Applying Regression Analysis: A Case Example

To demonstrate the utility of regression analysis, we will apply a simple linear regression technique to a hypothetical situation. Auto, Inc., a fictional automobile manufacturer, is interested in estimating the value derived from a proposed Strategic Alternative (SA). The SA, posed by the CEO of the company, is to acquire an elite, high-end auto company where the average retail price of a car is $80,000. As part of this task, the acquisition team develops a three-year market analysis to determine if adequate market demand exists for luxury automobiles. The team chooses to use the predictive power of regression analysis to help make these projections.

Step 1: Develop an Equation

The first step in this process is to understand what drives total market demand for elite, high-end luxury automobiles. After analyzing the industry, the group hypothesizes that gross domestic product, or GDP, is a key predictor of market demand for these automobiles. In this situation there is only one variable with a substantial relationship to total market demand for luxury vehicles. A simple linear regression analysis is used, represented by the equation:

In the equation, the variables represent the following:

• Y equals unit demand for elite, high-end luxury automobiles.

• x equals gross domestic product.

• a equals the variance in demand not explained by GDP.

• b equals the regression coefficient indicating the relationship between GDP and unit demand, or

This equation expresses that GDP is a key predictor for the market demand for elite, high-end luxury automobiles. With this hypothesis formalized, the company can now gather data for the analysis.

Step 2: Collect the Data

Now that Auto, Inc., has decided to analyze the relationship between GDP and unit demand for these automobiles, the company team can collect the data that will reveal the relationships between those variables. To gather historical GDP data, the team turns to online databases located on the Federal Reserve Board website.^[2] To gather data on new vehicle sales for elite, high-end luxury cars, it uses the Bureau of Labor Statistics' online databases on new vehicle car sales.^[3] Having consulted these research sources, the following data is gathered in Exhibit 9-1.

Exhibit 9-1: The GDP data for Auto, Inc.

Historical New Car Sales (Unit Demand) and GDP Data
Year	Demand1 (000's units sold)	GDP2 (billions of dollars)
1991	2294	5927.9
1992	2706	6221.7
1993	2947	6560.9
1994	2637	6948.8
1995	2619	7322.6
1996	2770	7700.1
1997	2734	8182.8
1998	3393	8636.3
1999	3652	9115.4
2000	3377	9571.9

While this example analyzes ten years of data, modern statistical software allows for a much more extensive analysis of time-series data. As a rule of thumb, a more complex analysis requires more data to achieve the same level of certainty around the relationships between them.

Step 3: Conduct and Interpret the Analysis

Because popular statistical software such as SPSS, SAS, and Minitab are often expensive, they decide to use the data analysis function, under the tools menu item, in the Microsoft Excel application.

When a regression analysis of this data is run in Excel, the result in a correlation coefficient (the "b" variable in the equation above) is .60. This coefficient means that 60 percent of the changes in unit demand for luxury automobiles can be explained by changes in the gross domestic product. Because the number is positive, the changes in each variable are directionally consistent. That is to say that when GDP increases, so do the sales of luxury automobiles. This number confirms to the team at Auto, Inc., that GDP is a valid predictor of luxury auto sales. With this confirmation, the team can now finish the forecasting process.

The regression analysis the team just performed on the unit demand and GDP data established an equation that describes the relationship between the two variables. This equation can be used to predict the unit demand for luxury cars based on different levels of GDP. Unit demand is the dependent variable, and the GDP is the independent variable in the equation. While this can be done manually, as with most statistical analyses, by "plugging in" predicted GDP values and solving this equation for the unit demand, it can also be done with the forecast function in Excel. This function uses regression analysis to forecast values for a given set of data. However, before the team can forecast unit demand for luxury autos over the next three-year period, the team will have to provide Excel estimates for GDP. Fortunately, the government provides GDP predictions in its historical databases. The team can simply extend the table that was originally created in Excel to include estimated GDP for the years 2001, 2002, and 2003. The forecast function can then be used to calculate predicted unit demand levels in those years. The outcome (illustrated in Exhibit 9-2) would resemble the following:

Exhibit 9-2: Unit demand predicted from estimated GDP (2001 to 2003) for Auto, Inc.

Unit Demand Predicted from Estimated GDP (2001–2003)
Year	Demand ('000s units sold)	GDP (billions of dollars)
1991	2294	5927.9
1992	2706	6221.7
1993	2947	6560.9
1994	2637	6948.8
1995	2619	7322.6
1996	2770	7700.1
1997	2734	8182.8
1998	3393	8636.3
1999	3652	9115.4
2000	3377	9571.9
Forecast for Unit Demand
2001	3604	10,041.3
2002	3736	10,502.4
2003	3873	10,982.8

The output of the analysis in Exhibit 9-2 shows that total unit demand for luxury cars, or number of cars sold, is predicted to reach 3,873 in the year 2003, provided that the GDP reaches its projected level of almost $11 trillion. Assuming an average price of $80,000 per car, the total market demand for elite, high-end luxury cars in 2003 is predicted to be $309,840,000:

Of course, the team realizes that Auto, Inc., does not own the market for elite, high-end luxury cars. Therefore, it must take this fact into consideration when attempting to predict the company's realistic market opportunity. Assuming Auto, Inc.'s market share will hover around 30 percent in 2003, the company would have a realistic market opportunity of $93 million:

The team has now completed its task of predicting total market demand, and the resulting market opportunity, for the Strategic Alternative proposed by the CEO of the company. However, its work does not stop there. To fully evaluate the proposed SA, the team will have to consider the costs of the Strategic Alternative by building similar predictions. By following a similar process, it can also apply regression analysis techniques to help predict other variables such as the cost of raw materials, labor, and other factors.

^[2]The figures under the column headed "Demand" (Exhibit 9-1) represent new vehicle purchases by the top 20 percent, according to household income, of the consumers in the United States. This information was found on the Federal Reserve Board website.

^[3]The figures under the column headed "GDP" (Exhibit 9-1) represent the total GDP output of the United States. This information was found on the Bureau of Labor Statistics website.