Post on 10-Apr-2018
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CORRELATION
Correlation is the statistical tool with the help
of which these relationships between two or
more than two variables is studied.
Correlation analysis refers to the techniques
used in measuring the closeness of the
relationship between the variables.
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Pos t v and N at vcorrelat on
S ple,Part al and Mult plecorrelat on
near and Non-linearcorrelation
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Specific Example
For sevenrandom summer
days, a personrecorded thetemperature andtheir water
consumption, duringa three-hour periodspent outside.
Temperature (F)
WaterConsumption
(ounces)
75 16
83 20
85 25
85 27
92 32
97 48
99 48
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How would you describe the graph?
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Methods of studying correlation
Commonly used methods for studying the correlation
between two variables are
Scatter diagram method.
Karl Pearson's coefficient of correlation (covariance
method).
Two-way frequency table.
Rank method.
Concurrent deviations method.
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REGRESSION
The meaning of the term Regression is the
act of returning or going back.
Regression is the statistical tool with the help
of which we are in a position to estimate or to
predict the unknown values of one variable
from known values of another variable.
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Correlation Vs. Regression Analysis
Correlation literally means the relationship between
two or more variables which vary. Regression means
stepping back or returning to the average value.
Correlation need not imply cause and effect
relationship between the variable under study.
Regression clearly indicates the cause and effectrelationship.
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Correlation coefficient is a linear relationship
between x and y and is independent of the units of
measurement. It is pure number lying between +
or 1. Regression is absolute measure and the
variable x and y are dependent on each other.
Correlation analysis is confined to only to study of
linear relationship between the variables and
therefore, has limited applications. Regression
analysis has wider application as it studies linearas well as non-linear relationship between the
variables.
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Regression: 3 ain Purposes
To describe (or model)
To predict (or estimate)
To control (or administer)
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Relationship Analysis
The examination of the association between
two or more variables. In marketing, some of
the more apparent relationships include
associations between advertising and sales,
company size and advertising budget, supply
and demand for products, and customersatisfaction and customer loyalty.
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DIFFERENCE BETWEENCORRELATIONANDDIFFERENCE BETWEENCORRELATIONAND
REGRESSIONREGRESSION
The objective of
regression analysis is to
study the nature of
relationship between thevariables
It is a measure of degree ofrelationship between the
variables
CORRELATION
REGREESSION
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INTERPRETING THECOEFFICIENTINTERPRETING THECOEFFICIENT
OFCORRELA
TIONOF
CORRELA
TION
When r= +1, there is a perfectpositive correlation
When r= -1, there is a perfectnegative correlation
When r= 0, there is no correlationbetween the variables
The closer r is to +1 or -1, the closerthe relationship between thevariables
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CONVERSION OF CORRELATION
INTO REGRESSION Regression= Correlation + Prediction
predicting y based on x
e.g., predicting.
throwing points (y)
based on distance from target (x)
Regression equation
formula that specifies a line
y = bx + a
plug in a x value (distance from target) and predict y (points) note
y= actual value of a score
y= predict value
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Steps to Reaching a Solution
Draw a scatter plot of the data.
Visually, consider the strength of the linearrelationship.
If the relationship appears relatively strong,find the correlation coefficient as a numericalverification.
If the correlation is still relatively strong, thenfind the simple linear regression line.
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DECISION TI E
If correlation analysis is a popular andinformative statistical method, why shouldresearchers bother using the somewhatintimidating multivariate statisticaltechniques? Do you feel there is reallymuch to gain from these methods?
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Vote of thanks
We are heartily thankful to r.
R K Singh sir who gave us thisproject which in turn became a
great learning experience of
management as well as its
practical application.
We would also like to thank
BI S faculty and staff
members for their support andfinally we thank our family,
friends and colleagues for their
helping nature.