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

Note Set 7 Handouts



  1. AWARD.WF1 Examples

    LS AWARD C JURY GOVT CORP SMLBIZ CHILD AREAPI DATE AGE EARN AGE*EARN
    ============================================================
    LS // Dependent Variable is AWARD                                     
    Date: 04/06/98   Time: 16:02                                          
    Sample(adjusted): 1 172                                               
    Included observations: 172 after adjusting endpoints                  
    ============================================================
          Variable      CoefficienStd. Errort-Statistic  Prob.            
    ============================================================
             C          -219.7246   99.70033  -2.203850   0.0290          
            JURY         131.2040   27.68902   4.738487   0.0000          
            GOVT         184.5739   51.71879   3.568797   0.0005          
            CORP         63.02345   41.15354   1.531422   0.1276          
           SMLBIZ        67.23727   44.28586   1.518256   0.1309          
           CHILD         20.42367   7.348645   2.779243   0.0061          
           AREAPI        0.006719   0.002257   2.977685   0.0034          
            DATE         12.01050   2.577396   4.659934   0.0000          
            AGE         -0.609246   1.694449  -0.359554   0.7197          
            EARN         10.72572   2.636861   4.067608   0.0001          
          AGE*EARN      -0.117276   0.058843  -1.993018   0.0479          
    ============================================================
    R-squared            0.672176    Mean dependent var 376.6977          
    Adjusted R-squared   0.651814    S.D. dependent var 266.3115          
    S.E. of regression   157.1431    Akaike info criter 10.17613          
    Sum squared resid    3975726.    Schwarz criterion  10.37742          
    Log likelihood      -1108.205    F-statistic        33.01174          
    Durbin-Watson stat   2.283853    Prob(F-statistic)  0.000000          
    ============================================================
    
    LS AWARD C JURY GOVT CORP SMLBIZ CHILD AREAPI DATE EARN AGE*EARN
    ============================================================
    LS // Dependent Variable is AWARD                                     
    Date: 04/07/98   Time: 12:07                                          
    Sample(adjusted): 1 172                                               
    Included observations: 172 after adjusting endpoints                  
    ============================================================
          Variable      CoefficienStd. Errort-Statistic  Prob.            
    ============================================================
             C          -245.6668   68.62174  -3.580014   0.0005          
            JURY         131.3667   27.61082   4.757799   0.0000          
            GOVT         183.7901   51.53379   3.566401   0.0005          
            CORP         62.49885   41.01699   1.523731   0.1295          
           SMLBIZ        67.41718   44.16387   1.526524   0.1288          
           CHILD         20.89521   7.211218   2.897598   0.0043          
           AREAPI        0.006692   0.002249   2.975284   0.0034          
            DATE         11.94563   2.564156   4.658699   0.0000          
            EARN         11.46113   1.659713   6.905491   0.0000          
          AGE*EARN      -0.133889   0.036336  -3.684737   0.0003          
    ============================================================
    R-squared            0.671913    Mean dependent var 376.6977          
    Adjusted R-squared   0.653686    S.D. dependent var 266.3115          
    S.E. of regression   156.7202    Akaike info criter 10.16531          
    Sum squared resid    3978918.    Schwarz criterion  10.34830          
    Log likelihood      -1108.274    F-statistic        36.86348          
    Durbin-Watson stat   2.292752    Prob(F-statistic)  0.000000          
    ============================================================
    
  2. DELIV.WF1 Examples

    ============================================================
    LS // Dependent Variable is MINS                                      
    Date: 04/07/98   Time: 14:51                                          
    Sample: 1 30                                                          
    Included observations: 30                                             
    ============================================================
          Variable      CoefficienStd. Errort-Statistic  Prob.            
    ============================================================
           1-DUM         30.48637   14.09972   2.162196   0.0396          
            DUM          142.0664   14.09972   10.07583   0.0000          
           DELIVS        8.714911   0.390256   22.33125   0.0000          
    ============================================================
    R-squared            0.966224    Mean dependent var 382.5833          
    Adjusted R-squared   0.963722    S.D. dependent var 96.97388          
    S.E. of regression   18.47030    Akaike info criter 5.926967          
    Sum squared resid    9211.101    Schwarz criterion  6.067087          
    Log likelihood      -128.4727    F-statistic        386.1960          
    Durbin-Watson stat   2.693715    Prob(F-statistic)  0.000000          
    ============================================================
    
