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Mathematics
Mathematics
Problem
A model of the form
y
=
a
x
y=ax
y
=
a
x
is used to approximate the data points
(
1
,
3
)
(1,3)
(
1
,
3
)
and
(
2
,
5
)
(2,5)
(
2
,
5
)
. The total error is defined as
S
(
a
)
=
(
3
−
a
(
1
)
)
2
+
(
5
−
a
(
2
)
)
2
S(a)= (3- a\thinspace\bigl(1\bigr))^{2} + (5- a\thinspace\bigl(2\bigr))^{2}
S
(
a
)
=
(
3
−
a
(
1
)
)
2
+
(
5
−
a
(
2
)
)
2
. Determine the value of
a
a
a
that minimizes
S
(
a
)
S(a)
S
(
a
)
.
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