Today we’re going to do some thinking and learn about statistical demand analysis. Why is statistical demand analysis important? Because estimating product demand is essential to reduce the risks inherent with pricing, production and inventory decisions. A failure to accurately estimate demand can lead to over or under production, and if priced incorrectly can negatively affect profits.

**How is demand determined?**

We’ll talk about two types of demand: Consumer demand and Market or Industry demand.

- Data on consumer demand is usually obtained through consumer surveys by asking how much they would purchase at a given price point (predictive) or how much they have purchased in the past (retrospective).

- Market Demand is looked at through a series of price changes over time and analyzing the subsequent change in purchasing activity. Finally, and the point we will focus on, using naturally observed data on price and quantity and subjecting them to statistical demand estimation.

**Statistical Demand Analysis using Liner Regression Model**

Recall that regression analysis is a statistical technique for estimating the relationship between variables. In this case, Demand as a result of price vs quantity sold, city, production, consumer demographics, etc. Demand, being the dependent variable, is shown in relation to and linked to various parameters (aka assumptions) explaining the relationship. This is shown by the following linear regression model:

*Q = a + bP + cM + dPR +u*

Q = quantity demanded (observed) and is the dependent variable

P,PR,M = price, price of related goods, income (observed) = independent variables.

u = random error (not observed)

a,b,c,d, = parameters – unknown and estimated.

Using regression analysis the analyst first obtains a set of survey data (regression data) for Q, P, Pr and M. Next an estimation of a, b, c, and d is used. These estimations are difficult and rely on experience, industry knowledge and internal data. When done, you test for significance of the parameter values and using the estimated values of the parameters for analysis, are able to predict the future value of the dependent variable, e.g. demand.

There are three types of regression data: Time series, Cross section and Panel data. Time series is an observation made of different time periods while Cross section is for different observations at the same point in time. Panel data is a combination of both. These are the Data for Q, P, Pr and M.

## Specify the Demand Model

Here we’re talking about the unknown or estimated parameters. It is up to the analyst to determine if she will rely on consumer behavior, price, income, price of related goods, size of market, tastes, price expectations etc. Then, choosing a functional form, usually a choice between liner form and power function.

Linear form looks like this:

*Qx – a + bPx + cPr + dM + eN + u*

The parameters in this linear function tell the change in Qx for 1-unit change in the associated variable. It looks like this”

b = ?Qx/?Pr ; c = ?Qx/?Pr; d = ?Qx/?M; e = ?Qx/?N

Determining demand is not an exact science and the accuracy of any prediction is based, in large part, on the experience, knowledge and industry expertise of the analyst. This is true because of the assumptions the analyst must make in determining the unobserved and unknown variables present in the linear regression analysis.

Linear regression analysis for statical demand gives a more accurate picture of future demand rather than relying on crude projections based on past sales.

We did not cover the power function which is used frequently if the analyst believes demand is non linear. If anyone can tell me how the power function would look, feel free to comment. See you next time in Making Molehills out of Mountains University, Market Analysis 101.