## Scatter diagram - correlation analysis, Applied Statistics

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Scatter Diagram

The first step in correlation analysis is to visualize the relationship. For each unit of observation in correlation analysis there is a pair of numerical values. One is considered the independent variable; the other is considered dependent upon it and is called the dependent variable. One of the easiest ways of studying the correlation between the two variables is with the help of a scatter diagram.

A scatter diagram can give us two types of information. Visually, we can look for patterns that indicate whether the variables are related. Then, if the variables are related, we can see what kind of line, or estimating equation, describes this relationship.

The scatter diagram gives an indication of the nature of the potential relationship between the variables.

Example

A sample of 10 employees of the Universal Computer Corporation was examined to relate the employees' score on an aptitude test taken at the beginning of their employment and their monthly sales volume. The Universal Computer Corporation wishes to estimate the nature of the relationship between these two variables

 Aptitude Test Score Monthly Sales (Thousands of Rupees) Aptitude Test Score Monthly Sales (Thousands of Rupees) X Y X Y 50 30 70 60 50 35 70 45 60 40 80 55 60 50 80 50 70 55 90 65

To determine the nature of the relationship for example, we initially draw a graph to observe the data points.

Figure 1

On the vertical axis, we plot the dependent variable monthly sales. On the horizontal axis we plot the independent variable aptitude test score. This visual display is called a scatter diagram.

In the figure given above, we see that larger monthly sales are associated with larger test scores. If we wish, we can draw a straight line through the points plotted in the figure. This hypothetical line enables us to further describe the relationship. A line that slopes upward to the right indicates that a direct, or a positive relation is present between the two variables. In the figure given above we see that this upward-sloping line appears to approximate the relationship being studied.

The figures below show additional relations that may exist between two variables. In figure 2(a), the nature of the relationship is linear. In this case, the line slopes downward. Thus, smaller values of Y are associated with larger values of X. This relation is called an inverse (linear) relation.

Figure 2

Figure 2(b) represents a relationship that is not linear. The nature of the relationship is better represented by a curve than by a straight line - that is, it is a curvilinear relation. The relationship is inverse since smaller values of Y are associated with larger values of X.

Figure 2(c) is another curvilinear relation. In this case, however, larger values of Y are associated with larger values of X. Hence, the relation is direct and curvilinear.

In figure 2(d), there is no relation between X and Y. We can draw neither a straight line nor a curve that adequately describes the data. The two variables are not associated.

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