Metric Relationship Analysis
In this spreadsheet we introduce you to ways of understanding relationships between supply and demand metrics.
The first thing we must do is define a metric that measures the extent of a relationship.
Think about the relationship between price (P) and quantity sold (Q). We know that as P is lowered Q increases.
But how much do changes in price explain changes in quantity sold? How much does variance in P explain variance in Q?
Is it 100% of the explanation? No, because we know that other variables such as the state of the economy also explain variance in Q.
Could P explain 50% of Q?
Possibly. It is this "relationship metric" called explained variance that we learn to think about in this
worksheet.
In the first worksheet below studying metric relationships, we look at the relationship between a brand's differentiation from its
competition and its profit margins.
We want you to learn to study the graph of the relationship and compute a correlation
coefficient.
The way you study the correlation between the metrics/measures is to compute a correlation coefficient that is called "r" for short.
If r is close to 1 there exists an extremely high positive correlation between the measures.
If r is close to zero there is no correlation. For example a correlation of 0.20 is a very weak positive relationship.
If r is close to 1 there is an extremely high, inverse or negative relationship between the measures: when one is high, the other is low.
A correlation coefficient of 0.7 when squared is 0.49 and this is the percentage of variance explained (49%).
Please remember this way of describing a relationship:
"the square of a correlation coefficient multiplied by 100 is the percentage
of variance in one variable explained by variance in the other, and vice versa."
A note about what percentage (%) means. 50% of something means half of something. 25% of something means one quarter of
something. 0.81 of something is 81% of something.
Below are presented three relationship studies where you will learn to understand graph analysis and explained variance analysis.
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How to compute and see the relationships between marketing supply and demand metrics
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Is Product Differentiation Profitable?
This relationship study is based on a report published by The Conference Board, New York, 1982, called Product Line Strategies.
It studied 25 brands in packaged goods categories sold in supermarkets, and specifically, the relationship between consumer brand
substitution (percentage of time brand is replaced by a substitute) which we call Sub% and the brand's net profit margin percentage
which we call Margin%.
The higher the margin%, the higher the brand's profit margin percentage.
The theory of product differentiation says that the more you distance yourself from the substitution competition of rivals
the greater your profit margins. You can test this proposition below.
When Sub% is low, product differentiation
is high so profit Margin% should be high.
When Sub% is high, product differentiation is low so Margin% should be low.
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 Spring '11
 Biritella
 Marketing, Correlation, Profit margin, Correlation and dependence, Pearson productmoment correlation coefficient, Spearman's rank correlation coefficient

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