## Recommended

###### Correlation PDF / PPT

CORRELATION

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CORRELATION

 Correlation is a statistical tool that helps to measure

and analyze the degree of relationship between two

variables.

 Correlation analysis deals with the association

between two or more variables.

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CORRELATION

 The degree of relationship between the variables

under consideration is measure through the

correlation analysis.

 The measure of correlation called the correlation

coefficient .

 The degree of relationship is expressed by

coefficient which range from correlation

( -1 ≤ r ≥ +1)

 The direction of change is indicated by a sign.

 The correlation analysis enable us to have an

idea about the degree & direction of the

relationship between the two variables under

study.

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TYPES OF CORRELATION – TYPE I

Correlation

Positive Correlation Negative Correlation

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TYPES OF CORRELATION TYPE I

 Positive Correlation: The correlation is said to be

positive correlation if the values of two variables

changing with same direction.

Ex. Pub. Exp. & Sales, Height & Weight.

 Negative Correlation: The correlation is said to be

negative correlation when the values of variables change

with opposite direction.

Ex. Price & Quantity demanded.

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DIRECTION OF THE CORRELATION

 Positive relationship – Variables change in the

same direction.

 As X is increasing, Y is increasing

 As X is decreasing, Y is decreasing

Indicated by

 E.g., As height increases, so does weight.

sign; (+) or (-).

 Negative relationship – Variables change in

opposite directions.

 As X is increasing, Y is decreasing

 As X is decreasing, Y is increasing

 E.g., As TV time increases, grades decrease

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EXAMPLES

Positive Correlation Negative Correlation

 Water consumption  Alcohol consumption

and temperature. and driving ability.

 Study time and  Price & quantity

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TYPES OF CORRELATION TYPE II

Correlation

Simple Multiple

Partial Total

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TYPES OF CORRELATION TYPE II

 Simple correlation: Under simple correlation

problem there are only two variables are studied.

 Multiple Correlation: Under Multiple

Correlation three or more than three variables

are studied. Ex. Qd = f ( P,PC, PS, t, y )

 Partial correlation: analysis recognizes more

than two variables but considers only two

variables keeping the other constant.

 Total correlation: is based on all the relevant

variables, which is normally not feasible.

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Types of Correlation

Type III

Correlation

LINEAR NON LINEAR

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TYPES OF CORRELATION TYPE

III

 Linear correlation: Correlation is said to be

linear when the amount of change in one

variable tends to bear a constant ratio to the

amount of change in the other. The graph of the

variables having a linear relationship will form

a straight line.

Ex X = 1, 2, 3, 4, 5, 6, 7, 8,

Y = 5, 7, 9, 11, 13, 15, 17, 19,

Y = 3 + 2x

 Non Linear correlation: The correlation

would be non linear if the amount of change in

one variable does not bear a constant ratio to

the amount of change in the other variable.

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CORRELATION & CAUSATION

 Causation means cause & effect relation.

 Correlation denotes the interdependency among the

variables for correlating two phenomenon, it is

essential that the two phenomenon should have

cause-effect relationship,& if such relationship does

not exist then the two phenomenon can not be

correlated.

 If two variables vary in such a way that movement

in one are accompanied by movement in other, these

variables are called cause and effect relationship.

 Causation always implies correlation but correlation

does not necessarily implies causation.

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DEGREE OF CORRELATION

 Perfect Correlation

 High Degree of Correlation

 Moderate Degree of Correlation

 Low Degree of Correlation

 No Correlation

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METHODS OF STUDYING CORRELATION

Birinder Singh, Assistant Professor, PCTE

Methods

Graphic Algebraic

Methods Methods

Karl

Scatter Correlation Rank Concurrent

Pearson’s

Diagram Graph Correlation Deviation

Coefficient

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SCATTER DIAGRAM METHOD

Scatter Diagram is a graph of

observed plotted points where each

points represents the values of X & Y

as a coordinate.

 It portrays the relationship between

these two variables graphically.

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A PERFECT POSITIVE

CORRELATION

Weight

Weight

of B

Weight A linear

of A

relationship

Height

Height Height

of A of B

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HIGH DEGREE OF POSITIVE

CORRELATION

 Positive relationship

r = +.80

Weight

Height

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DEGREE OF CORRELATION

 Moderate Positive Correlation

r = + 0.4

Shoe

Size

Weight

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DEGREE OF CORRELATION

 Perfect Negative Correlation

r = -1.0

TV

watching

per

week

Exam score

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DEGREE OF CORRELATION

 Moderate Negative Correlation

r = -.80

TV

watching

per

week

Exam score

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DEGREE OF CORRELATION

 Weak negative Correlation

Shoe

Size r = – 0.2

Weight

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DEGREE OF CORRELATION

 No Correlation (horizontal line)

r = 0.0

IQ

Height

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DEGREE OF CORRELATION (R)

r = +.80 r = +.60

r = +.40 r = +.20

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DIRECTION OF THE RELATIONSHIP

 Positive relationship – Variables change in the same

direction.

 As X is increasing, Y is increasing

Indicated by

 As X is decreasing, Y is decreasing

 E.g., As height increases, so does weight. sign; (+) or (-).

 Negative relationship – Variables change in opposite

directions.

 As X is increasing, Y is decreasing

 As X is decreasing, Y is increasing

 E.g., As TV time increases, grades decrease

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 Simple & Non Mathematical method

 Notinfluenced by the size of extreme

item

step in investing the relationship

 First

between two variables

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Can not adopt the an exact

degree of correlation

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CORRELATION GRAPH

300

250

200

150 Consumption

Production

100

50

0

2012 2013 2014 2015 2016 2017

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KARL PEARSON’S COEFFICIENT OF

CORRELATION

 It is quantitative method of measuring

correlation

 This method has been given by Karl Pearson

 It’s the best method

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PROPERTIES OF COEFFICIENT OF

CORRELATION

 Karl Pearson’s coefficient of correlation lies between –

1 & 1, i.e. – 1 ≤ r ≤ +1

If the scale of a series is changed or the origin is

Birinder Singh, Assistant Professor, PCTE

shifted, there is no effect on the value of ‘r’.

 ‘r’ is the geometric mean of the regression coefficients

byx & bxy, i.e. r = 𝑏𝑥𝑦 . 𝑏𝑦𝑥

 If X & Y are independent variables, then coefficient of

correlation is zero but the converse is not necessarily

true.

 ‘r’ is a pure number and is independent of the units of measurement.

 The coefficient of correlation between the two

variables x & y is symmetric. i.e. ryx = rxy

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