Question

Calculate the lines of regression for the following data:

X 15 17 21 18 14 12

Y 8 10 13 9 11 10

Also estimate the value if Y, if X= 9.

​

Answer 1

Hi

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.