Obtain 2 regression equations, from the following data:
X
2
4
6
8
10
Y
10
20
25
30
40
Answers
Answered by
9
Answer:
x y xy x
2
y
2
2 6 12 4 36
4 5 20 16 25
6 4 24 36 16
8 3 24 64 9
10 2 20 100 4
∑x=30 ∑y=20 ∑xy=100 ∑x
2
=220 ∑y
2
=90
x
ˉ
=
5
30
=6,
y
ˉ
=
5
20
=4
x
ˉ
=6,
y
ˉ
=4
b
xy
=
n∑x
2
−(∑x)
2
n∑xy−∑x∑y
=
5(220)−900
5(100)−30×20
b
yx
=
1100−900
500−600
=
200
−100
=
2
−1
Regression line y on x
y−
y
ˉ
=b
yx
(x−
x
ˉ
)
(y−4)=
2
−1
(x−6)
2y−8=−x+6
x+2y=14
b
xy
=
n∑y
2
−(∑y)
2
n∑xy−∑x∑y
=
5(90)−(400)
5(100)−(30)(20)
b
xy
=
450−400
500−600
b
xy
=
50
−100
=−2
Regression line x on y
(x−
x
ˉ
)=b
xy
(y−
y
ˉ
)
(x−6)=−2(y−4)
x−6=−2y+8
x+2y=14
x=−2y+14.
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