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Unformatted text preview: Regression Co efficient of Y on X
∑ xy 9
byx =
= = 0.9
∑ x 2 10
X= Hence regression equation of Y on X is
Y = Y + byx ( X − X )
= 4 + 0.9 ( X – 3 )
= 4 + 0.9X – 2.7
=1.3 + 0.9X
when X = 2.5
Y = 1.3 + 0.9 × 2.5
= 3.55
Regression co efficient of X on Y
∑ xy 9
= = 0.9
bxy =
∑ y 2 10
So, regression equation of X on Y is
X = X + bxy (Y − Y )
= 3 + 0.9 ( Y – 4 )
= 3 + 0.9Y – 3.6
= 0.9Y  0.6
Shortcut method
Example 5:
Obtain the equations of the two lines of regression for the data
given below:
X
Y 45
40 42
38 44
36 43
35 41
38
228 45
39 43
37 40
41 Solution:
X
46
42
44
A 43
41
45
43
40 Y
40
38 B
36
35
38
39
37
41 u = XA
3
1
1
0
2
2
0
3
0 u2
9
1
1
0
4
4
0
9
28 v = YB
2
0
2
3
0
1
1
3
0 ∑u
n
0
= 43
= 43 +
8
∑u
Y = B+
n
0
= 38
= 38 +
8
The regression Coefficient of Y on X is
n uv − ∑ u ∑ v
b1 = byx = ∑
2
n∑ u 2 − ( ∑ u )
X = A+ 8(−3) − (0)(0)
−24
=
= 0.11
2
8(28) − (0)
224
The regression coefficient of X on Y is
n uv − ∑ u ∑ v
b2 = bxy = ∑
2
n∑ v 2 − ( ∑ v )
= 8(−3) − (0)(0)
8(28) − (0) 2
−24
=
=  0.11
224
= 229 V2
4
0
4
9
0
1
1
9
28 uv
6
0
2
0
0
2
0
9
3 Hence the reression equation of Y on X is
Ye = Y + b1 ( X − X )
= 38 – 0.11 (X43)
= 38 – 0.11X + 4.73
= 42.73 – 0.11X
The regression equation of X on Y is
X e = X + b1 (Y − Y )
= 43 – 0.11 (Y38)
= 43 – 0.11Y + 4.18
= 47.18 – 0.11Y
Example 6:
In a correlation study, the following values are obtained Mean
S.D X
65
2.5 Y
67
3.5 Coefficient of correlation = 0.8
Find the two regression equations that are associated with the
above values.
Solution:
Given,
X = 65, Y = 67, σx = 2.5, σy= 3.5, r = 0.8
The regression coefficient of Y on X is
σ
byx= b1 = r y
σx
3.5
= 0.8 ×
= 1.12
2.5
The regression coefficient of X on Y is
σ
bxy = b2 = r x
σy
230 2.5
= 0.57
3.5
Hence, the regression equation of Y on X is
Ye = Y + b1 ( X − X )
= 67 + 1.12 (X65)
= 67 + 1.12 X  72.8
= 1.12X – 5.8
The regression equation of X on Y is
X e = X + b2 (Y − Y )
= 65 + 0.57...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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