Modeling

Companies develop models to support many business functions and activities. A Model represents a mathematical representation of an area of interest. Mainly, Models are used for forecasting and for gaining insights into how various factors interact. The subject being modeled is called the Dependent Variable and the factors used to "explain" the Dependent Variable are called the Independent Variables.

The typical modeling process is to gather the variables together and run multiple regression modeling software to obtain the model. The mathematics embedded in the software help sort out which of the Independent Variables are significant in statistical terms - meaning that they are very likely (with high assurance) to be actually related to determining the various values of the Dependent Variable in the data set. The resulting model can be used to forecast the Dependent Variable (variable of interest) if there are forecasts of the Independent Variables available.

A model is also very useful, however, to explain the relationships between the Dependent Variable and the other variables. For example, if the Dependent Variable was the Quantity of a product purchased over time, and one of the Independent Variables was the Price of the product over time - the resulting model would shed light on the relationship between the Price charged and the Quantity purchased - a relationship critical to virtually all businesses that can only be captured (cost effectively) in this manner.

Qualitative Variables

Modeling is very much a mathematical exercise, and the variables used are almost always a set of numbers representing direct measurements (like a consumer price index) or direct observations (like how many were purchased). Inclusion of softer variables - Qualitative Variables - like tactics, strategies, feelings, and other items of critical importance that do not easily lend themselves to quantification are not typically included in modeling efforts because there is no data to define them. That's where TrendIQ enters the process.

TrendIQ technologies can be used to quantify softer (qualitative) variables into quantitative form suitable for modeling purposes. This opens the door to both more sophisticated models that explain the Dependent Variable more fully, but to testing various softer factors to understand their relationship (if any) to the Dependent Variable.

Example: Forward PE Ratio - Wireless Communications Companies

Here we include an example of an actual model for Wireless Communications Companies (See list). Using only the public companies where Forward PE Ratios are available, TrendIQ maintains a model to explain the set of Forward PE Ratios for this industry group. Forward PE Ratios show the current price of a stock divided by the company forecast of future earnings, and the ratio therefore represents a measure of how expensive a company stock is relative to other stocks. Forward PE Ratios are useful for many purposes and here is a good reference.

The Model

Here we show a summary of the actual model. The R-Squared is 85% and is a measure of the percentage of the Dependent Variable (Forward PE Ratios) that was actually explained in the model. The Variable column lists the variables that were used. The Coefficient column represents the constants that are multiplied by the Variables for each company to get a mathematically based best forecast of a company's PE Ratio. The T-Statistics are a measure of the significance of each variable, and in this type of model (cross sectional - i.e. at a point in time), T-Statistics above 1 (in absolute value) are generally considered significant.

Multiple R Squared = .85

Variable	Coefficient	T-Statistic
Intercept	12.65268	+3.53
Variable 1	-3.03409	-1.88
Variable 2	-3.89002	-2.26
% Held By Institutions	8.990762	+2.17
Wireless Association	40.20196	+5.04
Large Business Market Association	1341.455	+2.05
Residential Customer Association	-55.8277	-2.53
Etc.

The "% Held By Institutions" is a Quantitative Variable that is readily available for each company - for example, see here for Airspan Networks. The model shows it is significant (T-Stat = 2.17) and that it is positively related to the Forward PE Ratio - that is, the higher the % stock held by Institutions the higher the Forward PE Ratio is likely to be; and the Coefficient says exactly how much. Variables 1 and 2 are not disclosed here to protect the investment of current TrendIQ customers, but three TrendIQ Qualitative Variables are included to demonstrate the power of this approach.

Wireless Association

The variable called "Wireless Association" is a TrendIQ generated measurement of the degree to which each company is actually associated with wireless - and it varies significantly across companies. The graph below shows the measured value for a subset of the companies in the analysis:

As it turns out, the TrendIQ generated variable is statistically significant (T-Stat = 5.04) and positively related to the Forward PE Ratio - meaning that the more a company is associated with Wireless, the higher the Forward PE Ratio is likely to be. Another interpretation is that companies with a higher association with wireless are more highly valued by investors than companies with a lower association.

Residential Association

Another variable in the model above is "Residential Association" - a TrendIQ generated variable that measures the degree of association of each company with the Residential customer market (home market). Here we have the interesting result (statistically significant) that there is a negative relationship. Companies that have a higher association with residential customers (i.e. companies that target this market more) are penalized by the market in terms of the value assigned to the company stock. The variable called "Large Business Market Association" can be similarly interpreted - but has a positive relationship to company valuation (Forward PE Ratio).

Conclusion

TrendIQ generated variables can add a significant new capability to traditional modeling by including concepts that were previously difficult to quantify. This capability not only improves models from the standpoint of forecasting a variable of interest - but also provides valuable insights into how softer variables actually relate to subjects of interest.

Statistical Note

For readers that are statisticians - certain liberties taken in the explanation above were to make the discussion more readable and understandable to a wider audience. All mathematical results are accurately provided.

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