Chapter 7: Projecting Retail Sales

The Regional Economic Analysis Division (READ) of the Bureau of Economic Analysis is a unit of the U.S. Department of Commerce. READ is responsible for developing and interpreting the regional economic accounts of the United States. READ develops methods for estimating gross state product; maintains and improves regional economic projections; and develops analytical techniques for regional economic impact studies.

READ performs regional economic impact analyses, which estimate the effect of a particular event or change in policy on a state's economy. In these analyses, one of the techniques READ economists use to estimate the mathematical relationships among economic variables is regression analysis.

For instance, READ analysts estimate that the total amount spent S in eating and drinking establishments in Ohio depends primarily on the number P of adults in the state and their level of disposable (after tax) personal income I. When either of these variables increases, there are more dollars spent on eating and drinking in Ohio restaurants and bars.



Using annual data on these three variables for the 1970 to 1991 period, READ has used multiple least squares regression methods, a variation of the least squares regression line discussed in Section 7.7, to determine that the actual relationship is



where S is retail sales of Ohio eating and drinking establishments in millions of dollars, I is disposable personal income in millions of dollars, and P is the adult (18+) population of Ohio, in thousands.

This regression equation shows that an increase of $1 million in Ohio income (I) will result in $38,000 more spent in Ohio's restaurants and bars (0.0385 X $1,000,000).

In the business world, it is useful to have an idea of the impact that forces outside a firm's control will have on a business. If projections of Ohio income and population are available, this equation will give an expected value for retail sales in eating and drinking establishments for future years.

These types of equations could be quite useful to firms in their planning process.

 

What Would You Do?

 

1. If Ohio's adult population increases by a thousand, what does the model predict about sales in restaurants and bars?

2. Suppose a recession is predicted to lead to a 7% overall drop in disposable income. What does the model predict about sales in restaurants and bars?

3. Explain the meaning of the partial derivatives

and

(See Section 7.4 for help with partial derivatives.)

4. Can you think of other variables that affect restaurant sales which might be added to the regression equation to improve its ability to predict?