# 线性代数网课代修|最小二乘法代写least squares method辅导|STAT615

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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|Goodness-of-Fit

In Section $1.3$ the $\chi^{2}$ (chi-squared) distribution was discussed. Under certain conditions, this distribution can be used to measure the goodness-offit of a least squares model. To apply the $\boldsymbol{\chi}^{2}$ distribution to the measurement of goodness-of-fit, one needs estimates of the uncertainties associated with the data points. In Sections $2.5$ and $2.6$ it was emphasized that only relative uncertainties were required to determine estimates of the uncertainties associated with the model parameters and the model predictions. However, for goodness-of-fit calculations, estimates of absolute uncertainties are required. When such estimates of the absolute uncertainties are unavailable, the best approach to testing whether or not the model is a good fit is to examine the residuals. This subject is considered in Section $3.9$.

The goodness-of-fit test is based upon the value of $S /(n-p)$. Assuming that $S$ is based upon reasonable estimates of the uncertainties associated with the data points, if the value of $S /(n-p)$ is much less than one, this usually implies some sort of misunderstanding of the experiment. If the value is much larger than one, then one of the following is probably true: 1) The model does not adequately represent the data. 2) Some or all of the data points are in error. 3) The estimated uncertainties in the data are erroneous.

## 线性代数作业代写linear algebra代考|Selecting the Best Model

When modeling data, we are often confronted with the task of choosing the best model out of several proposed alternatives. Clearly we need a definition of the word “best” and criteria for making the selection. At first glance one might consider using $\boldsymbol{S}$ (the weighted sum of the squares of the residuals) as the criterion for choosing the best model but this choice is flawed. As $\boldsymbol{p}$ (the number of unknown parameters included in the model) increases, the values of $\boldsymbol{S}$ decreases and becomes zero if $\boldsymbol{p}$ is equal to $\boldsymbol{n}$ (the number of data points).

To illustrate this point, consider the data shown in Figure 2.3.2. This data was generated based upon a parabolic model $(p=3)$ and included $5 %$ random noise. The 10 data points were fit using the following polynomial model with values of $\boldsymbol{p}$ varying from 2 to 8 : $$y=a_{1}+\sum_{k=2}^{k=p} a_{k} x^{k-1}$$ Results are included in Table 3.3.1. Note that the value of $\boldsymbol{S}$ decreases as $\boldsymbol{p}$ increases but that the minimum value of $S /(n-p)$ is achieved for $p=3$. This is encouraging because the minimum value of $S /(n-p)$ was obtained for the value of $\boldsymbol{p}$ upon which the data was generated. However, can we use this criterion (i.e., choose the model for which $S /(n-p)$ is minimized) as the sole criterion for selecting a model?

## 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