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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
====================================================
```