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

linearalgebra.me 为您的留学生涯保驾护航 在线性代数linear algebra作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的线性代数linear algebra代写服务。我们的专家在线性代数linear algebra代写方面经验极为丰富，各种线性代数linear algebra相关的作业也就用不着 说。

• 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|The t distribution

The $t$ distribution (sometimes called the student- $t$ distribution) is used for samples in which the standard deviation is not known. Using $\boldsymbol{n}$ observations of a variable $x$, the mean value $x_{\text {avg }}$ and the unbiased estimate $s$ of the standard deviation can be computed. The variable $t$ is defined as: $$t=\left(x_{a v g}-\mu\right) /(s / \sqrt{n})$$ The $\boldsymbol{t}$ distribution was derived to explain how this quantity is distributed. In our discussion of the normal distribution, it was noted that the quantity $\left(\boldsymbol{x}_{\boldsymbol{a v g}}-\boldsymbol{\mu}\right) /(\boldsymbol{\sigma} / \sqrt{\boldsymbol{n}})$ follows the standard normal distribution $\boldsymbol{u}$. When $\boldsymbol{\sigma}$ of the distribution is not known, the best that we can do is use $s$ instead. For large values of $\boldsymbol{n}$ the value of $\boldsymbol{s}$ approaches the true value of $\boldsymbol{\sigma}$ of the distribution and thus $t$ approaches a standard normal distribution. The mathematical form for the $\boldsymbol{t}$ distribution is based upon the observation that Equation $1.3 .19$ can be rewritten as:

$$t=\frac{\left(x_{a v g}-\mu\right)}{(\sigma / \sqrt{n})}(\sigma / s)$$ The term $\sigma / \boldsymbol{s}$ is distributed as $\left((\boldsymbol{n}-1) / \boldsymbol{\chi}^{2}\right)^{1 / 2}$ where $\chi^{2}$ has $\boldsymbol{n}$-1 degrees of freedom. Thus the mathematical form of the $t$ distribution is derived from the product of the standard normal distribution and $\left((\boldsymbol{n}-1) / \boldsymbol{\chi}^{2}(\boldsymbol{n}-1)\right)^{1 / 2}$. Values of $\boldsymbol{t}$ for various percentage levels for $\boldsymbol{n}$-1 up to 30 are included in tables in many sources [e.g., AB64, FR92]. The $t$ table is also available online [ST03]. For values of $\boldsymbol{n}>30$, the $\boldsymbol{t}$ distribution is very close to the standard normal distribution.

## 线性代数作业代写linear algebra代考|Parametric Models

Quantitative experiments are usually based upon parametric models. In this discussion we define parametric models as models utilizing a mathematical equation that describes the phenomenon under observation. The model equation (or equations) contains unknown parameters and the purpose of the experiment is often to determine the parameters including some indication regarding the accuracy of these parameters. There are many situations in which the values of the individual parameters are of no interest. All that is important for these cases is that the parametric model can be used to predict values of the dependent variable (or variables) for other combinations of the independent variables. In addition, we are also interested in some measure of the accuracy of the predictions.

We need to use mathematical terminology to define parametric models. Let us use the term $y$ to denote the dependent variable (or variables). Usually $y$ is a scalar, but when there is more than one dependent variable, $y$ can denote a vector. The parametric model is the mathematical equation that defines the relationship between the dependent and independent variables. For the case of a single dependent and a single independent variable we can denote the model as:

$$y=f\left(x ; a_{1}, a_{2} . ., a_{p}\right)$$ The $\boldsymbol{a}_{k}$ ‘s are the $\boldsymbol{p}$ unknown parameters of the model. The function $\boldsymbol{f}$ is based on either theoretical considerations or perhaps it is based on the behavior observed from the measured values of $\boldsymbol{y}$ and $\boldsymbol{x}$.

## 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