Multiple Regression Analysis

The final—and most significant—step of the findings is to decide the multivariate technique to be used for testing the hypotheses. An important factor in making this decision is the level of measurements used to depict the variables, as with every level of measurement different statistical techniques should be employed.

The relationships to be examined in this thesis, is between various independent variables with one dependent variable at a time. All the dependent (outcome) variables are measured at the ordinal level, as Likert scale questions were used to capture them.

However, it was decided to treat these questions as interval that allow additional tests, as this is a common approach in social science (Gob et al., 2007). Moreover, the predictor/independent variables were found to be nominal (e.g. duality), ordinal (e.g.

environmental dimensions measured in Likert scale) and interval/ratio (e.g. board size and

ratio of independent). As such, multiple regression analysis was chosen as the most appropriate method for analysis (Field, 2009; Hair et al, 2006).

The general form that the multiple regression equation has in representing its dependent and independent variables is:

Y=b₀+b₁X₁+b₂X₂+b₃X₃+…+bnX_n+e Where: y= dependent variable

b₀= intercept or constant

b_n= gradient or slope of straight line Xn= independent variable

e= error

In brief, the constant (b0) shows the value that y would have with the independent variables being zero. Moreover, the gradient (bn) shows the change to y for a unit change in Xn.

From the analysis output, there are three main measure that are used for interpretation and conclusions.

First, t-statistic tests the null hypothesis that b is 0. As such, if it is significant (e.g.

p<0.05) we gain the confidence that the b-value is significantly different than zero, which means the predictor makes a strong contribution to the outcome variable (Field, 2009).

Hence, the t-value represents the number of standard errors that the coefficient is from zero. For instance, Hair et al. (2006: 219) explain that a coefficient of 2.5 with standard error of 0.5 would have t value of 5 (which means coefficient is 5 standard errors from zero). The standard error is the expected variation of the coefficients (i.e. standard deviation) due to sampling error (Hair et al., 2006: 217)

Second, F-ratio that is a measure of how much the model improves the prediction of the outcome compared to the level of its inaccuracy. If a model is good, the F-ration should be large, i.e. greater than 1 (Field, 2009: 203).

Third, the adjusted R² is used, which results from R². The R², also called coefficient of determination, is a result of the method known as the method of least squares (Field, 2009: 202; Hair et al., 2006: 184). This process starts by calculating the difference between observed values of the outcome variable and its mean value—that is initially considered a good estimate model. All these differences need to be squared, to avoid having their sum being equal to zero. This sum is called total sum of squares (SSTotal).

The mean is a useful measure and easy to be calculated, however the regression line (line of best fit) is used as a further step, trying to find a better estimate model.

Similarly, the differences between each observed data and the value predicted by the regression line are calculated (i.e. vertically distance between observed data point and point on regression line). The sum of these differences is again calculated, after being squared. This result is the sum of squared error (SS_Error). The smaller this number, the better the prediction of the regression line model, which also shows improvement in relation to the mean as a model.

Finally, the difference between the SS_Total and the SS_Error (SS_T-SS_E), give the SS_Regression (SS_R)i.e. the sum of squares due to regression or sum of squares explained. The larger this number, the higher the difference of the regression model from using the mean to predict the dependent variable. Therefore, a large number indicates major improvement in predicting the dependent variable due to the regression model.

The R² is the division of SSR over SST and by multiplying the result with 100, the result can be interpreted as a percentage. This percentage represents the amount of variance of the dependent variable explained by the model and its predictors. Since by adding more predictors to the model the R² will keep increasing, adjusted R² takes into account the non-significant predictors as well as the sample size (Hair et al., 2006: 216), being a more objective measure and as such this measure will be used in the findings. In Chapter 7 the steps followed in running the regression analysis are discussed in detail.

4.7 Summary

This Chapter provided analytical explanation of the philosophical approach and the context of the study, as well as the research approach and design used, the sampling techniques and the methods selected to analyse the data collected. Next chapters will present the empirical part of this thesis, covering all methods described earlier, starting with the descriptive statistics that are presented in Chapter 5.

Chapter 5: Descriptive Statistics

5.1 Introduction

In this chapter, following the discussion on research approaches and methodology design of this thesis, an initial view of the data is provided through the presentation of descriptive statistics.

More particularly, frequencies of responses, measures of location (i.e. mean and mode) and standard deviation of variables will be presented, before proceeding to the following chapters, which will examine the relationships between the constructs, in order to test the hypotheses. The descriptive statistics will present data from all constructs including board roles, external environment as well as director, board and company characteristics.