Page 331 - DMTH404_STATISTICS

Unit 23: Regression Analysis

Calculation table Notes

Marks in Eco. Marks in Stat. 2 2
=
=
( X ) ( Y ) u X - 31 v Y - 41 uv u v
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
Total 10 - 30 - 123 150 488

From the table, we have

10 30
X = 31+ = 32 and Y = 41- = 38.
10 10
(a) The lines of regression
(i) Regression of Y on X

n uv - å )( v ) - 1230 300
å
( u å
+
b = 2 2 = = - 0.66
-
( u
å
n u - å ) 1500 100
a =Y - bX = 38 + 0.66 × 32 = 59.26
 Regression equation is
Y = 59.26 - 0.66X
C
(ii) Regression of X on Y
n uv - å )( v ) - 1230 300
+
å
( u å
d = 2 = = - 0.23
2
-
( v
å
n v - å ) 4880 900
+
c = X - dY = 32 0 23 38 = 4088
.
´
.
 Regression equation is
X = 40.88 – 0.23Y
C
(b) Coefficient of correlation
r = b d = - - 0.66 ´ - 0.23 = - 0.39
×
Note that r, b and d are of same sign.
(c) 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

LOVELY PROFESSIONAL UNIVERSITY 323