# 线性代数网课代修|最小二乘法代写least squares method辅导|ENGO361

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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|Applying Least Squares to Classification Problems

In the previous sections the dependent variable $y$ was assumed to be a continuous numerical variable and the method of least squares was used to develop models that could then be used to predict the value of $y$ for any combination of the independent $\boldsymbol{x}$ variable (or variables). There are, however, problems in which the dependent variable is a “class” rather than a con-tinuous variable. For example the problem might require a model that differentiates between two classes: “good” or “bad” or three levels: “low”, “medium” or “high”. Typically we have $\boldsymbol{n} \boldsymbol{l} \boldsymbol{n}$ learning points that can be used to create the model and then $\boldsymbol{n} \boldsymbol{t s t}$ test points that can be used to test how well the model predicts on unseen data. The method of least squares can be applied to classification problems in a very straight-forward manner.

The trick that allows a very simple least squares solution to classification problems is to assign numerical values to the classes (i.e., the $y$ values) and then make predictions based upon the computed value of $\boldsymbol{y}$ for each test point. For example, for two class problems we can assign the values 0 and 1 to the two classes (e.g., “bad” $=0$ and “good” $=1$ ). We then fit the learning data using least squares as the modeling technique and then for any combination of the $\boldsymbol{x}$ variables, we compute the value of $\boldsymbol{y}$. If it is less than $0.5$ the test point is assumed to fall within the “bad” class, otherwise it is classified as “good”. For 3 class problems we might assign 0 to class 1 , $0.5$ to class 2 and 1 to class 3 . If a predicted value of $y$ is less than $1 / 3$ then we would assign class 1 as our prediction, else if the value was less than $2 / 3$ we would assign class 2 as our prediction, otherwise the assignment would be class 3 . Obviously the same logic can be applied to any number of classes.

## 线性代数作业代写linear algebra代考|MODEL EVALUATION

Once a least squares analysis has been completed, we turn our attention to an evaluation of the results. Is the model an adequate representation of the data? Modeling data is not always based upon a “correct” mathematical model. Sometimes one is interested in comparing alternative theoretical models to determine which theory is most applicable to the experimental data. Sometimes the model is proposed as a series and one needs to make a decision regarding the number of terms to keep to best represents the data. There are many situations in which all that one is interested in is an analytical equation that can be used to describe the data. One might start with a simple model and then progressively add terms. At what point do the additional terms lead to a poorer model?

If the data is to be analyzed using the method of least squares, and if we have $\boldsymbol{n}$ data points, the maximum number of unknown parameters that can be determined is $\boldsymbol{n}-1$. If we also have $\boldsymbol{n}{\boldsymbol{b}}$ Bayesian estimators, then the maximum is increased to $\boldsymbol{n}+\boldsymbol{n}{\boldsymbol{b}}-1$. As the number of unknown parameters is increased, $S$ (the weighted sum of the residuals) decreases so at first glance one might think that the more unknown parameters included in the model, the better the fit. However, we reach a point where additional terms begin to model the noise in the data rather than the true signal. Fortunately, statistical methods are available for determining when we should stop adding terms to a model. In this chapter, statistical methods for evaluation of models are presented.

# 计量经济学代写

## 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