Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

532 CHAPTER 16 | Introduction to Regression
Note that a positive
slope means that Y
increases when X is
increased, and a negative
slope indicates that
Y decreases when X is
increased.
In the general linear equation, the value of b is called the slope. The slope determines
how much the Y variable changes when X is increased by one point. For the gym membership
example, the slope is b = $15 and indicates that your total cost increases by $15 each
month. The value of a in the general equation is called the Y-intercept because it determines
the value of Y when X = 0. (On a graph, the a value identifies the point where the line intercepts
the Y-axis.) For the gym example, a = $35; there is a $35 membership charge even
if you never visit the gym.
Figure 16.2 shows the general relationship between the total cost and number of months
for the gym example. Notice that the relationship results in a straight line. To obtain this
graph, we picked any two values of X and then used the equation to compute the corresponding
values for Y. For example,
when X = 3: when X = 8:
Y = bX + a
Y = bX + a
= $15(3) + $35 = $15(8) + $35
= $45 + $35 = $120 + $35
= $80 = $155
160
140
120
Total cost (Y )
100
80
F I G U R E 16.2
The relationship between total
cost and number of months of
gym membership. The gym
charges a $35 membership fee and
$15 per month. The relationship
is described by a linear equation
Y = 15X + 35 where Y is the
total cost and X is the number
of months.
60
35
0
1 2 3 4 5 6 7 8 9
Number of months (X )