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

Advantages of sampling, Advantages of Sampling Why should we settle on ...

Advantages of Sampling Why should we settle on a sample instead of studying the entire population?  Sampling has the following advantages over a census (study of the entire pop

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

Types of cost-reimbursable contracts, Types of cost-reimbursable contracts ...

Types of cost-reimbursable contracts are:   Cost Plus Fixed Fee contract (CPPF): Compensation is based on a fixed sum independent of the final project cost. The customer a

Managerial report, A. Compute descriptive statistics for each stock and the...

A. Compute descriptive statistics for each stock and the S&P 500. Comment on your results. Which stocks are most volatile?

Correlation, Definition of Correlation According  to prof, king correla...

Definition of Correlation According  to prof, king correlation means that between two series or group  of data  there  exists  some casual connection  prof, king  has also  exp

Random sampling method, Random Sampling Method In this method the units...

Random Sampling Method In this method the units are selected in such a way that every item in the whole universe has an equal chance of being included. In the words of croxton

Stream flow gauging, (a) At a stream gauging station, the following dischar...

(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1

Conduct a hypothesis testing, Celia is a nurse in a geriatric ward.  She no...

Celia is a nurse in a geriatric ward.  She noticed that older persons in her care are having problems sleeping at night.  She decided to introduce non-pharmocologic ways of relaxat

Calculate the ratio of the sample standard deviation, The Case Study includ...

The Case Study included information about the price for a full meal before and after the law change (in dollars).  Of interest is whether the differences in price for a full meal b

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

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