Chapter 7: Correlation and Multiple Regression Analysis
7.5 Multiple Regression Analysis and Hypothesis Testing
7.5.2 Testing Multicollinearity
Table 7.5 shows the multicollinearity results between the independent variables.
These results are important, in order to ensure that each independent variable is not explained by the other independent variables. Collinearity is the extent of correlation of one variable to another, while assessing multicollinearity checks the relationship of one variable with a set of independent variables. To test multicollinearity, several regression models are run. According to Hair et al. (2006: 227) in each model, one independent variable is treated as a dependent variable and all other independent variables as predictors of that variable. As a result R2 is calculated, showing the amount of variance for each independent variable, explained by the other independent variables.
Moreover, the tolerance—that is a direct measure for multicollinearity—is calculated as 1- R2. Therefore, the bigger the tolerance result the smaller degree of multicollinearity. In addition, VIF (i.e. variance inflation factor) is displayed in the results, which is calculated as the inverse of tolerance value, i.e. 1/tolerance (Hair et al., 2006:
227). As such, the smaller values of VIF are preferred to indicate low multicollinearity.
Specifically, the guidelines from different sources indicate that the tolerance value should not be below 0.1 and ideally not below 0.2; at the same time, the VIF should not exceed 10 and it is preferable not to be substantially greater than 1 (Curto and Pinto, 2011:
1500; Mason and Perrault, 1991: 270; Field, 2009: 242; Hair et al, 2006: 230).
The findings of the study on tolerance and VIF scores are satisfactory. All tolerance values are above the preferable limit of 0.2 ranging from 0.357 to 0.944. Similarly, the VIF scores are at an acceptable level as they range from 1.060 to 2.799.
Based on these findings, it was concluded that multicollinearity did not affect the results of the theoretical model’s statistical analysis.
Table 7.5 Multicollinearity Results
Dependent Controlling CEO Providing Service Controlling External Contingencies
Involvement in Strategy
Seeking Internal Information
Controlling TMT
Independent (Predictors)
Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF External Environment
Complexity 0.588 1.701 0.604 1.656 0.636 1.573 0.624 1.603 0.610 1.639 0.566 1.766
Macro-Envir. Hostility 0.757 1.320 0.710 1.408 0.718 1.394 0.705 1.419 0.722 1.385 0.748 1.337 Competitive Hostility 0.667 1.499 0.676 1.479 0.632 1.583 0.627 1.594 0.614 1.629 0.618 1.619
Dynamism 0.716 1.396 0.707 1.414 0.731 1.369 0.705 1.419 0.733 1.364 0.724 1.381
Board Characteristics Board Size
0.704 1.420 0.793 1.261 0.785 1.274 0.786 1.273 0.742 1.348 0.694 1.440
CEO Duality 0.716 1.398 0.761 1.314 0.758 1.320 0.750 1.334 0.717 1.394 0.718 1.393
Frequency of Meetings 0.865 1.156 0.944 1.060 0.932 1.073 0.924 1.082 0.875 1.142 0.876 1.142 Ratio of Independent 0.357 2.799 0.448 2.233 0.433 2.308 0.431 2.322 0.380 2.630 0.386 2.593 Director’s Status
Status in Board 0.390 2.566 0.503 1.987 0.517 1.935 0.528 1.893 0.462 2.162 0.432 2.313
Tenure in Board 0.791 1.264 0.849 1.178 0.864 1.158 0.859 1.164 0.809 1.236 0.798 1.253
7.6 Summary
In this chapter, after summarising all scales used in the study, the results of correlation analyses were provided, examining the relationship between environmental dimensions, board characteristics, status of respondents (directors) and board roles. The purpose was to conduct a preliminary investigation of the potential relationships based on the developed hypotheses from Chapter 3 as shown in Table 7.3.
Moreover, to further examine the hypothesised relationships, the ordinary least squares method was applied to estimate the unknown parameters of the six linear regression models of the study. Each of the six models had a role of directors as a dependent variable, which derived from the principal component analysis of Chapter 6.
The independent variables in all six models remained the same, assuming that they might predict any of the roles that the directors undertake when sitting in boards. These variables captured the three main independent constructs of the study. Firstly, external environment was measured with four dimensions (i.e. complexity, macro-environmental hostility, competitive hostility and dynamism). Secondly, board characteristics were measured with four variables (i.e. board size, CEO duality, frequency of meetings and ratio of independent). Thirdly, director’s status—capturing the status of respondents—was measured with two variables (i.e. status and tenure in board). Table 7.4 shows the results of all six regression models, while Table 7.5 shows the multicollinearity between the independent variables. The summary of hypotheses tested, both with correlation and regression analyses, is presented in Table 7.6.
The final chapter that follows provides the conclusions of the current study based on the findings, along with the contributions and limitations of the study, making also some recommendations for future researchers.
