Scatterplots: Graphing Relationships

1
Example 15.1

• Scatterplots Graphing Relationships

2
Background Information

• Pharmex is a chain of drugstores that operates
  around the country.
• To see how effective their advertising and other
  promotional activities are, the company has
  collected data from 50 randomly selected
  metropolitan regions.
• In each region it has compared its own
  promotional expenditures and sales to those of
  the leading competitor in the region over the
  past year.

3
Background Information -- continued

• There are two variables each of which are
  indexes, not dollar amounts.
• Promote Pharmexs promotional expenditures as a
  percentage of those of the leading competitor
• Sales Pharmexs sales as a percentage of those
  of the leading competitor
• The company expects that there is a positive
  relationship between the two variables, so that
  regions with relatively more expenditures have
  relatively more sales. However, it is not clear
  what the nature of this relationship is.

4
PHARMEX.XLS

• The data are listed in this file. Here is a
  partial listing.

• What type of relationship, if any, is apparent in
  a scatterplot?

5
Creating the Scatterplot

• In preparing to create the scatterplot we must
  decide which variable should be on the horizontal
  axis.
• In regression analysis, we always put the
  explanatory variable on the horizontal axis and
  the response variable on the vertical axis.
• In this example the store tends to believe that
  large promotional expenditures cause larger
  values of sales, so we put Sales on the vertical
  axis and Promote on the horizontal axis.

6
Creating the Scatterplot -- continued

• We create the following scatterplot using
  StatPros Scatterplot procedure.

7
Interpretation

• The scatterplot indicates that there is a
  positive relationship between Promote and Sales -
  the points tend to rise from bottom left to top
  right - but the relationship is not perfect.
• The correlation of 0.673 is shown automatically
  on the plot. The important things to note about
  the correlation is that it is positive and its
  magnitude is moderately large.

8
Causation

• Unless the data is obtained in a carefully
  controlled experiment - not the case here - we
  can never make definitive statements about
  causation in regression analysis.
• The reason for this is that we can almost never
  rule out the possibility that some other variable
  is causing the variation in both of the observed
  variables.