David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

2. 7 Diagrams, lines and equations
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Figure 2.3 Tube fares and revenues, 1999/00-2008/09
•
•
18.2 18.4 18.6 18.8 19.0
Real fare (08/09 pence)
It is useful to present evidence such as that in Table 2. 7 in a scatter diagram such
as Figure 2.3. The horizontal axis measures column (3), the real fare per passenger
kilometre. The vertical axis measures column (1), real revenue in constant million
pounds. Real revenue is the real fare per passenger kilometre multiplied by the
number of passenger kilometres travelled.
A scatter diagram plots
pairs of values simultaneously
observed for two different
variables .
From Figure 2.3 we can see a positive relationship between real fare and real revenue. Other things equal,
higher fares reduce the number of tube journeys, but if quantity demanded falls only a little, overall revenue
may rise when fares are increased. Certainly, in some years, passenger use rose strongly despite higher fares.
But we have not yet got to the bottom of things. We return to this issue in Section 2.8.
( ttd Diagrams, lines and equations
'II/I _ _ _ _ _
If we can draw a line or curve through all these points, this suggests, but does not prove, an underlying
relationship between the two variables. If, when the points are plotted, they lie all over the place, this
suggests, but does not prove, no underlying relationship between the two variables. Only if economics
were an experimental science, in which we could conduct controlled experiments guaranteeing that all
other relevant factors had been held constant, could we interpret scatter diagrams unambiguously.
Nevertheless, they often provide helpful clues.
Fitting lines through scatter diagrams
In Figure 2.3 we did draw a line through the scatter of points we plotted. The line shows the average
relation between fares and revenue between 1999/00 and 2008/09. We can quantify the average relation
between fares and usage.
Given a particular scatter of points, how do we decide where to draw the line, given that it cannot fit all the points
exactly? The details need not concern us here, but the idea is simple. Having plotted the points describing
the data, a computer works out where to draw the line to minimize the dispersion of points around the line.
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