# 线性代数网课代修|最小二乘法代写least squares method辅导|GIS-E3010

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## 线性代数作业代写linear algebra代考|Quantitative Experiments

Most areas of science and engineering utilize quantitative experiments to determine parameters of interest. Quantitative experiments are characterized by measured variables, a mathematical model and unknown parameters. For most experiments the method of least squares is used to analyze the data in order to determine values for the unknown parameters.

As an example of a quantitative experiment, consider the following: measurement of the half-life of a radioactive isotope. Half-life is defined as the time required for the count rate of the isotope to decrease by one half. The experimental setup is shown in Figure 1.1.1. Measurements of Counts (i.e., the number of counts observed per time unit) are collected from time 0 to time $\operatorname{tmax}$. The mathematical model for this experiment is:
$$\text { Counts }=\text { amplitude } \cdot e^{-\text {decay_}_{-} \text {constant } \cdot t}+\text { background }$$
For this experiment, Counts is the dependent variable and time $t$ is the independent variable. For this mathematical model there are 3 unknown parameters (amplitude, decay_constant and background). Possible sources of the background “noise” are cosmic radiation, noise in the instrumentation and sometimes a second much longer lived radioisotope within the source. The analysis will yield values for all three parameters but only the value of decay_constant is of interest. The half-life is determined from the resulting value of the decay constant:
\begin{aligned} &e^{-\text {decay_constant } \cdot \text { half_life }}=1 / 2 \ &\text { half_life }=\frac{0.69315}{\text { decay_constant }} \end{aligned}

## 线性代数作业代写linear algebra代考|Dealing with Uncertainty

The estimation of uncertainty is an integral part of data analysis. It is not enough to just measure something. We always need an estimate of the accuracy of our measurements. For example, when we get on a scale in the morning, we know that the uncertainty is plus or minus a few hundred grams and this is considered acceptable. If, however, our scale were only accurate to plus or minus 10 kilograms this would be unacceptable. For other measurements of weight, an accuracy of a few hundred grams would be totally unacceptable. For example, if we wanted to purchase a gold bar, our accuracy requirements for the weight of the gold bar would be much more stringent. When performing quantitative experiments, we must take into consideration uncertainty in the input data. Also, the output of our analysis must include estimates of the uncertainty of the results. One of the most compelling reasons for using least squares analysis of data is that uncertainty estimates are obtained quite naturally as a part of the analysis. For almost all applications the standard deviation $(\boldsymbol{\sigma})$ is the accepted measure of uncertainty. Let us say we need an estimate of the uncertainty associated with the measurement of the weight of gold bars. One method for obtaining such an estimate is to repeat the measurement $\boldsymbol{n}$ times and record the weights $\boldsymbol{w}{i}, \mathrm{i}=1$ to $\boldsymbol{n}$. The estimate of $\boldsymbol{\sigma}$ (the estimated standard deviation of the weight measurement) is computed as follows: $$\sigma^{2}=\frac{1}{n-1} \sum{i=1}^{i=n}\left(w_{i}-w_{a v g}\right)^{2}$$
In this equation $\boldsymbol{w}_{a v g}$ is the average value of the $\boldsymbol{n}$ measurements of $\boldsymbol{w}$. The need for $\boldsymbol{n}-1$ in the denominator of this equation is best explained by considering the case in which only one measurement of $\boldsymbol{w}$ is made (i.e., $\boldsymbol{n}=1$ ). For this case we have no information regarding the “spread” in the measured values of $\boldsymbol{w}$.

## 线性代数作业代写linear algebra代考|Quantitative Experiments

$$\text { Counts }=\text { amplitude } \cdot e^{-\text {decay }_{\text {_constant }} \cdot t}+\text { background }$$

## 线性代数作业代写linear algebra代考|Dealing with Uncertainty

$$\sigma^{2}=\frac{1}{n-1} \sum i=1^{i=n}\left(w_{i}-w_{\text {avg }}\right)^{2}$$

# 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