is to do with multicollinearity, which is investigated by considering the correlation among the independent variables. Tables 4.46 to 4.48 indicate the great majority of the correlations among the independent (i.e. predictor) variables of the study are not above .7, which demonstrates that the multicollinearity assumption is met.
Tables 4.46 to 4.48 also show that only the correlation coefficient between General autonomy and Expert teaching style is close to .3, and the rest of the predictor variables have an insignificant correlation with all autonomy scores. It is therefore, predicted that in the final results of regression, these insignificantly correlated predictor variables are not going to have significant contribution in terms of predicting autonomy. Nevertheless, the regression analysis was continued to observe which of these predictor variables would indeed have any prediction power in terms of different autonomy scores.
Table 4.46
General Autonomy Correlations
General autonomy
Expert
Formal authority
Personal model
Facilitator
Delegator
NLP
Pearson Correlation
General autonomy
1.000
.308
.156
.191
.292
.178
.088
Expert
.308
1.000
.716
.807
.718
.604
.281
Formal authority
.156
.716
1.000
.821
.689
.722
.392
Personal model
.191
.807
.821
1.000
.773
.667
.480
Facilitator
.292
.718
.689
.773
1.000
.769
.454
Delegator
.178
.604
.722
.667
.769
1.000
.452
NLP
.088
.281
.392
.480
.454
.452
1.000
Sig. (1-tailed)
General autonomy
.
.000
.038
.015
.000
.022
.160
Expert
.000
.
.000
.000
.000
.000
.001
Formal authority
.038
.000
.
.000
.000
.000
.000
Personal model
.015
.000
.000
.
.000
.000
.000
Facilitator
.000
.000
.000
.000
.
.000
.000
Delegator
.022
.000
.000
.000
.000
.
.000
NLP
.160
.001
.000
.000
.000
.000
.
N
General autonomy
129
129
129
129
129
129
129
Expert
129
129
129
129
129
129
129
Formal authority
129
129
129
129
129
129
129
Personal model
129
129
129
129
129
129
129
Facilitator
129
129
129
129
129
129
129
Delegator
129
129
129
129
129
129
129
NLP
129
129
129
129
129
129
129
Table 4.47
Curriculum Autonomy Correlations
Curriculum autonomy
Expert
Formal authority
Personal model
Facilitator
Delegator
NLP
Pearson Correlation
Curriculum autonomy
1.000
-.257
-.266
-.259
-.142
-.004
-.018
Expert
-.257
1.000
.716
.807
.718
.604
.287
Formal authority
-.266
.716
1.000
.821
.689
.722
.416
Personal model
-.259
.807
.821
1.000
.773
.667
.511
Facilitator
-.142
.718
.689
.773
1.000
.769
.464
Delegator
-.004
.604
.722
.667
.769
1.000
.439
NLP
-.018
.287
.416
.511
.464
.439
1.000
Sig. (1-tailed)
Curriculum autonomy
.
.002
.001
.002
.054
.480
.419
Expert
.002
.
.000
.000
.000
.000
.000
Formal authority
.001
.000
.
.000
.000
.000
.000
Personal model
.002
.000
.000
.
.000
.000
.000
Facilitator
.054
.000
.000
.000
.
.000
.000
Delegator
.480
.000
.000
.000
.000
.
.000
NLP
.419
.000
.000
.000
.000
.000
.
N
Curriculum autonomy
129
129
129
129
129
129
129
Expert
129
129
129
129
129
129
129
Formal authority
129
129
129
129
129
129
129
Personal model
129
129
129
129
129
129
129
Facilitator
129
129
129
129
129
129
129
Delegator
129
129
129
129
129
129
129
NLP
129
129
129
129
129
129
129
Table 4.48
Total Autonomy Correlations
Total
Autonomy
Expert
Formal authority
Personal model
Facilitator
Delegator
NLP
Pearson Correlation
Total
Autonomy
1.000
.191
.005
.051
.249
.207
.086
Expert
.191
1.000
.716
.807
.718
.604
.287
Formal authority
.005
.716
1.000
.821
.689
.722
.416
Personal model
.051
.807
.821
1.000
.773
.667
.511
Facilitator
.249
.718
.689
.773
1.000
.769
.464
Delegator
.207
.604
.722
.667
.769
1.000
.439
NLP
.086
.287
.416
.511
.464
.439
1.000
Sig. (1-tailed)
Autonomy
.
.015
.476
.281
.002
.009
.165
Expert
.015
.
.000
.000
.000
.000
.000
Formal authority
.476
.000
.
.000
.000
.000
.000
Personal model
.281
.000
.000
.
.000
.000
.000
Facilitator
.002
.000
.000
.000
.
.000
.000
Delegator
.009
.000
.000
.000
.000
.
.000
NLP
.165
.000
.000
.000
.000
.000
.
N
Autonomy
129
129
129
129
129
129
129
Expert
129
129
129
129
129
129
129
Formal authority
129
129
129
129
129
129
129
Personal model
129
129
129
129
129
129
129
Facilitator
129
129
129
129
129
129
129
Delegator
129
129
129
129
129
129
129
NLP
129
129
129
129
129
129
129
4.2.4.2. Assumption of Normality
Another assumption of multiple regression is the normality of the regression standardized residuals, which was checked via checking the Normal Probability Plot of the regression standardized residuals (Figures 4.4, 4.5 & 4.6). As shown in the figures, it can be said that the points have lain in an almost straight diagonal line from bottom left to top right without many deviations; therefore, it is assumed the assumption of normality of the regression standardized residuals is met for all the data.
