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2020년 12월 26일 (토) 04:59 판

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  1. The least squares method provides the overall rationale for the placement of the line of best fit among the data points being studied.[1]
  2. In contrast to a linear problem, a non-linear least squares problem has no closed solution and is generally solved by iteration.[1]
  3. An example of the least squares method is an analyst who wishes to test the relationship between a company’s stock returns, and the returns of the index for which the stock is a component.[1]
  4. The line of best fit determined from the least squares method has an equation that tells the story of the relationship between the data points.[1]
  5. When calculating least squares regressions by hand, the first step is to find the means of the dependent and independent variables.[2]
  6. Modeling Workhorse Linear least squares regression is by far the most widely used modeling method.[3]
  7. It is what most people mean when they say they have used "regression", "linear regression" or "least squares" to fit a model to their data.[3]
  8. Not only is linear least squares regression the most widely used modeling method, but it has been adapted to a broad range of situations that are outside its direct scope.[3]
  9. Linear least squares regression also gets its name from the way the estimates of the unknown parameters are computed.[3]
  10. One of the first applications of the method of least squares was to settle a controversy involving Earth’s shape.[4]
  11. Measuring the shape of the Earth using the least squares approximationThe graph is based on measurements taken about 1750 near Rome by mathematician Ruggero Boscovich.[4]
  12. The method of least squares is now widely used for fitting lines and curves to scatterplots (discrete sets of data).[4]
  13. There are multiple methods of dealing with this task, with the most popular and widely used being the least squares estimation.[5]
  14. The least-squares method is a crucial statistical method that is practised to find a regression line or a best-fit line for the given pattern.[6]
  15. The method of least squares is generously used in evaluation and regression.[6]
  16. The method of least squares actually defines the solution for the minimization of the sum of squares of deviations or the errors in the result of each equation.[6]
  17. The least-squares method is often applied in data fitting.[6]
  18. Introduction Curve Fitting Toolbox™ software uses the method of least squares when fitting data.[7]
  19. To obtain the coefficient estimates, the least-squares method minimizes the summed square of residuals.[7]
  20. Least Squares Curve Fitting Toolbox software uses the linear least-squares method to fit a linear model to data.[7]
  21. Fit the model by weighted least squares.[7]
  22. Least-squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns.[8]
  23. The following discussion is mostly presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions.[8]
  24. In that work he claimed to have been in possession of the method of least squares since 1795.[8]
  25. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution.[8]
  26. Variations of the problem of fitting a function to a set of data: curvilinear relationships, weighted least squares, nonlinear squares, etc. are analyzed by Draper and Smith (1966).[9]
  27. The least squares method allows one to estimate the line of a population regression for which the sum of the squares is a minimum.[9]
  28. The least squares method is a good procedure to estimate the regression line for the population.[9]
  29. 0 for all i ≠ j Bacon (1953) describes the least squares method of fitting a line for different conditions and analyzes the goodness of fitting results from different experiments.[9]
  30. , linear least squares fitting may be applied iteratively to a linearized form of the function until convergence is achieved.[10]
  31. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible.[11]
  32. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).[11]
  33. Ordinary least squares regression (OLS) is usually just called “regression” in statistics.[11]
  34. If you are performing regression analysis, either by hand or using SPSS or Excel, you’ll actually be using the least squares method.[11]
  35. When the sum of the squares of the residuals is minimized by a liner combination of unknown parameters (∑a i ･x i + b), the method is called linear least-squares method.[12]
  36. When a nonlinear function is used for fitting, it is called nonlinear least-squares method.[12]
  37. Nonlinear least-squares method includes cases where fitting of unknown parameters is executed by numerical calculations without assuming a specific nonlinear function.[12]
  38. However, most people consider the Least-Squares Method more accurate, as it computes Fixed and Variable Costs mathematically.[13]
  39. The Least Squares model aims to define the line that minimizes the sum of the squared errors.[13]
  40. We need to be careful with outliers when applying the Least-Squares method, as it is sensitive to strange values pulling the line towards them.[13]
  41. (–) The Least-Squares method might yield unreliable results when the data is not normally distributed.[13]
  42. Regression analysis makes use of mathematical methods such as least squares to obtain a definite relationship between the predictor variable (s) and the target variable.[14]
  43. The least-squares method is one of the most effective ways used to draw the line of best fit.[14]
  44. The least squares regression method works by minimizing the sum of the square of the errors as small as possible, hence the name least squares.[14]
  45. In this section, we will be running a simple demo to understand the working of Regression Analysis using the least squares regression method.[14]
  46. Very often the least squares method (LSM) is used for determination of estimation of unknown parameter values.[15]
  47. With a view toward facilitating proper use of computer curve‐fitting programs, the method of least squares for fitting smooth curves to experimental data is discussed.[16]
  48. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement.[17]
  49. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator.[17]
  50. The least squares estimator achieves the asymptotically optimal rate that is usually possessed by residual-based estimators only.[17]
  51. Nevertheless, most of the above methods, including the least squares method, only applied to nonparametric regression models with homoscedastic errors.[17]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Least Squares Method Definition
  2. ↑ Calculating a Least Squares Regression Line: Equation, Example, Explanation
  3. ↑ 3.0 3.1 3.2 3.3 4.1.4.1. Linear Least Squares Regression
  4. ↑ 4.0 4.1 4.2 least squares method | Definition & Explanation
  5. ↑ Least Squares Regression Line Calculator
  6. ↑ 6.0 6.1 6.2 6.3 Least Square Method
  7. ↑ 7.0 7.1 7.2 7.3 Least-Squares Fitting
  8. ↑ 8.0 8.1 8.2 8.3 Least squares
  9. ↑ 9.0 9.1 9.2 9.3 Least Squares Method - an overview
  10. ↑ Least Squares Fitting -- from Wolfram MathWorld
  11. ↑ 11.0 11.1 11.2 11.3 Least Squares Regression Line: Ordinary and Partial
  12. ↑ 12.0 12.1 12.2 Glossary of TEM Terms
  13. ↑ 13.0 13.1 13.2 13.3 Least Squares Method For Variable And Fixed Costs
  14. ↑ 14.0 14.1 14.2 14.3 A Tutorial On Least Squares Regression Method Using Python
  15. ↑ LEAST-SQUARES METHOD AND TYPE B EVALUATION OF STANDARD UNCERTAINTY
  16. ↑ Fitting Experimental Data Using the Method of Least Squares
  17. ↑ 17.0 17.1 17.2 17.3 A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

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