Probability and Statistics for Finance

Chapter 22. Testing the Assumptions of the Multivariate Linear Regression Model

As explained in Chapter 20, after we have come up with some regression model, we have to perform a diagnosis check. The question that must be asked is: How well does the model fit the data? This is addressed using diagnosis checks that include the coefficient of determination, R² as well as R²_adj, and the standard error or square root of the mean-square error (MSE) of the regression. In particular, the diagnosis checks analyze whether the linear relationship between the dependent and independent variables is justifiable from a statistical perspective.

As we also explained in Chapter 20, there are several assumptions that are made when using the general multivariate linear regression model. The first assumption is the independence of the independent variables used in the regression model. This is the problem of multicollinearity that we discussed in Chapter 21 where we briefly described how to test and correct for this problem. The second assumption is that the model is in fact linear. The third assumption has to do with assumptions about the statistical properties of the error term for the general multivariate linear regression model. Furthermore, we assumed that the residuals are uncorrelated with the independent variables. In this chapter, we look at the assumptions regarding the linearity of the model and the assumptions about the error term. We discuss the implications of the violation of these assumptions, ...