            
====================================================
Null HypothesisC(2)+C(5)=0                                    
====================================================
F-statistic     20.07858    Probability     0.000155          
Chi-square      20.07858    Probability     0.000007          
====================================================