CONCEPCIONES SOBRE LA ENSEÑANZA

Regression analysis includes techniques for modelling and analyzing several variables. The focus is on the relationship between independent and dependent variables. Regression analysis helps to understand changes that occur on independent variables and dependent variables. In testing the main hypotheses, the simple regression analysis is used. Meanwhile for hypotheses 1 to 4 and its sub-hypotheses, multiple regressions are employed.

3.16.1 Simple Regression Analysis

Simple regression is used to examine the main hypothesis of the study. Bivariate linear regression is used when there is only one independent variable and one dependent variable. The analysis gives the straight line that best fits the data on a scatter plot.

The purpose of regression analysis is to test the relationship between academic leadership and work-related attitude toward determining their significance of F-statistics with the R2. R2 indicates the explanatory power of the study’s research framework. R2 is supposed to have a high explanatory power (Selvarajah & Meyer, 2008). On the other hand, if this study shows a low R2 then it shows that other constructs should be considered. Overall, the R2 of the studies in leadership is relatively low (Blank et al., 1990). Thus this study also expects R2 to be low.

Meanwhile, the standardized coefficients (Beta value) mean that the values for each of the different variables are converted to the same scale. If it is significant at 0.01 the Beta value of academic leadership indicates the amount of contribution needs to explain the work-related attitude (Field, 2009).

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3.16.2 Multiple Regression Analysis

Multiple regression involves more than one independent variable. Multiple regression analysis is used in this study to test the relationship between each independent variable and four dependent variables. The analysis also examines the impact between independent variables and four dependent variables. In this study, the theoretical framework has not much been developed as for this study to apply the analysis of moderated multiple regression (MMR) and confirmatory factor analysis (CFA) on academic leadership and work-related attitude. Further, the association between academic leadership and work-related attitude constructs are not much explored by scholars. Thus, MMR and CFA are justified not to be used in the study’s analysis.

Multiple regression analysis is conducted to examine the strength of hypotheses 1 to 4 and the sub-hypotheses in their relationship between academic leadership and work- related attitude. The data of the study is examined using various types of multiple regression methods such as enter, stepwise, backward and forward. In this avenue, the statistical programme examines and selects which independent variables enter and in which order they go into the equation (Pallant, 2007).

Enter Method: The enter method is called the simultaneous method where

the researcher specifies the set of predictor variables that make up the model. The success of this model in predicting the criterion variable is then assessed (Brace, Kemp & Snelgar, 2009).

Stepwise Method: The stepwise method is the most sophisticated of the statistical methods (Brace et al., 2009). Each variable is entered in sequence and its value assessed. If adding the variable contributes to the model then it is retained, but all other variables in the model are then re-tested to see if they are still contributing to the success of the model. If they no longer contribute significantly they are removed. Brace et al. (2009) conclude that the method should ensure that you end up with the smallest possible set of predictor variables included in your model.

Forward Method: The forward method enters the variables into the model

one at a time in an order determined by the strength of their correlation with the criterion variable. The effect of adding each is assessed as it is entered,

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and variables that do not significantly add to the success of the model are excluded (Brace et al., 2009).

Backward Method: The backward method enters all the predictor variables

into the model (Brace et al., 2009). The weakest predictor variable is then removed and the regression re-calculated. If this significantly weakens the model then the predictor variable is re-entered – otherwise it is deleted. This procedure is then repeated until only useful predictor variables remain in the model.

In running the multiple regression analysis, the sample size is important for a reliable regression model. Moreover, a sample size of 200 is always sufficient in expecting a medium effect in the multiple regression analysis (Miles & Shevlin, 2001). Also, the study carries out the preliminary analyses to ensure that there are no violations of the assumptions of normality, linearity, multicollinearity and homoscedasticity.

The most common measures for checking on multicollinearity are the variance inflation factor (VIF) and tolerance. The VIF indicates whether a predictor has a strong linear regression with the other predictors. The assumption is of no multicollinearity if the VIF value follows the suggested value for the good VIF which is not greater than 10 and the average is not greater than 1 (Myers 1990; Bowerman & O’Connell, 1990). The tolerance (1/VIP) for each predictor should not be less than 0.1.

The normality of data in this study is checked for univariate normality of the distribution using the Kolmogorov-Smirnov test. The normality of the distribution is also tested and supported by the low skewness and kurtosis statistics and the examination of histograms with a super-imposed normal curve.

The threat of heteroscedasticity is checked by examining the residual plot of the actual standardized residual values of the dependent variable against the predicted residual values. The scatter plot of the standard residual shows the graph of the data which display the points as randomly and evenly dispersed throughout the plot. This indicates the assumption of linearity and homoscedasticity have been met. The residual is a roughly rectangular distribution, with most scores concentrated in the centre of 0 point which are displayed in the scatter plot of less than 3.3 or more than -3.3 (Tabachnick &

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Fidell, 2007). The presence of outlier cases can be detected if a standardized residual is not within this limit.