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Outlines
Least Squares Curve Fitting
Use of Software
ME 3023
Measurements in Mechanical Systems
Fall 2010
Dr. Gautam Chandekar
Prepared on: October 6, 2009
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
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Least Squares Curve Fitting
Use of Software
Least Squares Curve Fitting
LeastSquares Curve Fitting
Linear Regression
Linear Regression Example
Nonlinear Regression
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
Outlines
Least Squares Curve Fitting
Use of Software
Use of Software
Use of Software
Excel
MATLAB
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
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Part I
LeastSquares Curve Fitting
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
LeastSquares Curve Fitting
Linear Regression
Linear Regression Example
Nonlinear Regression
LeastSquares Curve Fitting
Experimental data always has a ﬁnite amount of error included
in it, due to both accumulated instrument inaccuracies and
also imperfections in the physical system being measured.
Even data describing a linear system won’t all fall on a single
straight line.
Leastsquares curve ﬁtting is a method to ﬁnd parameters
that ﬁt the errorladen data as best we can.
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
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Linear Regression
Linear Regression Example
Nonlinear Regression
Linear Regression
Linear regression
is the method of ﬁnding the slope and
y
intercept
of a line that best ﬁts a set of data, and is the most common
leastsquares method used in mechanical engineering.
Consider a series of data points (
x
1
,
y
1
), (
x
2
,
y
2
),
· · ·
, (
x
n
,
y
n
).
A linear function that attempts to ﬁt this data would be
y
=
a
0
+
a
1
x
, where
a
0
and
a
1
are constants not yet
determined.
After plugging each known value
x
i
into the equation, we’ll
ﬁnd some amount of error between the
y
i
points in the
original data the the predicted
y
value from the linear model.
This error
e
i
is found with the relationship
e
i
=
y
i

a
0

a
1
x
i
.
ME 3023
Measurements in Mechanical Systems
Fall 2010
Least Squares Curve Fitting Use of Software
LeastSquares Curve Fitting
Linear Regression
Linear Regression Example
Nonlinear Regression
Linear Regression (continued)
The error
e
i
at each point may be positive or negative, large or
small. One way to quantify how good a ﬁt a particular line is
would be to:
Treat negative and positive errors the same.
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This note was uploaded on 02/09/2011 for the course ME 3023 taught by Professor Chandekar during the Fall '10 term at TN Tech.
 Fall '10
 Chandekar

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