## 数学代写|线性代数代写linear algebra代考|MTH 2106

2022年7月13日

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• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 数学代写|线性代数代写linear algebra代考|Confidence Intervals

You may have heard the term “confidence interval,” which often confuses statistics newcomers and students. A confidence interval is a range calculation showing how confidently we believe a sample mean (or other parameter) falls in a range for the population mean.

Based on a sample of 31 golden retrievers with a sample mean of $64.408$ and a sample standard deviation of $2.05$, I am 95\% confident that the population mean lies between $63.686$ and 65.1296. How do I know this? Let me show you, and if you get confused, circle back to this paragraph and remember what we are trying to achieve. I highlighted it for a reason!

I first start out by choosing a level of confidence (LOC), which will contain the desired probability for the population mean range. I want to be $95 \%$ confident that my sample mean falls in the population mean range I will calculate. That’s my LOC. We can leverage the central limit theorem and infer what this range for the population mean is. First, I need the critical $z$-value which is the symmetrical range in a standard normal distribution that gives me $95 \%$ probability in the center as highlighted in Figure 3-14.

How do we calculate this symmetrical range containing 95 of the area? It’s easier to grasp as a concept than as a calculation. You may instinctively want to use the CDF, but then you may realize there are a few more moving parts here.

First you need to leverage the inverse CDF. Logically, to get $95 \%$ of the symmetrical area in the center, we would chop off the tails that have the remaining $5 \%$ of area. Splitting that remaining $5 \%$ area in half would give us $2.5 \%$ area in each tail. Therefore, the areas we want to look up the $\mathrm{x}$-values for are $.025$ and $.975$ as shown in Figure 3-15.

## 数学代写|线性代数代写linear algebra代考|Understanding P-Values

When we say something is statistically significant, what do we mean by that? We hear it used loosely and frequently but what does it mean mathematically? Technically, it has to do with something called the p-value, which is a hard concept for many folks to grasp. But I think the concept of p-values makes more sense when you trace it back to its invention. While this is an imperfect example, it gets across some big ideas.
In 1925, mathematician Ronald Fisher was at a party. One of his colleagues Muriel Bristol claimed she could detect when tea was poured before milk simply by tasting it. Intrigued by the claim, Ronald set up an experiment on the spot.

He prepared eight cups of tea. Four had milk poured first; the other four had tea poured first. He then presented them to his connoisseur colleague and asked her to identify the pour order for each. Remarkably, she identified them all correctly, and the probability of this happening by chance is 1 in 70 , or $0.01428571$.

This $1.4 \%$ probability is what we call the p-value, the probability of something occurring by chance rather than because of a hypothesized explanation. Without going down a rabbit hole of combinatorial math, the probability that Muriel completely guessed the cups correctly is $1.4 \%$. What exactly does that tell you?

When we frame an experiment, whether it is determining if organic donuts cause weight gain or living near power lines causes cancer, we always have to entertain the possibility that random luck played a role. Just like there is a $1.4 \%$ chance Muriel identified the cups of tea correctly simply by guessing, there’s always a chance randomness just gave us a good hand like a slot machine. This helps us frame our null hypothesis $\left(H_{0}\right)$, saying that the variable in question had no impact on the experiment and any positive results are just random luck. The alternative hypothesis $\left(H_{1}\right)$ poses that a variable in question (called the controlled variable) is causing a positive result.

# 线性代数代考

## 数学代写|线性代数代写linear algebra代考| Understanding P-Values

1925年，数学家罗纳德·费舍尔（Ronald Fisher）参加了一个聚会。他的一位同事穆里尔·布里斯托尔（Muriel Bristol）声称，她只需品尝一下，就可以察觉到什么时候在牛奶之前倒茶。罗纳德对这种说法很感兴趣，于是在现场做了一个实验。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。