Least Squares using MatLab

Aug 15, 2014

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Least Squares using MatLab. Adam Q. Colley EMIS8381 March 31, 2012. Least Squares Overview. One Dependent Variable One or more (n) Independent Variables (Independent to the Dependent Variable) More data points than number of Variables Find one equation with least amount of error.

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Least Squares using MatLab

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Partial Least Squares

Partial Least Squares. Very brief intro. Multivariate regression. The multiple regression approach creates a linear combination of the predictors that best correlates with the outcome

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Least Squares example

Least Squares example. There are 3 mountains u,y,z that from one site have been measured as 2474 ft., 3882 ft., and 4834 ft.. But from u, y looks 1422 ft. taller and the z looks 2354 ft. taller , and from y, z looks 950 ft. taller. Set up the overdetermined system. 2474 3882 4834 1422

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Ordinary Least-Squares

Ordinary Least-Squares. Outline. Linear regression Geometry of least-squares Discussion of the Gauss-Markov theorem. One-dimensional regression. One-dimensional regression. Find a line that represent the ”best” linear relationship:. One-dimensional regression.

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Least Squares Regression

Least Squares Regression. Fitting a Line to Bivariate Data. Correlation tells us about strength (scatter) and direction of the linear relationship between two quantitative variables.

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Ordinary least Squares

Ordinary least Squares. Introduction. Describe the nature of financial data. Assess the concepts underlying regressions analysis Describe some examples of financial models. Examine the Ordinary least Squares (OLS) technique and hypothesis testing. Financial data.

631 views • 21 slides

Least-Squares Regression

Least-Squares Regression. Section 3.3. Recall from 3.2:. Correlation measures the strength and direction of a linear relationship between two variables. How do we summarize the overall pattern of a linear relationship? Draw a line!. Least-Squares Regression.

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Parameter Estimation using Least Squares

Parameter Estimation using Least Squares. u nknown parameters. Least Squares. s calar variables. m easured value. Least squares identification. attempts to find values for theta for which the left- and the right-hand-sides of differ by the smallest possible error. More precisely,

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Least Squares

By: Sean DuBois. Least Squares. What are Least Squares?. The method of least squares attempts to answer what linear line the data lies on. It can also be used to predict values. In other words it attempts to find the line of best fit. . Uses. Can be used to predict: gas prices

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Linear Least Squares

Linear Least Squares. Paul Heckbert Computer Science Department Carnegie Mellon University. Orthogonal and Hermitian Matrix. A square matrix Q is orthogonal iff Q -1 = Q T Q T Q = QQ T = I its rows are orthonormal  its columns are orthonormal

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Nonlinear least squares

Nonlinear least squares. Given m data points (t i , y i ) i=1,2,…m, we wish to find a vector x of n parameters that gives a best fit in the least squares sense to a model m. For example consider the exponential decaying model: m(x,t)=x 1 e -x 2 t

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Least-Squares Regression

Least-Squares Regression. Correlation coefficient – r r describes the strength of the relationship In regression r 2 = fraction of variation in values of Y that is explained by X Example: The correlation between IQ and GPA was found to be a: r=0.50 b: r=0.99

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Least Squares Regression

Describe relationship in words. Could you predict gas consumption for a 22 degree-day? A 65 degree-day?. Least Squares Regression. Section 3.3 (First Part). Regression Line. Describes how response variable y changes as explanatory variable x changes. Used to make predictions.

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Least squares

Least squares. CS1114 http://cs1114.cs.cornell.edu. Robot speedometer. Suppose that our robot can occasionally report how far it has traveled (mileage) How can we tell how fast it is going? This would be a really easy problem if: The robot never lied

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Least Squares

Least Squares. 给定一组测量或观测值. 假设 y 是 n 个函数的线性组合. 设 m×n 矩阵 X 定义为. 所以. β = Xy. 直线：. 多项式：. 有理函数：. 指数：. Log-linear:. Gaussians:. 中国人口预测. p = 1e4*[ ]'; t = (1949:1:2005)'; x = (1940: 0.2 :2019)'; w = 2010; d = 3; s = (t-1979)/30; c = polyfit(s,p,d);

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LEAST SQUARES DATUMING

LEAST SQUARES DATUMING. Yanwei Xue Sep. 18, 2009. OUTLINE. Theory VSP->SWP. OBS Data Example. Application on Target Oriented RTM. VSP surface related multiples->SSP. Flat 3 layer model example. SEG/EAGE model Example. Two state model. State 1. State 2. State 1. State 2. OUTLINE.

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Method of Least Squares (Least Squares Regression):

6. Method of Least Squares:. (pp. 1001). Method of Least Squares (Least Squares Regression):. Examp 6.1:. : Sum of squares of errors. y=a+bx. a=1.188 b=0.484. y=1.188+0.484x. mls.txt. 3 -5,-2 2,4 7,3.5. Sub mlsquares_Click () ' Change File mls.txt for different problems ' y=a+b*x

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Least squares method

Least squares method. Let adjustable parameters for structure refinement be u j Then if R = S w( hkl ) (|F obs | – |F calc |) 2 = S w D 2 Must get ∂R/∂u i = 0 one eqn/parameter. hkl. hkl. hkl. hkl. Least squares method.

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Least Squares Migration

Least Squares Migration. d=Lm. Forward Model:. m mig =L T d. Standard Migration:. m =[L T L] -1 L T d. Migration Decon:. Least Sq. Migration :. m =[L T L] -1 m. mig. 5D input. 3D input. Motivation: Poor Acquisition Geomtery. Motivation: Poor Illumination. *. g. SALT.

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Linear Least Squares

Linear Least Squares. ELEC 413. Regression Analysis. The study and measure of the statistical relationship that exists between two or more variables Two variables  simple regression Three or more variables  multiple regression

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Least-squares Meshes

Least-squares Meshes. Olga Sorkine and Daniel Cohen-Or Tel-Aviv University SMI 2004. Our goal. Shape approximation Connectivity data Sparse geometric data Exploit information in the mesh graph. Connectivity Shapes. Connectivity has geometric information in it

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Linear Least Squares

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Regression Analysis Using Least Squares

Regression Analysis Using Least Squares. Using Microsoft Excel. Spectroscopy Data. Plot of Data. Calibration Line. In olden days (pre 1975) we would have plotted this data on a sheet of graph paper and then used a straight edge to determine the best straight line through this data.

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