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

PREVIEW
In Chapter 15, we noted that one common application
of correlations is for purposes of prediction. Whenever
there is a consistent relationship between two variables,
it is possible to use the value of one variable to predict
the value of another. Managers at the electric company,
for example, can use the weather forecast to predict
power demands for upcoming days. If exceptionally
hot summer weather is forecast, they can anticipate an
exceptionally high demand for electricity. In the field of
psychology, a known relationship between certain environmental
factors and specific behaviors can allow us to
predict that individuals living with those environmental
factors are more likely to display those behaviors. For
example, Astudillo et al. (2014) examined the relationship
between alcohol use and the concentration of alcohol
outlets (bars, clubs, and other on-site drinking establishments)
for different geographical regions of Switzerland.
They obtained alcohol use scores from a previous study
of 5519 Swiss men measuring both alcohol consumption
and drinking consequences. The results showed a positive
relationship between alcohol consumption and the
density of outlets in an area, but no consistent association
between outlets and drinking consequences. From these
results, the researchers were able to predict the level of
alcohol consumption within geographic regions based on
the density of outlets in each region.
The correlations introduced in Chapter 15 allow
researchers to measure and describe correlations, and
the hypothesis tests allow researchers to evaluate the
significance of correlations. However, we now want to
go one step further and actually use correlations to make
predictions.
In this chapter we introduce some of the statistical
techniques that are used to make predictions based on
correlations. Whenever there is a linear relationship
(Pearson correlation) between two variables, it is possible
to compute an equation that provides a precise,
mathematical description of the relationship. With the
equation, it is possible to plug in the known value for
one variable (for example, the density of alcohol outlets),
and then calculate a predicted value for the second variable
(for example, the level of alcohol consumption). The
general statistical process of finding and using a prediction
equation is known as regression.
Beyond finding a prediction equation, however, it is reasonable
to ask how good the predictions it makes are. For
example, I can make predictions about the outcome of a
coin toss by simply guessing. However, my predictions are
correct only about 50% of the time. In statistical terms, my
predictions are not significantly better than chance. In the
same way, it is appropriate to challenge the significance of
any prediction equation. In this chapter we introduce the
techniques that are used to find prediction equations, as
well as the techniques that are used to determine whether
their predictions are statistically significant. Incidentally,
although the results from the Astudillo et al. (2014) study
may seem obvious and predictable, they are useful. Specifically,
the results suggest that authorities should consider
the density of alcohol outlets in an area when planning
regional programs to prevent alcohol abuse.
16.1 Introduction to Linear Equations and Regression
LEARNING OBJECTIVES
1. Define the equation that describes a linear relationship between two variables.
2. Compute the regression equation (slope and Y-intercept) for a set of X and Y scores.
In the previous chapter, we introduced the Pearson correlation as a technique for describing
and measuring the linear relationship between two variables. Figure 16.1 presents
hypothetical data showing the relationship between SAT scores and college grade point
average (GPA). Note that the figure shows a good, but not perfect, positive relationship.
Also note that we have drawn a line through the middle of the data points. This line serves
several purposes.
1. The line makes the relationship between SAT and GPA easier to see.
2. The line identifies the center, or central tendency, of the relationship, just as the
mean describes central tendency for a set of scores. Thus, the line provides a
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