Page 47 - Intermediate Statistics for Dummies

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Part I: Data Analysis and Model-Building Basics
some way, they’re not quantitative variables, so you can’t discuss their rela-
tionship in terms of a correlation. (In this case, you would use the term asso-
ciation; in Chapter 14, you see how to test for association of two categorical
variables.)
The long and short of correlation is the following: Correlation is a number
between –1.0 and +1.0. Positive one indicates a perfect positive relationship;
in other words, as you increase one variable, the other one increases in per-
fect sync. On the other side of the coin, a correlation that is –1.0 indicates a
perfect negative relationship between the variables. As one variable increases,
the other one decreases in perfect sync. A correlation of zero indicates that
you found no linear relationship at all between the variables. Most correla-
tions in the real world aren’t exactly +1.0, –1.0, or 0 — they fall somewhere in
between. The closer to +1.0 or –1.0, the stronger the relationship is; the
closer to 0, the weaker the relationship is.
Figure 1-5 shows an example of a plot showing the number of coffees sold
at football games in Buffalo, New York, as well as the air temperature (in
Fahrenheit) at each game. This data set seems to follow a downhill straight line
fairly well, indicating a negative correlation. When you calculate the correla-
tion, you get the value of –0.741. This value says that coffees sold has a fairly
strong negative relationship with the temperature of the football game. This
makes sense, because on days when the temperature is low, people will get
cold and want more coffee. On days when the temperature is higher, people
will tend to drink less coffee and perhaps tend more toward soft drinks, which
are cold. I discuss correlation further, as it applies to model building, in
Chapter 4.
Number of Coffees Sold versus Temperature
70000
60000
50000
Coffees 40000
Figure 1-5: 30000
Coffees sold
at various 20000
air tem-
10000
peratures
on football 0
-10 0 10 20 30 40 50 60 70
game day.
Temperature (ºF)