Page 231 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Marks in Eco. (X) Marks in Stat. (Y) u = X – 31 v = Y – 41 uv u v 2
2
25 43 – 6 2 – 12 36 4
28 46 – 3 5 – 15 9 25
Quantitative Techniques-II
35 49 4 8 32 16 64
32 41 1 0 0 1 0
31 36 0 – 5 0 0 25
Notes
36 32 5 – 9 – 45 25 81
29 31 – 2 – 10 20 4 100
38 30 7 – 11 – 77 49 121
34 33 3 – 8 – 24 9 64
32 39 1 – 2 – 2 1 4
Total 10 – 30 – 123 150 488

From the table, we have

10 30
X = 31  10  32 and Y  41  10  38

1. The lines of regression
(a) Regression of Y on X

n  uv   u   v  1230 300

b = 2    0.66

2
n  u   u  1500 100
a = Y bX = 38 + 0.66 × 32 = 59.26
 Regression equation is
Y = 59.26 – 0.66X
C
(b) Regression of X on Y

n  uv   u   v  1230 300

d = 2    0.23
2

n  v    v 4880 900
c = X dY = 32 + 0.23 × 38 = 40.88
 Regression equation is
X = 40.88 – 0.23Y
C
2. Coefficient of correlation


r = b d    0.66   0.23   0.39
Note that r, b and d are of same sign.
3. 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
Self Assessment

Fill in the blanks:

1. The regression line can, alternatively, be written as a deviation of Y from Y i.e. Y – Y =
i Ci i Ci
……………………
2. A different …………………….means a different pair of constants a and b.

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