The R squared values in the econometric model explain the percentage of the dependent variables explained by the independent variables (goodness of fit). R squared lies between the values of 0 and 1 (Campbell, Lo and MacKinlay, 1997). Thus in our case, the value of R squared closer to one shows that market capitalisation, return on total assets, price to book value ratio, gearing ratio, shareholders concentration, CEO duality, board size and procedures involved in enforcing the contract, explain most of the variation in the value of a firm.
The t test will be used to check the significance of individual parameters (hypotheses) in the regression relevant for the study. These individual hypotheses are related to the relationship between market capitalisation, return on total assets, price to book value ratio, gearing ratio, shareholders concentration, CEO duality, board size and procedures involved in enforcing the contract with the value of a firm.
Furthermore, the f test will make the partial slopes of coefficient equal to zero and will check the significance of all the parameters (hypotheses) in the model. The significant f statistic will show a relationship between the dependent variable (value of a firm) and independent variables mentioned above.
The relationship between the dependent and independent variables will be tested by accepting or rejecting the alternative hypothesis. In this study, the alternative hypothesis will be tested against the null hypothesis, which suggests a lack of relationship between the value of a firm and corporate governance instruments in developing and developed financial markets.
The t and f statistics in the CGVF models will only give us the correct results if the model follows the classic linear regression assumptions (Gujarati, 1995). These assumptions are as follows:
1) the error terms have a constant variance in all the observations in the CGVF; 2) there is a lack of a relationship between the regressors of the CGVF models in
3) the explanatory variables in the model for the CGVF must take a fixed value in the repeated samples;
4) there is a linear relationship between dependent and independent variables, and the error term of the CGVF models;
5) the expected value of the error term is zero for all the observations in the CGVF model; and
6) the error terms are independent of each other in different observations in the CGVF models.
In case of the violation of the classic linear regression assumptions, the following problems will arise.
Multicollinearity
According to Cuthbertson (1996), multicollinearity takes place in the model when the independent variables are related to each other. Multicollinearity will arise in the CGVF models if the independent variables (market capitalisation, return on total assets, price to book value ratio, gearing ratio, CEO duality, board size, shareholders concentration and procedures involved in enforcing the contract) of the models in the current study are related to each other. Multicollinearity will be detected when the model has a high R squared, but insignificant t ratios of the above-mentioned variables.
The high standard errors of the variables will also be a sign of high collinearity. In contrast, indeterminate coefficients with large standard errors will show a perfect collinearity in all the above-mentioned variables (Gujarati, 1995).
The tolerance factor and variance inflation factor of each corporate governance variable in all the CGVF models in developing and developed financial markets will be calculated to detect multicollinearity. The value of the variance inflation factor greater than 10 and the tolerance factor closer to 0 will show the presence of multicollinearity in the CGVF models.
variables (board size, shareholders concentration, CEO duality, market capitalisation, price to book value ratio, gearing ratio, return on total assets and procedures) the dependent variable and calculating R squared. R squared will be substituted in the formula below to get the final value.
The formula below is used to calculate the variance inflation factor:
VIF = 1 / 1 - R2 (4.19)
The tolerance factor in the CGVF models will be calculated by making all the above- mentioned variables as the dependent variable and calculating R squared. Finally, the R squared will be subtracted from one to get the value for the tolerance factor.
The formula below is used to calculate the tolerance factor:
TF = 1 - R2 (4.20)
The variables of the CGVF models having multicollinearity will be exchanged with new variables to solve the problem.
Autocorrelation
The relation of the error term of the CGVF models Ut in the first time period will be
checked with the error term of the model in the next time period to detect autocorrelation with in the model.
The problem of autocorrelation will emerge in the CGVF models if the error terms of the models for two different time periods are related to each other. The estimators of the model will be inefficient in the presence of autocorrelation, but remain consistent and unbiased. In addition, the econometric results of the hypotheses relevant to the CGVF will not be robust in the presence of autocorrelation.
The Durbin Watson test will be used to detect autocorrelation in the CGVF model. A value of Durbin Watson statistic lower or higher than 2 will show the presence of
autocorrelation. In the case of a lower or higher value, we will take standard remedial measures to remove the autocorrelation from the CGVF model.
Heteroscedasticity
The variance of the error term of CGVF models will also be observed. The variable variance will lead us to the problem of heteroscedasticity. The estimators of the model in this case will be inefficient, but will remain unbiased and consistent making the results of study unreliable.
White diagonal measure will be used to remove the heteroscedasticity in the CGVF models. This treatment will be used to correct the variance of the error term of the model as we will divide the error term with its variance. The estimation will be different from OLS estimation because we will minimise the weighted sum of residual squares. The method is known as generalized least square (GLS) estimation and will enable us to get a reliable result about the acceptance and rejection of hypotheses relevant for the CGVF models.