Scatter diagram - correlation analysis, Applied Statistics

Assignment Help:

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.


Related Discussions:- Scatter diagram - correlation analysis

Regression model, Using a random sample of 670 individuals for the populati...

Using a random sample of 670 individuals for the population of people in the workforce in 1976, we want to estimate the impact of education on wages. Let wage denote hourly wage in

Calculate the damping ratio for each system, (i) Plot the step responses of...

(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl

Estimate a linear probability model, Estimate a linear probability model: ...

Estimate a linear probability model: Consider the multiple regression model: y = β 0 +β 1 x 1 +.....+β k x k +u Suppose that assumptions MLR.1-MLR4 hold, but not assump

Hortons initial infiltration capacity, (a) The Horton's initial infiltratio...

(a) The Horton's initial infiltration capacity for a catchment is 204 mm/h and the constant infiltration value at saturation is 60 mm/h. For a rainfall in excess of 204 mm/h mainta

Determine the maximum weight rounded down, Assume that the pulley at A is a...

Assume that the pulley at A is a small frictionless pulley. The cord AB is only allowed to support a maximum tension in Newtons as given in P4, and the cord supporting the block ca

Age at first marrage, get a questionnaire that captured age at first marria...

get a questionnaire that captured age at first marriage

Calculate the length of the rope, The tension, T, in the tow rope pulling t...

The tension, T, in the tow rope pulling the car in Newtons is given in P8.  Determine the minimum length of the rope l, between A and B, so that the tension in either AB or AC equa

Continuous frequency distribution, Formation of Continuous Frequency Distri...

Formation of Continuous Frequency Distribution:    Continuous frequency distribution is most popular in practice. With reference to the formation of this type of frequency distr

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd