Page 332 - DMTH404_STATISTICS

Statistics

Notes
Example 3:
Obtain the two lines of regression from the following data and estimate the blood pressure
when age is 50 years. Can we also estimate the blood pressure of a person aged 20 years on the
basis of this regression equation? Discuss.

Age (X) (in years) : 56 42 72 39 63 47 52 49 40 42 68 60
Blood Pressure (Y) : 127 112 140 118 129 116 130 125 115 120 135 133
Solution.
Calculation table

X Y u = X - 52 v =Y - 125 uv u 2 v 2
56 127 4 2 8 16 4
42 112 - 10 - 13 130 100 169
72 140 20 15 300 400 225
39 118 - 13 - 7 91 169 49
63 129 11 4 44 121 16
47 116 - 5 - 9 45 25 81
52 130 0 5 0 0 25
49 125 - 3 0 0 9 0
40 115 - 12 - 10 120 144 100
42 120 - 10 - 5 50 100 25
68 135 16 10 160 256 100
60 133 8 8 64 64 64
Total 6 0 1012 1404 858

From the table, we have
6
X = 52 + = 52.5 and Y =125
12
(a) Regression of Y on X

å
n uv - å )( v ) 12 1012 6 0
´
( u å
´
-
b = 2 = 2 = 0.72
2
´
( u
å
n u - å ) 12 1404 - ( ) 6
´
-
Also a = Y bX = 125 0.72 52.5 = 87.2
-
 The line of regression of Blood pressure (Y) on Age (X) is
Y = 87.2 + 0.72X
C
(b) Regression of X on Y
´
-
( u å
´
å
n uv - å )( v ) 12 1012 6 0
d = 2 2 = = 1.18
-
´
å
n v - å ) 12 858 0
( v
Also c = X dY = 52.5 1.18 125 = - 95
´
-
-
 Line of regression of Age (X) on Blood pressure (Y) is
X = - 95 + 1.18Y
C
324 LOVELY PROFESSIONAL UNIVERSITY