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					APPENDIX 5                                                                                                            175

               ASSUMPTIONS OF CORRECTNESS OF REGRESSION MODEL

The Indian models for both Tech marks and English at Tech need to be
diagnosed for assumption correctness.

Technikon Mark

Checking the assumption that normality of residuals holds true for both
factors.


                   Histogram
                   Dependent Variable: TECHMARK
              12


              10


               8


               6


               4
  Frequency




                                                                                                     Std. Dev = .97
               2
                                                                                                     Mean = 0.00
               0                                                                                     N = 41.00
                   -2.00                     -1.00          0.00         1.00          2.00
                               -1.50                 -.50          .50          1.50          2.50


                   Regression Standardized Residual




                                                  Normal P-P Plot of Regression Standardized Residual
                                                  Dependent Variable: TECHMARK
                                           1.00




                                            .75
                       Expected Cum Prob




                                            .50




                                            .25



                                           0.00
                                              0.00          .25          .50       .75          1.00

                                                  Observed Cum Prob




As can be seen from both the histogram of residuals and the normal
probability plot the residuals from the above model seem to have a normal
distribution.
This is further substantiated by performing a Kolmogorov-Smirnov and a
Shapiro-Wilk Test for normality, the results of which are highlighted below.
APPENDIX 5                                                                                                           176




                                                                     Tests of Normality
                                                                                 a
                                                           Kolmogorov-Smirnov                         Shapiro-Wilk
                                                    Statistic      df        Sig.         Statistic        df        Sig.
  Standardized Residual                                  .076         41       .200*           .976           41       .620
                          *. This is a lower bound of the true significance.
                          a. Lilliefors Significance Correction




The p-value is 0.62 for the Shapiro and 0.020 for the Kolmogorov tests,
indicating there is not sufficient evidence to reject the possibility of normality of
residuals in the model.

Further linearity diagnostics on the model by running the standard residual
and dependent variable plots : i.e :

               a)                  Standardized Residuals vrs Predicted Values.
               b)                  Dependent Variable vrs the first independent Variable.
               c)                  Dependent variable vrs the second independent Variable




(a)
                          3




                          2




                          1
  Standardized Residual




                          0




                          -1



                          -2
                               0               10               20                   30


                               Unstandardized Predicted Value
APPENDIX 5                                                                   177


(b)
                   Partial Regression Plot
                   Dependent Variable: TECHMARK
             10




               0




             -10
  TECHMARK




             -20
                  -60      -40         -20       0        20   40

                   ENGTECH

(c )

                   Partial Regression Plot
                   Dependent Variable: TECHMARK
             10

              8

              6

              4

              2

              0
  TECHMARK




             -2

             -4

             -6
               -20               -10         0       10        20

                   SHOLMARK

There does not seem to be any significant patterns of assumption violation
from any of the three diagrams for the model.
APPENDIX 5                                                                                                                                                                 178

Technikon English Mark


Checking the assumption of normality of residuals holds true for both factors.
                   Histogram
                   Dependent Variable: ENGTECH
              12


              10


              8


              6


              4
  Frequency




                                                                                                               Std. Dev = .98
              2
                                                                                                               Mean = .02

              0                                                                                                N = 42.00
                   -4.00                       -3.00       -2.00     -1.00          0.00         1.00
                       -3.50                           -2.50   -1.50         -.50          .50          1.50


                   Regression Standardized Residual




                                                        Normal P-P Plot of Regression Standardized Residual
                                                        Dependent Variable: ENGTECH
                                                1.00




                                                  .75




                                                  .50
                           Expected Cum Prob




                                                  .25



                                                0.00
                                                   0.00            .25          .50              .75            1.00


                                                        Observed Cum Prob




While the Kolmogorov test provided an acceptable result (R2 = 0.20) the
Shapiro-Wilk test did not (R2 = 0.10). As can be seen from both the histogram
of residuals and the normal probability plot the residuals from the above
model does not seem to have a normal distribution.



                                                                                                                           Tests of Normality
                                                                                                                                       a
                                                                                              Kolmogorov-Smirnov                                            Shapiro-Wilk
                                                                                       Statistic      df        Sig.                            Statistic       df         Sig.
   Standardized Residual                                                                    .103         42       .200*                              .893           42       .010**
               *. This is a lower bound of the true significance.
               **. This is an upper bound of the true significance.
               a. Lilliefors Significance Correction
APPENDIX 5                                                                      179


In the Shapiro -Wilk test, the p-value is 0.01 indicating there is sufficient
evidence to reject the possibility of normality of residuals in the model.


