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

SECTION 16.1 | Introduction to Linear Equations and Regression 531
4.00
3.50
F I G U R E 16.1
The relationship between SAT
scores and college GPA with a
line drawn through the middle of
the data points. The line defines
a precise one-to-one relationship
between each X value (SAT
score) and a corresponding
Y value (GPA).
Grade point average
3.00
2.50
2.00
1.50
1.00
0.50
420 460 500 540 580 620
SAT scores
660 700
simplified description of the relationship. For example, if the data points were
removed, the straight line would still give a general picture of the relationship
between SAT and GPA.
3. Finally, the line can be used for prediction. The line establishes a precise, one-toone
relationship between each X value (SAT score) and a corresponding Y value
(GPA). For example, an SAT score of 620 corresponds to a GPA of 3.25 (see
Figure 16.1). Thus, the college admissions officers could use the straight-line
relationship to predict that a student entering college with an SAT score of
620 should achieve a college GPA of approximately 3.25.
Our goal in this section is to develop a procedure that identifies and defines the straight
line that provides the best fit for any specific set of data. This straight line does not have to
be drawn on a graph; it can be presented in a simple equation. Thus, our goal is to find the
equation for the line that best describes the relationship for a set of X and Y data.
■ Linear Equations
In general, a linear relationship between two variables X and Y can be expressed by the
equation
Y = bX + a (16.1)
where a and b are fixed constants.
For example, a local gym charges a membership fee of $35 and a monthly fee of $15
for unlimited use of the facility. With this information, the total cost for the gym can be
computed using a linear equation that describes the relationship between the total cost (Y)
and the number months (X).
Y = 15X + 35