Classification of Correlation

Classification of Correlation

Correlation can be classified in different ways. The following are the most important classifications

1. Positive and Negative correlation
2. Simple, partial and multiple correlation
3. Linear and Non-linear correlation

Positive and Negative Correlation 

Positive Correlation 

When the variables are varying in the same direction, it is called positive correlation. In other words, if an increase in the value of one variable is accompanied by an increase in the value of other variable or if a decrease in the value of one variable is accompanied by a decree se in the value of other variable, it is called positive correlation.

Negative Correlation: 

When the variables are moving in opposite direction, it is called negative correlation. In other words, if an increase in the value of one variable is accompanied by a decrease in the value of other variable or if a decrease in the value of one variable is accompanied by an increase in the value of other variable, it is called negative correlation.

Simple, Partial and Multiple correlation 

Simple Correlation 

In a correlation analysis, if only two variables are studied it is called simple correlation. Eg. the study of the relationship between price & demand, of a product or price and supply of a product is a problem of simple correlation.

Multiple correlation 

In a correlation analysis, if three or more variables are studied simultaneously, it is called multiple correlation. For example, when we study the relationship between the yield of rice with both rainfall and fertilizer together, it is a problem of multiple correlation.

Partial correlation 

In a correlation analysis, we recognize more than two variable, but consider one dependent variable and one independent variable and keeping the other Independent variables as constant. For example yield of rice is influenced b the amount of rainfall and the amount of fertilizer used. But if we study the correlation between yield of rice and the amount of rainfall by keeping the amount of fertilizers used as constant, it is a problem of partial correlation.

Linear and Non-linear correlation 

Linear Correlation 

In a correlation analysis, if the ratio of change between the two sets of variables is same, then it is called linear correlation.

For example when 10% increase in one variable is accompanied by 10% increase in the other variable, it is the problem of linear correlation.

Non-linear correlation 

In a correlation analysis if the amount of change in one variable does not bring the same ratio of change in the other variable, it is called non linear correlation.

CORRELEATION ANALYSIS

CORRELATION ANALYSIS 

Introduction: 

In practice, we may come across with lot of situations which need statistical analysis of either one or more variables. The data concerned with one variable only is called univariate data. For Example: Price, income, demand, production, weight, height marks etc are concerned with one variable only. The analysis of such data is called univariate analysis. 

The data concerned with two variables are called bivariate data. For example: rainfall and agriculture; income and consumption; price and demand; height and weight etc. The analysis of these two sets of data is called bivariate analysis. 

The date concerned with three or more variables are called multivariate date. For example: agricultural production is influenced by rainfall, quality of soil, fertilizer etc. 

The statistical technique which can be used to study the relationship between two or more variables is called correlation analysis. 

Definition: 

Two or more variables are said to be correlated if the change in one variable results in a corresponding change in the other variable. 

According to Simpson and Kafka, “Correlation analysis deals with the association between two or more variables”. 

Lun chou defines, “ Correlation analysis attempts to determine the degree of relationship between variables”. 

Boddington states that “Whenever some definite connection exists between two or more groups or classes of series of data, there is said to be correlation.” 

In nut shell, correlation analysis is an analysis which helps to determine the degree of relationship exists between two or more variables. 

Correlation Coefficient: 

Correlation analysis is actually an attempt to find a numerical value to express the extent of relationship exists between two or more variables. The numerical measurement showing the degree of correlation between two or more variables is called correlation coefficient. Correlation coefficient ranges between -1 and +1. 

SIGNIFICANCE OF CORRELATION ANALYSIS 

Correlation analysis is of immense use in practical life because of the following reasons: 

1. Correlation analysis helps us to find a single figure to measure the degree of relationship exists between the variables. 

2. Correlation analysis helps to understand the economic behavior. 

3. Correlation analysis enables the business executives to estimate cost, price and other variables. 

4. Correlation analysis can be used as a basis for the study of regression. Once we know that two variables are closely related, we can estimate the value of one variable if the value of other is known. 

