correlationppt sunil 23
TRANSCRIPT
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LOGO
CORRELATIONCOEFFICIENT
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Introduction
Correlation a LINEAR association between two
random variables
Correlation analysis show us how to determineboth the nature and strength of relationship
between two variables
When variables are dependent on time correlationis applied
Correlation lies between +1 to -1
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A zero correlation indicates that there is no
relationship between the variables
A correlation of 1 indicates a perfect negativecorrelation
A correlation of +1 indicates a perfect positivecorrelation
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Types of Correlation
There are three types of correlation
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If two related variables are such
that when one increases
(decreases), the other also
increases (decreases).If two variables are such that when
one increases (decreases), the other
decreases (increases)
If both the variables are independent
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When plotted on a graph it tends to be a perfectline
When plotted on a graph it is not a straight line
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Two independent and one dependent variable
One dependent and more than one independentvariables
One dependent variable and more than oneindependent variable but only one independentvariable is considered and other independentvariables are considered constant
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Methods of Studying Correlation
Scatter Diagram Method
Karl Pearson Coefficient Correlation of
Method
Spearmans Rank Correlation Method
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Drug A (dose in mg)
S
ymptomI
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Drug B (dose in mg)
SymptomInde
Very good fit Moderate fit
Correlation: LinearRelationships
Strong relationship = good linear fit
Points clustered closely around a line show a strong correlation.The line is a good predictor (good fit) with the data. The morespread out the points, the weaker the correlation, and the lessgood the fit. The line is a REGRESSSION line (Y = bX + a)
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Coefficient of CorrelationA measure of the strength of the linear relationship
between two variables that is defined in terms of the
(sample) covariance of the variables divided by their
(sample) standard deviations
Represented by r
r lies between +1 to -1
Magnitude and Direction
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-1 < r< +1
The + and signs are used for positive linearcorrelations and negative linear correlations,
respectively
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[ ] [ ]2222 )()(
=
YYnXXn
YXXYn
rxy Shared variability of X and Y variables on thetopIndividual variability of X and Y variables on thebottom
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Interpreting CorrelationCoefficient r
strong correlation: r> .70 or r< .70
moderate correlation: ris between .30 &.70
or ris between .30 and .70weak correlation: ris between 0 and .30
or ris between 0 and .30 .
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Coefficient of Determination
Coefficient of determination lies between 0 to 1
Represented by r2
The coefficient of determination is a measure of
how well the regression line represents the data
If the regression line passes exactly through
every point on the scatter plot, it would be able
to explain all of the variation
The further the line is away from the points, the
less it is able to explain
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r2,is useful because it gives the proportion of the
variance (fluctuation) of one variable that is
predictable from the other variable
It is a measure that allows us to determine how
certain one can be in making predictions from a
certain model/graph
The coefficient of determination is the ratio of the
explained variation to the total variation
The coefficient of determination is such that 0 < r2