The confidence interval is based on
mean square error. T<span>he </span>mean squared error<span> (</span>MSE<span>) </span><span>of an </span>estimator<span> measures the </span>average<span> of the squares of the </span>errors<span> or </span>deviations.<span> MSE is calculated by the formula attached in the picture, where Xbar is a vector of predictions, X is the vector of predicted values. </span>
Answer:
4x+2h
Step-by-step explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
lim
h
→
0
4
x
+
2
h
=
4
x
Answer:
What do u mean?
Step-by-step explanation:
Answer:
are you mad
Step-by-step explanation:
you are the funniest person
Answer:
10.7 units
Step-by-step explanation:
distance formula