5. Correlation analysis helps to reduce the range of uncertainty associated with decision making. The prediction based on correlation analysis is always near to reality. 

6. It helps to know whether the correlation is significant or not. This is possible by comparing the correlation co-efficient with 6PE. It ‘r’ is more than 6 PE, the correlation is significant. 

USES OF QUANTITATE TECHNIQUES

USES OF QUANTITATE TECHNIQUES 

Business and Industry 

 Quantitative techniques render valuable services in the field of business and industry. Today, all decisions in business and industry are made with the help of quantitative techniques.

 Some important uses of quantitative techniques in the field of business and industry are given below:

 1. Quantitative techniques of linear programming is used for optimal allocation of scarce resources in the problem of determining product mix

2. Inventory control techniques are useful in dividing when and how much items are to be purchase so as to maintain a balance between the cost of holding and cost of ordering the inventory

3. Quantitative techniques of CPM, and PERT helps in determining the earliest and the latest times for the events and activities of a project. This helps the management in proper deployment of resources.

4. Decision tree analysis and simulation technique help the management in taking the best possible course of action under the conditions of risks and uncertainty.

5. Queuing theory is used to minimize the cost of waiting and servicing of the customers in queues.

6. Replacement theory helps the management in determining the most economic replacement policy regarding replacement of an equipment.

Limitations of Quantitative Techniques: 

Even though the quantitative techniques are inevitable in decision-making process, they are not free from short comings. The following are the important limitations of quantitative techniques:

1. Quantitative techniques involves mathematical models, equations and other mathematical expressions
2. Quantitative techniques are based on number of assumptions. Therefore, due care must be ensured while using quantitative techniques, otherwise it will lead to wrong conclusions.
3. Quantitative techniques are very expensive.
4. Quantitative techniques do not take into consideration intangible facts like skill, attitude etc.
5. Quantitative techniques are only tools for analysis and decision-making. They are not decisions itself. 

QUANTITATIVE TECHNIQUES

QUANTITATIVE TECHNIQUES 

Meaning and Definition: 

Quantitative techniques may be defined as those techniques which provide the decision makes a systematic and powerful means of analysis, based on quantitative data. It is a scientific method employed for problem solving and decision making by the management. With the help of quantitative techniques, the decision maker is able to explore policies for attaining the predetermined objectives. In short, quantitative techniques are inevitable in decision-making process. 

Classification of Quantitative Techniques: 

There are different types of quantitative techniques. We can classify them into three categories. They are: 

1. Mathematical Quantitative Techniques 

2. Statistical Quantitative Techniques 

3. Programming Quantitative Techniques 

Mathematical Quantitative Techcniques: 

A technique in which quantitative data are used along with the principles of mathematics is known as mathematical quantitative techniques. Mathematical quantitative techniques involve:

1. Permutations and Combinations: Permutation means arrangement of objects in a definite order. The number of arrangements depends upon the total number of objects and the number of objects taken at a time for arrangement. The number of permutations or arrangements is calculated by using the following formula:- 

Npr = n!/(n-r)!

The combination means selection or grouping objects without considering their order. The number of combinations is calculated by using the following formula:-  

Ncr = n!/(n-r)!

2. Set Theory:- Set theory is a modern mathematical device which solves various types of critical problems

3. Matrix Algebra: Matrix is an orderly arrangement of certain given numbers or symbols in rows and columns. It is a mathematical device of finding out the results of different types of algebraic operations on the basis of the relevant matrices.

4. Determinants: It is a powerful device developed over the matrix algebra. This device is used for finding out values of different variables connected with a number of simultaneous equations. 

5. Differentiation: It is a mathematical process of finding out changes in the dependent variable with reference to a small change in the independent variable. 

6. Integration: Integration is the reverse process of differentiation. 

7. Differential Equation: It is a mathematical equation which involves the differential coefficients of the dependent variables.