Page 194 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 9: Regression Analysis

3. The most likely marks in statistics when marks in economics are 30. Notes
Marks in Eco. : 25 28 35 32 31 36 29 38 34 32
Marks in Stat. : 43 46 49 41 36 32 31 30 33 39
Solution:
Calculation table

.
31 41
25 43 6 2 12 36 4
28 46 3 5 15 9 25
35 49 4 8 32 16 64
32 41 1 0 0 1 0
31 36 0 5 0 0 25
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
10 30 123 150 488

From the table, we have
10 30
X =31+ =32 and Y = 41- =38.
10 10
1. The lines of regression
(a) Regression of Y on X

n uv u v 1230 300
b 2 0.66
n u 2 u 1500 100

a =Y - bX = 38 + 0.66 × 32 = 59.26
Regression equation is

YC = 59.26 - 0.66X
(b) Regression of X on Y

n uv u v 1230 300
d 0.23
2 4880 900
n v 2 v

c X dY 32 0.23 38 40.88
Regression equation is
XC = 40.88 - 0.23Y

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