Question

Use the given data to find the equation of the regression line. Fill out the table below and show how you calculate each value below. Round the final values of a and b to three decimal places, if necessary. 5) x 10 3 4 5 12 y 18 2 6 9 12 5) y = Y x-X y-у (x - 2)2 (x - x)(y-y) y 8 0 3 2 4 6 5 9 12 12 b = ge ý=

Answer 1

As , the data given in the Question , we have

T
= 4.8   $\overline{y}$ = 7.4

x	y	x- T	y-$\overline{y}$	(x- T )^2	(A-2-2)
0	8	-4.8	0.6	23.04	-2.88
3	2	-1.8	-5.4	3.24	9.72
4	6	-0.8	-1.4	0.64	1.12
5	9	0.2	1.6	0.04	0.32
12	12	7.2	4.6	51.84	33.12

The regression line is given by :

Yi = a + b* ri + €

now ,

b Sry ST CT
and
a=y-b*

ту

(A-2-2)
= 41.4

SIE
(x-
T
)^2 = 78.8

b = 0.525

a = 4.878

Hence the requried regression equation is given by,

$\widehat{y_i} = 4.878 + 0.525*\ x_i + \epsilon _i$

T

We were unable to transcribe this image

T

We were unable to transcribe this image

T

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

We were unable to transcribe this image

T

We were unable to transcribe this image