Question

For y=25 what is the estimated values of x from the following data x:11 1215 16 19 21 y:21 15 13 12 11 10 9​

Answer 1

Step-by-step explanation:

X

14

12

13

14

16

10

13

12

Y

14

23

17

24

18

25

23

24

XY

196

276

221

336

288

250

299

288

X

2

196

144

169

196

256

100

169

144

∑X=104 ⇒

X

_

=

8

104

=13

∑Y=168 ⇒

Y

_

=

8

168

=21

∑XY=2154

∑X

2

=1374

Regression line if of form y=a+bx

b=

S

xx

S

xy

,S

xy

=∑xy−

n

∑x∑y

,S

xx

=∑x

2

−

n

(∑x)

2

⇒S

xy

=2154−

8

(104)(168)

=−30

⇒S

xx

=1374−

8

(104)

2

=22

⇒b=

22

−30

=−

11

15

a=

y

_

−b

x

_

⇒a=21+

11

15

(13)

⇒a=

11

426

y=

11

426

−

11

15

x

11y+15x=426

Put y=16

15x=250

x=

15

250

=

3

50