Page 195 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 2. Coefficient of correlation
r b d 0.66 0.23 0.39

Note that r, b and d are of same sign.

Since we have to estimate marks in statistics denoted by Y, therefore, regression of Y on X
will be used. The most likely marks in statistics when marks in economics are 30, is given
by
Y = 59.26 – 0.66 × 30 = 39.33
C

Example: For a bivariate data, you are given the following information:

2
(X – 58) = 46 (X – 58) = 3086
2
(Y – 58) = 9 (Y – 58) = 483
(X – 58)(Y – 58) = 1095.
Number of pairs of observations = 7. You are required to determine (i) the two regression
equations and (ii) the coefficient of correlation between X and Y.

Solution:
Let u = X – 58 and v = Y – 58. In terms of our notations, we are given Su = 46, Su2 = 3086, Sv = 9,
Sv2 = 483, Suv = 1095 and n = 7.

46 9
Now X = 58 + = 64.7 and Y = 58 + = 59.29
7 7
1. For regression equation of Y on X, we have
7 1095 46 9
b 2 0.37
7 3086 46

and a Y bX 59.29 0.37 64.57 35.40
The line of regression of Y on X is given by
Y = 35.40 + 0.37X
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2. For regression equation of X on Y, we have

7 1095 46 9
d 2 2.20
7 483 9
and c X dY 64.57 2.2 59.29 65.87
The line of regression of X on Y is given by
X = - 65.87 + 2.2Y
C
3. The coefficient of correlation

r b d 0.37 2.2 0.90

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