Two separate models were developed using Ordinary Least Squares model to assess the causality between the market share and concentration of the banks and their ROA and ROE. For a typical OLS model, the ANOVA table checks the validity of the regression model as a whole. For the F-test in ANOVA, the null and the alternative hypotheses are:
H0: All the coefficients are simultaneously equal to zero
H1: At least one of the coefficients estimated in the model is statistically different from zero
Thus, for a model to be statistically significant, it is important that the null hypothesis in the above set of hypotheses be rejected.
The individual estimates of the coefficients then show their share of causation on the dependent variable. Here also, the coefficients need to be checked if they are statistically different from zero. This done through the t-test which has the following set of hypotheses:
H0: The coefficient is statistically not different from zero
H1: The coefficient is statistically different from zero
The model clearly points that for a unit increase in market size of the bank, the ROA is expected to increase by 0.026 ceteris paribus. Similarly, all other things held constant, if the deposit increase by a unit, the ROA is expected to increase by 3.211 x 10-12. Likewise, if all the other variables are held static, or a unit increase in GDP, the ROA of the banks is likely to go down by a fraction of 1.072 x 10-14. The other variables are statistically not significant which means that their effect on the dependent variable is so small that they can be safely ignored.
Thus, the model of ROA shows that the market share and the deposits of the bank affect it positively while the GDP of the economy affects it negatively.