# 线性代数网课代修|最小二乘法代写least squares method辅导|ECON301

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• 数值分析
• 高等线性代数
• 矩阵论
• 优化理论
• 线性规划
• 逼近论

## 线性代数作业代写linear algebra代考|Statistical Learning

The term statistical learning is used to cover a broad class of methods and problems that have become feasible as the power of the computer has grown. An in-depth survey of this field is covered in a fairly recent book by Hastie, Tibshirani and Friedman entitled The Elements of Statistical Learning: Data Mining, Inference and Prediction [HA01]. Their book covers both supervised and unsupervised learning. The goal of supervised learning is to predict an output variable as a function of a number of input variables (or as they are sometimes called: indicators or predictors). In unsupervised learning there is no particular output variable and one is interested in finding associations and patterns among the variables. The cornerstone of statistical learning is to learn from the data. The analyst has access to data and his or her goal is to make sense out of the available information.

Supervised learning problems can be subdivided into regression and classification problems. The goal in regression problems is to develop quantitative predictions for the dependent variable. The goal in classification problems is to develop methods for predicting to which class a particular data point belongs. An example of a regression problem is the development of a model for predicting the unemployment rate as a function of economic indictors. An example of a classification problem is the development of a model for predicting whether or not a particular email message is a spam message or a real message. In this book, although classification problems are discussed (see Sections $2.8$ and 7.8), the emphasis is on regression problems.

## 线性代数作业代写linear algebra代考|THE METHOD OF LEAST SQUARES

The first published treatment of the method of least squares was included in an appendix to Adrien Marie Legendre’s book Nouvelles methods pour la determination des orbites des cometes. The 9 page appendix was entitled Sur la methode des moindres quarres. The book and appendix was published in 1805 and included only 80 pages but gained a 55 page supplement in 1806 and a second 80 page supplement in 1820 [ST86]. It has been said that the method of least squares was to statistics what calculus had been to mathematics. The method became a standard tool in astronomy and geodesy throughout Europe within a decade of its publication. The method was also the cause of a dispute between two giants of the scientific world of the $19^{\text {th }}$ century: Legendre and Gauss. Gauss in 1809 in his famous Theoria Motus claimed that he had been using the method since 1795. That book was first translated into English in 1857 under the authority of the United States Navy by the Nautical Almanac and Smithsonian Institute [GA57]. Another interesting aspect of the method is that it was rediscovered in a slightly different form by Sir Francis Galton. In 1885 Galton introduced the concept of regression in his work on heredity. But as Stigler says: “Is there more than one way a sum of squared deviations can be made small?” Even though the method of least squares was discovered about 200 years ago, it is still “the most widely used nontrivial technique of modern statistics” [ST86].

The least squares method is discussed in many books but the treatment is usually limited to linear least squares problems. In particular, the emphasis is often on fitting straight lines or polynomials to data. The multiple linear regression problem (described below) is also discussed extensively (e.g., [FR92, WA93]). Treatment of the general nonlinear least squares problem is included in a much smaller number of books. One of the earliest books on this subject was written by W. E. Deming and published in the pre-computer era in 1943 [DE43]. An early paper by R. Moore and R. Zeigler discussing one of the first general purpose computer programs for solving nonlinear least squares problems was published in 1960 [MO60]. The program described in the paper was developed at the Los Alamos Laboratories in New Mexico. Since then general least squares has been covered in varying degrees and with varying emphases by a number of authors (e.g., DR66, WO67, BA74, GA94, VE02).

## 在这种情况下，如何学好线性代数？如何保证线性代数能获得高分呢？

1.1 mark on book

【重点的误解】划重点不是书上粗体，更不是每个定义，线代概念这么多，很多朋友强迫症似的把每个定义整整齐齐用荧光笔标出来，然后整本书都是重点，那期末怎么复习呀。我认为需要标出的重点为

A. 不懂，或是生涩，或是不熟悉的部分。这点很重要，有的定义浅显，但证明方法很奇怪。我会将晦涩的定义，证明方法标出。在看书时，所有例题将答案遮住，自己做，卡住了就说明不熟悉这个例题的方法，也标出。

B. 老师课上总结或强调的部分。这个没啥好讲的，跟着老师走就对了

C. 你自己做题过程中，发现模糊的知识点

1.2 take note

1.3 understand the relation between definitions