# Chapt2 - ME 4905 Advanced Numerical Methods Least-Squares Regression Lecturer T.Y Ng(PhD Email [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ Curve Fitting Describes

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ME 4905 Advanced Numerical Methods Least-Squares Regression Lecturer: T.Y. Ng (PhD) Email: [email protected]

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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 best-fit 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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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 s 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 n i n y y i , , 1 K = = - = - = 2 ) ( 1 y y S n S S i t t y ( ) 1 / 2 2 2 - - = n n y y S i i y

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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.

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Chapt2 - ME 4905 Advanced Numerical Methods Least-Squares Regression Lecturer T.Y Ng(PhD Email [email protected] Curve Fitting Describes

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