Question

Q.1 Marks 2 (CLO 3)

From the following data, you are required to: -

(a) Fit the regression line Y on X and predict Y if x = 20

(b) Fit the regression line X on Y and predict X if y = 10

Y	X
14	4
4	12
2	8
2	6
4	4
6	4
4	16
12	8

Note : Answers should be in Word or Excel Format

Answer 1

x	y	xy	x²	y²
4	14	56	16	196
12	4	48	144	16
8	2	16	64	4
6	2	12	36	4
4	4	16	16	16
4	6	24	16	36
16	4	64	256	16
8	12	96	64	144
∑x=62	∑y=48	∑xy=332	∑x²=612	∑y²=432

Regression of y on x:

      y can be written as    y=(a)+(b*x)

• ∑y =( n*a)+(b*∑x) & ∑xy =(a*∑x)+(b*∑x²)    n is the no of observations=8

• 48=8a+62b                 &     332=62a+612b

By solving above two equations we get a=8.357 & b=-0.304

Therefore regression of y on x will be y=(8.357)-(0.304*x)

At x=20   => y=8.357-(0.304*20)    =>   y=2.277

Regression of x on y:

Equation of x can be written as x=(c)+(d*y)

• ∑x =( n*c)+(d*∑y)     &    ∑xy =(c*∑y)+(d*∑y²)

• 62=8c+48d                 &    332=48c+432d

By solving above two equations we get c=9.417 & d=-0.278

Regression of x on y will be x=(9.417)-(0.278*y)

At y=10     => x=9.417-(0.278*10)   =>    x=6.637