Page 330 - DMTH404_STATISTICS

Statistics

Notes Solution.

Calculation table
2 2
X Y XY X Y
10 6 60 100 36
9 3 27 81 9
7 2 14 49 4
8 4 32 64 16
11 5 55 121 25
45 20 188 415 90

(a) Regression of Y on X

n XY - å )( Y ) 5 188 45 20
å
( X å
-
´
´
b = 2 2 = 2 = 0.8
n X - å ) 5 415 - ( )
å
45
´
( X
45 20
Also, X = = 9 and Y = = 4
5 5
Now a =Y - bX = 4 - 0.8 × 9 = - 3.2
 Regression of Y on X is Y = - 3.2 + 0.8X
C
(b) Regression of X on Y
( X å
´
-
´
n XY - å )( Y ) 5 188 45 20
å
d = 2 2 = 2 = 0.8
20
( Y
´
n Y - å ) 5 90 - ( )
å
Also, c = X - dY = 9 - 0.8 × 4 = 5.8
 The regression of X on Y is X = 5.8 + 0.8Y
C
´
.
(c) Coefficient of correlation r = b d = 0.8 0.8 = 0.8
Example 2:
From the data given below, find :
(a) The two regression equations.
(b) The coefficient of correlation between marks in economics and statistics.
(c) The most likely marks in statistics when marks in economics are 30.
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.

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