Table 7.6 Summary of Hypotheses Testing
Propositions Hypotheses Correlation
Result
Regression Result PA1: Board Control is related to environmental complexity. Not supported Not supported
HA1a: Controlling CEO is positively related to environmental complexity.
Not supported Not supported HA1b: Controlling TMT is positively related to
environmental complexity.
Not supported Not supported
HA1c: Seeking internal information is positively related to environmental complexity.
Not supported Not supported
PA2: Board Control is related to environmental dynamism. Partially supported
Not supported HA2a: Controlling CEO is positively related to
environmental dynamism.
Not supported*
Not supported
HA2b: Controlling TMT is positively related to environmental dynamism.
Not supported*
Not supported
HA2c: Seeking internal information is positively related to environmental dynamism.
Not Supported Not supported
PA3: Board Control is related to environmental munificence. Not supported Not supported HA3a: Controlling CEO is positively related to
macro-environmental hostility.
Not supported Not supported HA3b: Controlling TMT is positively related to
macro-environmental hostility.
Not supported Not supported
HA3c: Seeking internal information is positively related to macro-environmental hostility.
Not supported Not supported
HA3d: Controlling CEO is positively related to competitive hostility.
Not supported Not supported HA3e: Controlling TMT is positively related to
competitive hostility.
Not supported Not supported
HA3f: Seeking internal information is positively related to competitive hostility.
Not supported Not supported
PA4: Board Control is related to various board characteristics. Partially supported
HA4d: Controlling CEO is lower when there is CEO duality.
Supported Not supported
HA4e: Controlling TMT is lower when there is CEO duality.
Not supported Not supported HA4f: Seeking internal information is lower Not supported Supported
when there is CEO duality.
HA4g: Controlling CEO is positively related to the ratio of independent directors.
Supported Supported HA4h: Controlling TMT is positively related to
the ratio of independent directors.
HA4j: Controlling CEO is positively related to frequency of meetings.
Not supported Not supported HA4k: Controlling TMT is positively related to
frequency of meetings.
Not supported Supported
HA4l: Seeking internal information is positively related to frequency of meetings.
Not supported Not supported PA5: Board Control is related to respondent’s status in board. Partially
supported HA5d: Controlling CEO is positively related to
the respondent’s tenure in board.
Not supported Supported HA5e: Controlling TMT is positively related to
the respondent’s tenure in board.
Not supported Not supported HA5f: Seeking internal information is
positively related to the respondent’s tenure in board. HB1b: Controlling external contingencies is
positively related to environmental complexity. HB2b: Controlling external contingencies is
positively related to environmental dynamism.
HB3b: Controlling external contingencies is positively related to macro-environmental hostility.
Not supported Not supported
HB3c: Providing Service is positively related to competitive hostility.
Not supported Supported
HB3d: Controlling external contingencies is positively related to competitive hostility. HB4b: Controlling external contingencies is
positively related to board size.
Not supported Not supported
HB4c: Providing Service is lower when there is CEO duality.
Not supported Not supported
HB4d: Controlling external contingencies lower when there is CEO duality.
Not supported Not supported
HB4e: Providing Service is positively related to the ratio of independent directors.
Not supported Not supported
HB4f: Controlling external contingencies is positively related to the ratio of independent
HB4h: Controlling external contingencies is positively related to frequency of meetings. HB5b: Controlling external contingencies is
higher when respondent’s status is HB5d: Controlling external contingencies is
positively related to the respondent’s tenure in board.
Supported Not supported
PC1: Strategic Involvement is related to environmental complexity.
Supported Supported
HC1a: Strategic Involvement is positively related to environmental complexity.
Supported Supported PC2: Strategic Involvement is related to environmental
dynamism.
Not supported Not supported
HC2a: Strategic Involvement is positively related to environmental dynamism.
Not supported Not supported PC3: Strategic Involvement is related to environmental Not supported Not supported
munificence.
HC3a: Strategic Involvement is positively related to macro-environmental hostility.
Not supported Not supported HC3b: Strategic Involvement is positively
related to competitive hostility.
Not supported Not supported PC4: Strategic Involvement is related to various board
characteristics.
Partially supported
Partially supported HC4a: Strategic Involvement has an
inverted-U relationship with board size.
Not supported Not supported HC4b: Strategic Involvement is lower when
there is CEO duality.
Not supported Supported
HC4c: Strategic Involvement is negatively related to the ratio of independent directors.
Not supported Not supported HC4d: Strategic Involvement is positively
related to frequency of meetings.
Supported Supported PC5: Strategic Involvement is related to respondent’s status in
board.
Not supported Not supported HC5a: Strategic Involvement is higher when
respondent’s status is independent.
Not supported Not supported HC5b: Strategic Involvement has an
inverted-U relationship with the respondent’s tenure in board.
Not supported Not supported
*Opposite relationship found