Correlation PDF / PPT

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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

  grades. demanded

 

 

 

 

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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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ADVANTAGES OF SCATTER DIAGRAM

 Simple & Non Mathematical method

 Notinfluenced by the size of extreme

 item

      step in investing the relationship

 First

 between two variables

 

 

 

 

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DISADVANTAGE OF SCATTER DIAGRAM

 

 

 

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