Data Normalization

#1
I have a problem that is challenging to me about fitting coefficient parameter. Here is the problem data (simple example)

Customers____________________Demand_____________________Price
C_A____________________________50__________________________3.3
C_A____________________________60__________________________3.1
C_A____________________________40__________________________3.4
C_B____________________________300_________________________2.6
C_B____________________________250_________________________2.7
C_B____________________________350_________________________2.35

The goal is to fit the coefficient parameter (A) about how demand responds to price changes. That is, Demand = C + A*Price + Error.

My point is that, such data cannot be directly used in fitting A, because there are big differences in bases of customer needs and pricing strategy differences for various customers. Herein, such two variations need to be removed by NORMALIZATION before we do regression. The normalization procedure means to put demand and price into the same level. After normalization, the data becomes as below:

Customers________________Normalized Demand________________Normalized Price
C_A_______________________50*(175/50) = 175___________________________2.94
C_A_______________________60*(175/50) = 210___________________________2.76
C_A_______________________40*(175/50) = 140___________________________3.03
C_B_______________________300*(175/300) = 175_________________________2.97
C_B_______________________250*(175/300) = 146_________________________3.08
C_B_______________________350*(175/300) = 204_________________________2.68

In the table, 175 is the overall demand average.

The purpose of the normalization procedure is to remove the variations existed in customer need bases and pricing differences for different customers. However, it still well preserves the sensitivity of prices on demand for each customer, and put them into the same level. We can then do parameter A fitting after normalization.

My question to you is that: Do you think whether this method is statistically valid? If not, do you know any existing statistical method to handle such data issue? Appreciate your help for this.
 
Last edited:

rogojel

TS Contributor
#2
hi,
one method you could use instead of the normalitation, would be to define price classes . So, all prices in the range of 20-100 would be in class C1 Prices in range 200-500 in range C2 etc. Using a class dummy variable you could model the different baselines and if you add interaction terms of the class and demand variables then even (possibly) different reaction in different price classe to a change in demand.

regards