Figure 4.4. The Normal Probability Plot of the Regression Standardized Residuals Dependent Variable: General Autonomy
Figure 4.5. The Normal Probability Plot of the Regression Standardized Residuals – Dependent Variable: Curriculum Autonomy
Fig
ur
e 4.6. The Normal Probability Plot of the Regression Standardized Residuals Dependent Variable: Total Autonomy
4.2.4.3. Assumption of Homoscedasticity
Figures 4.7 to 4.9 also present scatter plots of the standardized residuals which indicate that there are only a few negligible outliers which have lain outside the rectangular cluster of the data in the center with regard to the large sample size in this study. Moreover, since there is a clear or systematic pattern to the residuals (e.g. curvilinear or higher on one side than the other) with very few deviations from a centralized rectangle, it is assumed that there is no violation of homoscedasticity in all the data for all the autonomy scores and the independent variables.
Figure 4.7. Scatterplot of the Standardized Residuals – Dependent Variable: General Autonomy
Figure 4.8. Scatterplot of the Standardized Residuals – Dependent Variable: Total Autonomy
Figure 4.9. Scatter Plot of the Standardized Residuals-Dependent Variable: Curriculum Autonomy
Tables 4.49 to 4.51 present the descriptive statistics for all the variables, and Tables 4.52 to 4.54 demonstrate what variables are going to be entered into the regression analysis. Since the literature suggested no order for entering the variables in the regression model and there was almost no logic for this issue, the method of regression was chosen to be simultaneous multiple regression analysis for all autonomy scores.
Table 4.49
Descriptive Statistics of General Autonomy, Styles and NLP
Mean
Std. Deviation
N
General autonomy
39.2248
5.24142
129
Expert
3.8117
.53063
129
Formal authority
3.6609
.57158
129
Personal model
3.8556
.64337
129
Facilitator
3.9002
.58887
129
Delegator
3.5530
.53970
129
NLP
143.5504
11.64847
129
Table 4.50
Descriptive Statistics of Curriculum Autonomy, Styles and NLP
Mean
Std. Deviation
N
Curriculum autonomy
16.8915
2.98758
129
Expert
3.8117
.53063
129
Formal authority
3.6609
.57158
129
Personal model
3.8556
.64337
129
Facilitator
3.9002
.58887
129
Delegator
3.5530
.53970
129
NLP
143.5504
11.64847
129
Table 4.51
Descriptive Statistics of Total Autonomy, Styles and NLP
Mean
Std. Deviation
N
Autonomy
56.1163
4.43112
129
Expert
3.8117
.53063
129
Formal authority
3.6609
.57158
129
Personal model
3.8556
.64337
129
Facilitator
3.9002
.58887
129
Delegator
3.5530
.53970
129
NLP
143.5504
11.64847
129
Table 4.52
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
NLP, Expert, Delegator, Formal authority, Facilitator, Personal modelb
.
Enter
a. Dependent Variable: General autonomy
b. All requested variables entered.
Table 4.53
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
NLP, Expert, Delegator, Formal authority, Facilitator, Personal modelb
.
Enter
a. Dependent Variable: Autonomy
b. All requested variables entered.
Table 4.54
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
NLP, Expert, Delegator, Formal authority, Facilitator, Personal modelb
.
Enter
a. Dependent Variable: Curriculum autonomy
b. All requested variables entered.
In Tables 4.55 to 4.57, the value given under the heading R Square indicates how much of the variance in the dependent variable (i.e. General, Curriculum and Total autonomy) is explained by the model (which includes the entered variables). In the case of General autonomy, the value is .139 which, expressed as a percentage, explains 13 percent of the variance in General autonomy. In the case of Total autonomy, the value is .184 which, expressed as a percentage, explains 18 percent of the variance in Total autonomy. Finally, In the case of Curriculum autonomy, the value is .175 which, expressed as a percentage, explains 17 percent of the variance in Curriculum autonomy.
Table 4.55
Model Summaryb (General Autonomy)
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.373a
.139
.097
4.98209
a. Predictors: (Constant), NLP, Expert, Delegator, Formal authority, Facilitator, Personal model
b. Dependent Variable: General autonomy
Table 4.56
Model Summaryb (Total Autonomy)
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.429a
.184
.144
4.10078
a. Predictors: (Constant), NLP, Expert, Delegator, Formal authority, Facilitator, Personal model
b. Dependent Variable: Autonomy
Table 4.57
Model Summaryb (Curriculum Autonomy)
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.418a
.175
.134
2.78016
a. Predictors: (Constant), NLP, Expert, Delegator, Formal authority, Facilitator, Personal model
b. Dependent Variable: Curriculum autonomy
To assess the statistical significance of the above results, it is necessary to look in Tables 4.58 to 4.60. The ANOVA tests the null hypothesis that multiple R in the population equals 0. As the results indicate, the model reaches statistical significance in all autonomy scores; therefore, all the predictor variables together make significant predictive contribution to the models.