Answer:
Given information:
To obtain the equation of the regression line for the given data.
The equation of regression line of y on x is given by:
y
−
¯
y
=
b
y
x
(
x
−
¯
x
)
;
w
h
e
r
e
,
y
=
d
e
p
e
n
d
e
n
t
v
a
r
i
a
b
l
e
x
=
i
n
d
e
p
e
n
d
e
n
t
v
a
r
i
a
b
l
e
b
y
x
=
s
l
o
p
e
o
f
r
e
g
r
e
s
s
i
o
n
l
i
n
e
¯
x
=
m
e
a
n
o
f
x
¯
y
=
m
e
a
n
o
f
y
y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy
The calculations for the equation of regression line is tabulated below:
The regression coefficient of y on x is given by:
b
y
x
=
∑
x
y
−
1
n
∑
x
∑
y
∑
x
2
−
1
n
(
∑
x
)
2
=
1944
−
1
5
×
98
×
69
2580
−
1
5
(
98
)
2
=
591.6
659.2
=
0.898
byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898
Mean of x is calculated as:
¯
x
=
1
n
∑
x
=
1
5
×
98
=
19.6
x¯=1n∑x=15×98=19.6
Mean of y is calculated as:
¯
y
=
1
n
∑
y
=
1
5
×
69
=
13.8
y¯=1n∑y=15×69=13.8
The equation of regression line is given as:
y
−
¯
y
=
b
y
x
(
x
−
¯
x
)
y
−
13.8
=
0.898
(
x
−
19.6
)
y
=
0.898
x
−
3.8
y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8
Therefore, the required equation of regression line is y = 0.898x - 3.8.