Financial Risk Manager Part 1

The omission of a crucial explanatory variable, which has significant influence on the explanatory variables included as well as the dependent variable, can lead to an overstatement of the explanatory power of regression analysis. This is because the omitted variable can have a significant effect on both the dependent variable and the included explanatory variables. This violates one of the assumptions of the Ordinary Least Squares (OLS) model, which states that the error term should be conditionally independent of the explanatory variables. When this assumption is violated, the error term can become correlated with the explanatory variables, leading to biased and inconsistent estimates. This can incorrectly increase the explanatory power of the regression, leading to misleading conclusions about the relationships between the variables.

Choice A is incorrect. The normal distribution of the residual term does not lead to an overstatement of the explanatory power of regression analysis. In fact, it is one of the assumptions in a standard linear regression model.

Choice B is incorrect. The lack of correlation among explanatory variables does not result in an overstatement of the explanatory power. On contrary, multicollinearity (high correlation among predictors) can inflate the variance of the coefficient estimates and make them unstable and difficult to interpret.

Choice D is incorrect. The number of explanatory variables itself doesn't lead to an overstatement or understatement of regression's explanatory power. It's more about whether these variables are relevant and correctly specified in relation to dependent variable.