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Mathematics
Mathematics
Problem
Consider the three data points
(
0
,
1
)
(0,1)
(
0
,
1
)
,
(
1
,
2
)
(1,2)
(
1
,
2
)
, and
(
2
,
2
)
(2,2)
(
2
,
2
)
. A line
y
=
m
x
+
b
y=mx+b
y
=
m
x
+
b
is used to model these data. Define the total squared deviation
E
(
m
,
b
)
=
∑
i
=
1
3
(
y
i
−
(
m
x
i
+
b
)
)
2
E(m,b)=\sum_{i=1}^{3}(y_i-(mx_i+b))^{2}
E
(
m
,
b
)
=
∑
i
=
1
3
(
y
i
−
(
m
x
i
+
b
)
)
2
. Determine the ordered pair
(
m
,
b
)
(m,b)
(
m
,
b
)
that minimizes
E
(
m
,
b
)
E(m,b)
E
(
m
,
b
)
.
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