Q.1: What appears to happen to the average levels of duplication as you look across the columns from left to right? When we look across the columns from left to right, the average levels of duplication reduces. The purchase duplication table has been rearranged by the size of the brand, with rows and columns in descending brand penetration level. Average duplications of each brand are calculated. This clearly shows that the proportion of the buyers of one brand who also bought another particular brand in the time period covered by data reduces as the penetration level also reduces. In other words, it shows that the brands follow the Duplication of Purchase (DoP) law. This law states that brands share customers in line with market share (Ehrenberg & Goodhard, 1969). That is customers will opt of a different product similar to the one they were buying from another brand based on its market share. Quantitatively speaking, when we scatter plot the penetration vs. average duplication, be get a strong linear relationship between the two variables.
Q 2: What is your interpretation of this result? Explain what “duplication = 2 x penetration” means.
The result from the scatter plot of the penetration (in X axis) and duplication (in Y axis) shows a strong linear relationship between the two variables Penetration and Duplication. The equation y = 1.978x is written as: Duplication = 2 x Penetration
This is the relationship between duplication and penetration used to create ‘expected’ purchase duplications for each combination of brands. This is useful to quickly summarize the extent of purchase sharing in the market and to identify exceptions.
According to the relationship derived from the graph, the average duplication for a brand is around twice its penetration, except for the largest brand.
Q3: What is the average duplication and average penetration for the brands in this table?
The average duplication over all brands is 33 and average penetration...