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ME 4905
Advanced Numerical Methods
LeastSquares Regression
Lecturer: T.Y. Ng (PhD)
Email: [email protected]
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View Full Document Curve Fitting
s
Describes techniques to fit curves (
curve fitting
) to
discrete data to obtain intermediate estimates.
s
There are two general approaches two curve fitting:
s
Data exhibit a significant degree of scatter
. The
strategy is to derive a single curve that represents
the general trend of the data.
s
Data is very precise.
The strategy is to pass a curve
or a series of curves through each of the points.
s
In engineering two types of applications are
encountered:
s
Trend analysis  Predicting values of dependent
variable, may include extrapolation beyond data
points or interpolation between data points.
s
Hypothesis testing  Comparing existing
mathematical model with measured data.
Regression Analysis
Regression analysis is one of the important
problem in approximation theory. Generally
speaking, suppose we have a set of data
points, the question that we are interested in
is:
Can we find a ‘nice’ curve such that the curve
can bestfit all the data points? In other words,
we try to obtain a curve such that the deviation
between all data points and the curve is
minimal.
There are many types of regressions such as
linear regression, polynomial regression,
nonlinear regression, multiple regression etc.
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View Full Document Statistics
s
In course of engineering study, if several measurements are made
of a particular quantity, additional insight can be gained by
summarizing the data in one or more well chosen statistics that
convey as much information as possible about specific
characteristics of the data set.
s
These descriptive statistics are most often selected to represent
s
The location of the center of the distribution of the data,
s
The degree of spread of the data.
Mean and Standard Deviation
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Arithmetic mean
 The sum of the individual data points (yi) divided
by the number of points (n).
s
Standard deviation
 The most common measure of a spread for a
sample
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Variation
s
Variance
 Representation of spread by the square of the standard
deviation.
s
Coefficient of variation
 Has the utility to quantify the spread of data.
1
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This note was uploaded on 01/17/2010 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.
 Spring '08
 LUI

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