The scatter diagram

Chapter 3

Simple linear regression

Introduction

In day-to-day decisions-making situations, businesspersons and economists frequently draw conclusions and make recommendations based on the relationship between two variables. For example, a marketing manager may project sales volume based upon observed relations between advertising expenditures and sales volume. Although in some instances the manager will rely on his or her intuition as to how the variables are related, the safest approach, by far, is to collect data on the two variables and then evaluate their relationship statistically. These relationships are expressed mathematically as

where the function may follow linear and nonlinear forms.

The scatter diagram

As a first step in determining if a relationship exists between two variables we could plot or graph the available data for the two variables. Suppose that a sales manager has recorded containing data on annual sales and years of experience. The information is given in the following table:

Salesperson
Years of experience
Annual sales ($1000’s)

Let us plot these data on a graph with years of selling experience on the horizontal axis and annual sales on the vertical axis. We now have a scatter diagram. It is given this name because the plotted points are “scattered” over the graph or diagram. The scatter diagram for these data is shown in Figure 3.1.

In regression analysis statisticians commonly will classify a variable as an independent or a dependent variable. The classification is used to indicate which variable is doing the predicting or explaining (independent variable) and which variable is being predicted or explained (dependent variable). In our example, the years of selling experience is referred to as the independent variable. It is used to predict the sales volume, or dependent variable.

Does the scatter diagram in Fig. 3.1 allow us to draw conclusions?

It gives us an overview of the data. It indicates that in this case there is a good chance that the variables are related. In fact, it appears that the relationship between these two variables may be approximated by a straight line or linear function.

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