Page 134 - Statistics II for Dummies

118 Part II: Using Different Types of Regression to Make Predictions

Table 7-1 Number of People Knowing a
Secret over a 6-Day Period
x (Day) y (Number of People)
1 1
2 2
3 5
4 7
5 17
6 30

In this situation, the explanatory variable, x, is day, and the response variable,
y, is the number of people who know the secret. Looking at Figure 7-2, you
can see a pattern between the values of x and y. But this pattern isn’t linear. It
curves upward. If you tried to fit a line to this data set, how well would it fit?

Correlation r = 0.906
Number of people who know the secret
35

25

20
Figure 7-2: 30
A scatter- 15
plot show-
ing the 10
spread of a 5
secret over
a six-day 0
period. 1 2 3 Day 4 5 6

To figure this out, look at the correlation coefficient between x and y, which
is found on Figure 7-2 to be 0.906 (see Chapter 4 for more on correlation).
You can interpret this correlation as a strong, positive (uphill) linear relation-
ship between x and y. However, in this case, the correlation is misleading
because the scatterplot appears to be curved.
If the correlation looks good (close to +1 or –1), don’t stop there. As with any
regression analysis, it’s very important to take into account both the scatterplot
and the correlation when making a decision about how well the model being con-
sidered would fit the data. The contradiction in this example between the scatter-
plot and the correlation is a red flag that a straight-line model isn’t the best idea.

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