Question

From the data given below, obtain two regression lines and also find best estimated when value of is 120 units.​

Answer 1

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.

Step-by-step explanation:

Answer 2

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