  3. AWARD.WF1 Examples (Cont.)

    LS AWARD IND JURY GOVT CORP SMLBIZ CHILD AREAPI DATE AGE EARN AGE*EARN
    ============================================================
    LS // Dependent Variable is AWARD                                     
    Date: 04/06/98   Time: 16:06                                          
    Sample(adjusted): 1 172                                               
    Included observations: 172 after adjusting endpoints                  
    ============================================================
          Variable      CoefficienStd. Errort-Statistic  Prob.            
    ============================================================
            IND         -219.7246   99.70033  -2.203850   0.0290          
            JURY         131.2040   27.68902   4.738487   0.0000          
            GOVT        -35.15074   99.41821  -0.353564   0.7241          
            CORP        -156.7012   95.99882  -1.632324   0.1046          
           SMLBIZ       -152.4873   96.92565  -1.573240   0.1176          
           CHILD         20.42367   7.348645   2.779243   0.0061          
           AREAPI        0.006719   0.002257   2.977685   0.0034          
            DATE         12.01050   2.577396   4.659934   0.0000          
            AGE         -0.609246   1.694449  -0.359554   0.7197          
            EARN         10.72572   2.636861   4.067608   0.0001          
          AGE*EARN      -0.117276   0.058843  -1.993018   0.0479          
    ============================================================
    R-squared            0.672176    Mean dependent var 376.6977          
    Adjusted R-squared   0.651814    S.D. dependent var 266.3115          
    S.E. of regression   157.1431    Akaike info criter 10.17613          
    Sum squared resid    3975726.    Schwarz criterion  10.37742          
    Log likelihood      -1108.205    F-statistic        33.01174          
    Durbin-Watson stat   2.283853    Prob(F-statistic)  0.000000          
    ============================================================
    
    Under View, this is the Representation of the above equation:
    Estimation Command:
    =====================
    LS AWARD IND JURY GOVT CORP SMLBIZ CHILD AREAPI DATE AGE EARN AGE*EARN
    
    Estimation Equation:
    =====================
    AWARD = C(1)*IND + C(2)*JURY + C(3)*GOVT + C(4)*CORP + C(5)*SMLBIZ + 
    C(6)*CHILD + C(7)*AREAPI + C(8)*DATE + C(9)*AGE + C(10)*EARN + C(11)*(AGE*EARN)
    
    Substituted Coefficients:
    =====================
    AWARD = -219.72462*IND + 131.20403*JURY - 35.150743*GOVT - 156.70117*CORP
     - 152.48734*SMLBIZ + 20.423668*CHILD + 0.006719395*AREAPI + 12.010495*DATE
     - 0.60924639*AGE + 10.725716*EARN - 0.11727551*(AGE*EARN)
    
    To test whether amount paid by corporations was different from that paid by individuals:
    ====================================================
    Wald Test:                                                    
    Equation: Untitled                                            
    ====================================================
    Null HypothesisC(1)=C(4)                                      
    ====================================================
    F-statistic     2.345254    Probability     0.127628          
    Chi-square      2.345254    Probability     0.125665          
    ====================================================
    
    To test whether or not the amount paid by corporations differed from that paid by small business:
    ====================================================
    Wald Test:                                                    
    Equation: Untitled                                            
    ====================================================
    Null HypothesisC(4)=C(5)                                      
    ====================================================
    F-statistic     0.019177    Probability     0.890034          
    Chi-square      0.019177    Probability     0.889861          
    ====================================================
    
    To test whether or not governments, corporations, and small businesses all paid the same amounts:
    ====================================================
    Wald Test:                                                    
    Equation: Untitled                                            
    ====================================================
    Null HypothesisC(3)=C(5)                                      
                   C(4)=C(5)                                      
    ====================================================
    F-statistic     5.449718    Probability     0.005127          
    Chi-square      10.89944    Probability     0.004298          
    ====================================================