Scatter diagram - correlation analysis, Applied Statistics

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

2406_scatter diagram.png

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

705_scatter diagram1.png

 

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.

Posted Date: 9/15/2012 4:09:26 AM | Location : United States







Related Discussions:- Scatter diagram - correlation analysis, Assignment Help, Ask Question on Scatter diagram - correlation analysis, Get Answer, Expert's Help, Scatter diagram - correlation analysis Discussions

Write discussion on Scatter diagram - correlation analysis
Your posts are moderated
Related Questions
The manager of Pizza Hut provides a delivery service for customers who telephone in an order. The manager would like to give callers an idea of the time it will take to deliver an

real time applications on graphical representation of o-give curves

Applications of Standard Error   Standard Error is used to test whether the difference between the sample statistic and the population parameter is significant or is d

The first step in this case is to ensure that you are adequately clear on the General Linear Model and its relationship to both ANOVA and regression. The distinction is approxim

The file Midterm  Data.xls has a tab labeled "National Grid vs. Alcoa" which presents historical price data for two stocks.  Using the National Grid price as the X-value and the Al

Examples of grouped, simple and frequency distribution data

Ask 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each

how to get statistical quality control assignment in brief?

Empirical Mode Where mode is ill-defined, its value may be ascertained by the following formula based upon the empirical relationship between Mean, Median and Mode: Mode = 3

Correlation The board of directors of Bata Company is faced with the problem of estimating what the annual sales might be in a shop to be opened in Bagpur where Bata has not op