# How to Calculate a Demand Function Using Regression Analysis

by Jan Gerards; Updated September 26, 2017Statistics can help us break down human behavior into mathematical relationships, and help us predict future behavior. In economics and business, demand functions can be used to help predict the price and success of goods in the future. Multiple regression analysis is used to obtain the demand function. This can be done on dedicated statistical packages, or on spreadsheet programs which often have optional statistical packages.

Gather your data. You must include a variable representing demand (price), as well as producing a list of variables that determine demand; examples can be found in standard economics textbooks. You must have access to quantitative data on these variables. One type of variable is the price of substitute or complement goods. Taking the example of a producer of corn flakes, a substitute for their good is bran flakes. A complement to corn flakes is milk. Another important determinant is the income of consumers.

Organize your data into vertical columns in a spreadsheet. In our example, we could have the price of cornflakes in consecutive months throughout a two-year period in the left-most column (the dependent variable). The next column could be the price of bran flakes at each date, followed by the price of milk, the income of the consumers, the dummy variable for exports, and so on. Each row contains all the variables for a given date.

Download and install a statistical package for your spreadsheet software. For Microsoft Excel, this is the “Data Analysis ToolPak.” Alternatively, use a dedicated statistical package such as "Eviews."

Select the regression option in your software package. In Excel, select “Data Analysis” under “Tools,” and select the multiple regression option.

Input the data for the dependent variable (Y) and the independent variables (X). In our example, price is the dependent variable, in the left-most column, and the price of bran flakes, milk, and the income of consumers are the independent variables.

Run the regression. This should give you the coefficients, or the parameters of your demand function. In our example, the first coefficient will be a number quantifying the impact of the price of bran flakes on the price of cornflakes. The next coefficient will be for milk, and so on. Include only those that are statistically significant. You must decide on your level of significance, whether it is at the 10 percent level, the 5 percent level or the 1 percent level. The significance is given by the “P value,” given alongside the coefficient, where P=0.01 for a 1 percent significance level.

Write up your demand function in the form: Y=b1x1+b2x2+b3x3, where Y is the dependent variable (price, used to represent demand), X1, X2 and X3 are the independent variables (price of corn flakes, etc.) and b1, b2 and b3 are the coefficients or parameters of your equation.

#### References

- "Applied Regression Analysis"; Draper, N. and Smith, H.; 1998

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