Question

The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.) X: y : 3 3 5 6 3 5 6 7 7 7 Click here for the Excel Data File + a. The regression equation is ý = b. When x is 6 this gives y =

Answer 1

1. Find Regression line equations from the following data

X	Y
3	3
5	6
3	5
6	7
7	7

Solution:

x	y	x2	y2	x⋅y
3	3	9	9	9
5	6	25	36	30
3	5	9	25	15
6	7	36	49	42
7	7	49	49	49
---	---	---	---	---
∑x=24	∑y=28	∑x2=128	∑y2=168	∑xy=145

Mean ˉx=∑x / n

=24 / 5

=4.8


Mean ˉy=∑y / n

=28 / 5

=5.6


byx={n∑xy-(∑x)(∑y)} / {n∑x^2-(∑x)^2}

={5⋅145-24⋅28}/{5⋅128-(24)^2}

={725-672} / {640-576}

=53 / 64

=0.8281


Regression Line y on x
y-ˉy=byx (x-ˉx)

y-5.6=0.8281(x-4.8)

y-5.6=0.8281x-3.975

y=0.8281x-3.975+5.6
The regression equation is :
y= 0.8281 x + 1.625

when x=6 , y=0.8281*6+1.625 = 6.5936