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The principle of all statistical models is to fit observable attributes, such as financial variables of firms, to variables to be predicted, such as default or non-default, or the rating of the firm.

The simplest technique for doing so is the simple linear regression, or variations of this technique. This technique provides valuable findings. For instance, it is relatively easy to show that risk decreases when the size of the firm increases, at least over some range of size values, measured by sales or total assets. A common finding of many simple or elaborated models is that the operating profitability, such as operating income or EBITDA to total assets—or Return On Assets (ROA) is a good predictor of risk and of default. Note that such findings are purely empirical, although they comply with intuition. Variables listed in Chapter 35 on rating systems are good candidates for such ingredients of empirical models.

However, simple multivariate analysis (linear regression, because it assumes a linear relation between predicted outputs and inputs) suffers from important limitations. This is why various other techniques were implemented. For instance, the relationship between rating and size, measured by assets or sales of firms, is not linear, but large firms tend to have better ratings. The RiskCalc documentation (Moodys Investors Service, 2000b) visualizes some of them. Size does not discriminate as much against smaller firms, because their credit standing depends on other factors, such as operating profitability and leverage. Note that simple regressions accommodate many non-linear relationships to a certain extent. For example, it is possible to use the logarithm of size, measured by total assets or sales, rather than asset or sale values, to better mimic the actual relations observed.