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CORRELATION important topic in statistics, Essays (university) of Statistics

Basic correlation important topic in statistics it will be very useful

Typology: Essays (university)

2020/2021

Uploaded on 07/12/2021

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CORRELATION
Correlatio
n
A measure of the strength of association among
the between variables
Meaning of correlation:
Correlation is defined as Relationship between two or
more variables. Co – Together ; Relation – Connection
Definition:
“The degree of association between two variables”
“A measure of the strength of association among
and between variables”
Example:
1) Income and standard of living of a person
2) Monsoon and agricultural production at a particular
season
3) Relationship between price and demand
Types of Correlation
Uses of correlation:
Before going to deal with the various methods of correlation, it is
necessary to know the various uses of correlation is statistical analysis
which can be cited as follows:
1) It is used in deriving precisely the degree, and direction
of relationship between variables like price and
demand, advertising expenditure and sales, rainfalls
and crops yield etc.
2) It is used in developing the concept of regression, and
ratio of variation which help in estimating the values of
one variable for a given value of another variable.
3) It is used in reducing the range of uncertainty in the
matter of prediction.
4) It is used in presenting the average relationship
between any two variables through a single value of co-
efficient of correlation.
5) In the field of economics it is used in understanding the
economic behaviour, and locating the important
variables on which the others depend.
6) In the field of business it is used advantageously to
estimate the cost of sales, volume of sales, sales price,
and any other values on the basis of some other
variables which are financially related to each other.
7) In the field of science and philosophy, also, the
methods of correlation are profusely used in making
progressive developments in the respective lines.
8) In the field of nature also, it is used in observing the
multiplicity of the inter-related forces.
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CORRELATION

Correlatio n A measure of the strength of association among the between variables  Meaning of correlation: Correlation is defined as Relationship between two or more variables. Co – Together ; Relation – Connection  Definition:  “The degree of association between two variables”  “A measure of the strength of association among and between variables”  Example:

  1. Income and standard of living of a person
  2. Monsoon and agricultural production at a particular season
  3. Relationship between price and demand  Types of Correlation  Uses of correlation: Before going to deal with the various methods of correlation, it is necessary to know the various uses of correlation is statistical analysis which can be cited as follows:
  4. It is used in deriving precisely the degree, and direction of relationship between variables like price and demand, advertising expenditure and sales, rainfalls and crops yield etc.
  5. It is used in developing the concept of regression, and ratio of variation which help in estimating the values of one variable for a given value of another variable.
  6. It is used in reducing the range of uncertainty in the matter of prediction.
  7. It is used in presenting the average relationship between any two variables through a single value of co- efficient of correlation.
  8. In the field of economics it is used in understanding the economic behaviour, and locating the important variables on which the others depend.
  9. In the field of business it is used advantageously to estimate the cost of sales, volume of sales, sales price, and any other values on the basis of some other variables which are financially related to each other.
  10. In the field of science and philosophy, also, the methods of correlation are profusely used in making progressive developments in the respective lines.
  11. In the field of nature also, it is used in observing the multiplicity of the inter-related forces.
  1. In terms of direction of variables:  Scatter plots are constructed by plotting two variables along the horizontal ( x ) and vertical ( y ) axes.  Note that the more closely the cluster of dots represents a straight line, the stronger the correlation. POSITIVE CORRELATION NEGATIVE CORRELATION NO CORRELATION Meaning: The two random variables increases (decrease) together. There is a positive correlation One of the random variables increases as the other decreases. There is no linear relationship between the two random variables. Example : There is a positive correlation between height and weight: weight increases as height increases. There is a negative correlation between speed and the amount of time it takes to get somewhere: as speed increases, it takes a shorter amount of time to There is no correlation between being able to write in cursive and the number of fish in the ocean. get to a destination.
  2. In terms of number of variables:
  1. In terms of Shape:  Distinction between linear and non – linear correlation is based upon the constancy of the ratio of change between the variables. Linear Correlation Non – Linear Correlation Meaning: If the amount of change in one variable tends to bear constant ratio to the amount of change in the other variable then the Correlation is said to be linear. In other words, when all the points on the scatter diagram tend to lie near a line which looks like a straight line, the correlation is said to be linear. Correlation is said to be non linear if the ratio of change is not constant. In other words, when all the points on the scatter diagram tend to lie near a smooth curve, the correlation is said to be non linear (curvilinear). Example: When the amount of output in a factory is doubled by doubling the number of workers, this is an example of linear correlation.  Representation of Correlation: Correlation between two random variables is typically presented graphically using a scatter plot, or numerically using a correlation coefficient

SCATTER DIAGRAM also known as

SCATTER PLOT, SCATTER CHART & SCATTERGRAM

Scatter Diagram is referred to as a plot or a mathematical diagram. The Scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. Merits of Scatter Diagram Limitations of Scatter Diagram When to use Scatter diagram  It shows the relationship between two variables  It is the best method to show you a non- linear pattern  The range of data flow i.e., maximum and minimum values can be easily determined  Observation and reading is straightforward.  Plotting the diagram is relatively simple.  Scatter diagrams are unable to give you the exact extent of correlation.  Scatter diagram, does not show you the quantitative measure of the relationship between the variables. It only shows the quantitative expression of the quantitative change.  This chart does not show you the two variables.  When you have paired numerical data.  When your dependent variable may have multiple values for each value of your independent variable.  When trying to determine whether the two variables are related, such as,

  • When trying to identify potential root causes of problems.
  • When testing for autocorrelation before constructing a control chart. It shows the STRENGTH (Strong or weak) of the two or more variables graphically. The purpose of Scatter Diagram is to plot relationship between multiple variables for a set of data in a single view. It helps to identify the direction of the association between two variables under study but it fails to tell us about the intensity of the correlation or association between two variables, which can be calculated by correlation coefficient, gives direction and intensity.

How do we use Scatter Diagram?