Instructor: Quanlei Fang
Dept. of Math, University at Buffalo, Spring 2009
Welcome
to
Math 122 Lecture 8
Survey of Calculus and its Applications I1
!
Partial Derivatives
!
Finding Relative Maxima and Minima
!
Lagrange Multipliers and Constrained
Optimization
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§ 7.5
!
Least Squares Error
!
Least Squares Line (Regression Line)
!
Determining a Least Squares Line
Definition
Example
Least Squares Error
:
The total error in
approximating the data points (
x
1
,
y
1
),
....
,
(
x
N
,
y
N
) by a line
y
=
Ax
+
B
, measured by
the sum
E
of the squares of the vertical
distances from the points to the line,
Example is
forthcoming.
Definition
Example
Least Squares Line
(
Regression Line
):
A
straight line
y
=
Ax
+
B
for which the error
E
is
as small as possible.
Example is
forthcoming.
Table 5 shows the 1994 price of a gallon (in U.S. dollars) of fuel and the
average miles driven per automobile for several countries.
(a) Find the straight line that provides the best least-squares fit to these data.
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- Spring '08
- BUETTGENS
- Derivative, Least Squares, Regression Analysis, Optimization, japan, Mathematical optimization
-
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