Question

Between two variables analyzing with basic correlation and regreation with getting at least 11 datas. What Y=? When X=9

(Determine the datas by yourself)

Answer 1

Consider the two variables are:

x	1	2	3	4	5	6	7	8	9	10	11
Y	9	8	10	12	11	13	14	16	15	17	18

Straight line equation is y = a+ bx.

The normal equations are
∑y = an + b ∑x
∑xy = a ∑x + b ∑x²

x	y	x²	xy
1	9	1	9
2	8	4	16
3	10	9	30
4	12	16	48
5	11	25	55
6	13	36	78
7	14	49	98
8	16	64	128
9	15	81	135
10	17	100	170
11	18	121	198
∑x = 66	∑y = 143	∑ x² = 506	∑xy = 965

Substituting these values in the normal equations
143 = 11a + 66b

965 = 66a + 506b

Solving these two equations using Elimination method,
11a + 66b = 143

11(a+6b)=11⋅13

a + 6b =13     --------------------------(1)

and

66a + 506 b = 965------------------(2)

Equation (1) ×66⇒

66a + 396b = 858

equation (2) ×1⇒

66a + 506b = 965

Substracting ⇒

-110b = -107

110b = 107

b = 107 / 110

b = 0.97

Putting b=107 / 110 in equation (1), we have

a + 6(107 / 110) = 13
a =13 - (321 / 55)

a=394 / 55

a= 7.16

a=394 / 55 and   b=107 / 110

N ow substituting this values in the equation is y= a + bx, we get

y = (394 / 55) + (107 / 110) x

y= 7.16 + 0.97x

when x = 9

y = 7.16 + (0.97)(9)

y = 15.89