correlation & regression - 3 presentation - unitedworld school of business

7/28/2019 Correlation & Regression - 3 Presentation - Unitedworld School of Business

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Correlation-Regression


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Methods of Measuring correlation

1. Graphic Method2. Diagramatic Method- Scatter Diagram

3. Algebraic method

a. Karl Pearsons Coefficient of correlationb. Spearmans Rank Co-efficient Correlationc. Coefficient of Concurrent deviations

d. Least Squares Method


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Karl Pearsons Coefficient of Correlation

dx dy ( Gamma) = -------------------------

dx2 dy2

dx dy= -------------------------

N xy

dx = x-xbardy = y- ybar

dx dy = sum of products of deviations from respective

arithmetic means of both series


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Karl Pearsons Coefficient of Correlation

After calculating assumed or working mean Ax & Ay dx dy ( dx) *( dy) ( Gamma) = --------------------------------

[ N dx2 - ( dx)2 * [ Ndy2 - ( dy)2 ]

dx dy = total of products of deviation from assumedmeans of x and y series

dx = total of deviations of x series dy = total of deviations of y series

dx2 = total of squared deviations of x series dy2 = total of squared deviations of y series

N= No. of items ( no. of paired items


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Karl Pearsons Coefficient of CorrelationAfter calculating assumed or working mean Ax &

Ay

dx x dy

dx dy - ----------------N

( Gamma) = -------------------------

( dx)2

( dy)2

[ dx2 - --------- ] x [ dy2 - ------------]N N


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Assumptions of Karl Pearsons Coefficient of Correlation

1. Linear relationship exists between the variablesProperties of Karl Pearsons Coefficient of Correlation1.value lies between +1 & - 1

2.Zero means no correlation

3. ( Gamma) = bxy X byxWhere bxy X byx are regression coefficicent

Merit

Convenient for accurate interpretation as it gives degree &

direction of relationship between two variables


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Limitations

1. Assumes linear relationship , even though itmay not be

2. Method & process of calculation is difficult &

time consuming3. Affected by extreme values in distribution


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Probable Error of Karl Pearsons Coefficient of

Correlation

1- 2

Probable Error of ( Gamma) = 0.6745 -------- N


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Q7.Calculate coefficient of correlation for following data

X65 63 67 64 68 62 70 66 68 67 69 71

Y 68 66 68 65 69 66 68 65 71 67 68 70

Ans dx dy ( Gamma) = ------------------------- dx2 dy2

dx dy= -------------------

N xy


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1 2 3 4 5 6 7 8 9 10 11 12

Su

mX Xbar

X 65 63 67 64 68 62 70 66 68 67 69 71 800 66.67

Y 68 66 68 65 69 66 68 65 71 67 68 70 811 67.58

dx=x-xbar -1.67 -3.67 0.33 -2.67 1.33 -4.67 3.33 -0.67 1.33 0.33 2.33 4.33

dx2 2.78 13.44 0.11 7.11 1.78 21.78 11.11 0.44 1.78 0.11 5.44 18.78

84.

67

dx.dy -0.69 5.81 0.14 6.89 1.89 7.39 1.39 1.72 4.56 -0.19 0.97 10.47

40.

33

dy=y-ybar 0.42 -1.58 0.42 -2.58 1.42 -1.58 0.42 -2.58 3.42 -0.58 0.42 2.42

dy2 0.17 2.51 0.17 6.67 2.01 2.51 0.17 6.67 11.67 0.34 0.17 5.84

38.

92

dx dysum dx2*

sumdy2

3294.

9

dx2 dy2 57.40

coeff of

correlation = 0.70


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Q8. following information about age of husbands

& wives. Find correlation coefficient

Husband

23 27 28 29 30 31 33 35 36 39

Wife 18 22 23 24 25 26 28 29 30 32

( Gamma) =0.99


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1 2 3 4 5 6 7 8 9 10

Sum

X Xbar

X 23 27 28 29 30 31 33 35 36 39 311 31.10

Y 18 22 23 24 25 26 28 29 30 32 257 25.70

dx=x-

xbar -8.10 -4.10 -3.10 -2.10 -1.10 -0.10 1.90 3.90 4.90 7.90

dx2 65.61 16.81 9.61 4.41 1.21 0.01 3.61 15.21 24.01 62.41

202.

9

dx.dy 62.37 15.17 8.37 3.57 0.77 -0.03 4.37 12.87 21.07 49.77

178.

3

dy=y-

ybar -7.70 -3.70 -2.70 -1.70 -0.70 0.30 2.30 3.30 4.30 6.30

dy2 59.29 13.69 7.29 2.89 0.49 0.09 5.29 10.89 18.49 39.69

158.

1

dx dy sum dx2* sumdy232078.

49

dx2 dy2 179.10

coeff of correlation

= 1.00


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Q9. ten competitors in a cooking competition are

ranked by three judges in the following way .byusing rank coorelation method find out which

pair of judges have nearest approach

Ans P&Q= -0.21 , Q &R=--0.3 P &R = +0.64


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Q9. ten competitors in a cooking competition are ranked

by three judges in the following way .by using rank

coorelation method find out which pair of judges havenearest approach

P Q R

1 1 3 6

2 6 5 43 5 8 9

4 10 4 8

5 3 7 1

6 2 10 27 4 2 3

8 9 1 10

9 7 6 5

10 8 9 7


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Rank coefficient of correlation

6 d2 (rho) = 1 - -------------------

N3-N

d2 = total of squared differenceN = number of items


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P Q R

Rp-

Rq dpq2

Rq-

Rr dqr2

Rp-

Rr dpr2

1 1 3 6 -2 4 -3 9 -5 25

2 6 5 4 1 1 1 1 2 4

3 5 8 9 -3 9 -1 1 -4 16

4 10 4 8 6 36 -4 16 2 4

5 3 7 1 -4 16 6 36 2 4

6 2 10 2 -8 64 8 64 0 0

7 4 2 3 2 4 -1 1 1 1

8 9 1 10 8 64 -9 81 -1 1

9 7 6 5 1 1 1 1 2 4

10 8 9 7 -1 1 2 4 1 1

1000 200 214 0 60

6Sigma d2 1200 1284 360

N3-N 990 6Sigma d2/N3-N 1.21 1.297 0.3636

P= -0.21 -0.297 0.636364

C O i


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Campus Overview

907/A Uvarshad,

Gandhinagar

Highway, Ahmedabad382422.

Ahmedabad Kolkata

Infinity Benchmark,

10th Floor, Plot G1,

Block EP & GP,

Sector V, Salt-Lake,

Kolkata700091.

Mumbai

Goldline Business Centre

Linkway Estate,

Next to Chincholi Fire

Brigade, Malad (West),

Mumbai400 064.


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Thank You

correlation & regression - 3 presentation - unitedworld school of business

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