Further diagnostics on the Shapiro model by running the standard residual
plots : i.e :


                   a) Standardized Residuals vrs Predicted Values.
                   b) Dependent variables vrs the first independent Variable.
                   c) Dependent vrs the second independent Variable

indicate outcomes as indicated below.

(a)

                           2



                           1



                           0



                           -1
   Standardized Residual




                           -2



                           -3



                           -4
                               20       30       40        50    60   70   80


                                Unstandardized Predicted Value
APPENDIX 5                                                                  180


(b)
                      Partial Regression Plot
                      Dependent Variable: ENGTECH
                30


                20

                10


                 0


                -10


                -20
      ENGTECH




                -30

                -40
                  -10                       0               10


                      TECHMARK




(c)

                      Partial Regression Plot
                      Dependent Variable: ENGTECH
                20


                10


                  0


                -10


                -20
  ENGTECH




                -30


                -40
                      -3    -2    -1    0       1   2   3        4


                      ENGTECH1



The above model violates the assumptions of normality of residuals, this is
possibly caused by the existence of a large outlier. The outlier was found in
record 9, which was deleted. This resulted in the model below. As can be
seen, R 2 has improved to 0.828 from 0.768 . Also the model assumptions in
this case are not violated.
APPENDIX 5                                                                                                                                       181


                                            Model Summary

                                                                                                              Std. Error
                                                                                 Adjusted                       of the
 Model                           R      R Square                                 R Square                     Estimate
 1                                .895a     .801                                     .796                       6.3117
 2                                .910b     .828                                     .819                       5.9480
             a. Predictors: (Constant), TECHMARK
             b. Predictors: (Constant), TECHMARK, ENGTECH1




                                                                                               a
                                                                                   Coefficients

                                                                                                                  Standardi
                                                                                                                     zed
                                                              Unstandardized                                      Coefficien
                                                                Coefficients                                          ts
 Model                                                         B        Std. Error                                  Beta         t      Sig.
 1                       (Constant)                           21.920        3.273                                               6.697     .000
                         TECHMARK                              2.276         .184                                      .895    12.376     .000
 2                       (Constant)                           21.526        3.089                                               6.969     .000
                         TECHMARK                              1.904         .232                                      .749     8.203     .000
                         ENGTECH1                              1.821         .757                                      .220     2.406     .021
             a. Dependent Variable: ENGTECH



                 Histogram
                 Dependent Variable: ENGTECH
             6


             5


             4


             3


             2
 Frequency




                                                                                                     Std. Dev = .97
             1
                                                                                                     Mean = .02
             0                                                                                       N = 41.00
                 -1.75   -1.25    -.75          -.25          .25         .75          1.25
                     -1.50   -1.00       -.50          0.00         .50         1.00          1.50


                 Regression Standardized Residual
APPENDIX 5                                                                                                         182


                                              Normal P-P Plot of Regression Standardized Residual
                                              Dependent Variable: ENGTECH
                                     1.00




                                      .75




                 Expected Cum Prob
                                      .50




                                      .25



                                     0.00
                                            0.00        .25       .50      .75        1.00

                                              Observed Cum Prob




                                                               Tests of Normality
                                                                           a
                                                          Kolmogorov-Smirnov                        Shapiro-Wilk
                                                   Statistic      df        Sig.        Statistic        df        Sig.
  Standardized Residual                                 .074         41       .200*          .951           41       .115
    *. This is a lower bound of the true significance.
    a. Lilliefors Significance Correction




The p value is 0.115 indicating there is not sufficient evidence to reject the
possibility of normality of residuals in the model.

Further linearity diagnostics on the model were taken by running the standard
residual and dependent variable plots : i.e :

   a) Standardized Residuals vrs Predicted Values.
   b) Dependent variables vrs the first independent Variable.
   c) Dependent vrs the second independent Variable
APPENDIX 5                                                                                          183


(a)
                            2.0


                            1.5


                            1.0


                             .5


                            0.0
   Standardized Residual




                             -.5


                           -1.0


                           -1.5

                           -2.0
                                  20            30        40           50   60       70        80


                                      Unstandardized Predicted Value



(b)

                                  Partial Regression Plot
                                  Dependent Variable: ENGTECH
                           30


                           20


                           10


                             0


                           -10
  ENGTECH




                           -20

                           -30
                             -10                                   0                      10

                                  TECHMARK



(c )


                                  Partial Regression Plot
                                  Dependent Variable: ENGTECH
                           20




                           10




                             0
  ENGTECH




                           -10



                           -20
                                 -3        -2        -1        0        1   2    3        4

                                  ENGTECH1

				
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