### 统计代写|商业分析作业代写Statistical Modelling for Business代考|The Car Mileage Case: Estimating Mileage

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Auto Fuel Economy

Part 1: Auto Fuel Economy Personal budgets, national energy security, and the global environment are all affected by our gasoline consumption. Hybrid and electric cars are a vital part of a long-term strategy to reduce our nation’s gasoline consumption. However, until use of these cars is more widespread and affordable, the most effective way to conserve gasoline is to design gasoline powered cars that are more fuel efficient. ${ }^{5}$ In the short term, “that will give you the biggest bang for your buck,” says David Friedman, research director of the Union of Concerned Scientists’ Clean Vehicle Program.”

In this case study we consider a tax credit offered by the federal government to automakers for improving the fuel econonny of gasuline-powered midsize cars. According to The Fuel Economy Guide-2015 Model Year, virtually every gasoline-powered midsize car equipped with an automatic transmission and a six-cylinder engine has an EPA combined city and highway mileage estimate of 26 miles per gallon (mpg) of less. ${ }^{7}$ As a matter of fact, when this book was written, the mileage leader in this category was the Honda Accord, which registered a combined city and highway mileage of $26 \mathrm{mpg}$. While fuel economy has seen improvement in almost all car categories, the EPA has concluded that an additional $5 \mathrm{mpg}$ increase in fuel economy is significant and feasible. ${ }^{8}$ Therefore, suppose that the government has decided to offer the tax credit to any automaker selling a midsize model with an automatic transmission and a six-cylinder engine that achieves an EPA combined city and highway mileage estimate of at least $31 \mathrm{mpg}$.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Sampling a Process

Part 2: Sampling a Process Consider an automaker that has recently introduced a new midsize model with an automatic transmission and a six-cylinder engine and wishes to demonstrate that this new model qualifies for the tax credit. In order to study the population of all cars of this type that will or could potentially be produced, the automaker will choose a sample of 50 of these cars. The manufacturer’s production operation runs 8 -hour shifts, with 100 midsize cars produced on each shift. When the production process has been finetuned and all start-up problems have been identified and corrected, the automaker will select one car at random from each of 50 consecutive production shifts. Once selected, each car is to be subjected to an $\mathrm{EP}^{3} \mathrm{~A}$ test that determines the EPA combined city and highway mileage of the car.

To randomly select a car from a particular production shift, we number the 100 cars produced on the shift from 00 to 99 and use a random number table or a computer software package to obtain a random number between 00 and 99 . For example, starting in the upper left-hand corner of Table 1.4(a) and proceeding down the two leftmost columns, we see that the first three random numbers between 00 and 99 are 33,3 , and 92 . This implies that we would select car 33 from the first production shift, car 3 from the second production shift, car 92 from the third production shift, and so forth. Moreover, because a new group of 100 cars is produced on each production shift, repeated random numbers would not be discarded. For example, if the 15 th and 29 th random numbers are both 7 , we would select the 7 th car from the 15th production shift and the 7th car from the 29th production shift.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The Sample and Inference

Part 3: The Sample and Inference Suppose that when the 50 cars are selected and tested, the sample of 50 EPA combined mileages shown in Table $1.7$ is obtained. A time series plot of the mileages is given in Figure 1.5. Examining this plot, we see that, although the mileages vary over time, they do not seem to vary in any unusual way. For example, the mileages do not tend to either decrease or increase (as did the basic cable rates in Figure 1.3) over time. This intuitively verifies that the midsize car manufacturing process is producing consistent car mileages over time, and thus we can regard the 50 mileages as an approximately random sample that can be used to make statistical inferences about the porpulation of all

possible midsize car mileages. ${ }^{9}$ Therefore, because the 50 mileages vary from a minimum of $29.8 \mathrm{mpg}$ to a maximum of $33.3 \mathrm{mpg}$, we might conclude that most midsize cars produced by the manufacturing process will obtain between $29.8 \mathrm{mpg}$ and $33.3 \mathrm{mpg}$.

We next suppose that in order to offer its tax credit, the federal government has decided to define the “typical” EPA combined city and highway mileage for a car model as the mean of the population of EPA combined mileages that would be obtained by all cars of this type. Therefore, the government will offer its tax credit to any automaker selling a midsize model equipped with an automatic transmission and a six-cylinder engine that achieves a mean EPA combined mileage of at least $31 \mathrm{mpg}$. As we will see in Chapter 3 , the mean of a population of measurements is the average of the population of measurements. More precisely, the population mean is calculated by adding together the population measurements and then dividing the resulting sum by the number of population measurements. Because it is not feasible to test every new midsize car that will or could potentially be produced, we cannot obtain an EPA combined mileage for every car and thus we cannot calculate the population mean mileage. However, we can estimate the population mean mileage by using the sample mean mileage. To calculate the mean of the sample of 50 EPA combined mileages in Table 1.7, we add together the 50 mileages in Table $1.7$ and divide the resulting sum by 50 . The sum of the 50 mileages can be calculated to be
$$30.8+31.7+\cdots+31.4=1578$$
and thus the sample mean mileage is $1578 / 50=31.56$. This sample mean mileage says that we estimate that the mean mileage that would be obtained by all of the new midsize cars that will or could potentially be produced this year is $31.56 \mathrm{mpg}$. Unless we are extremely lucky, however, there will be sampling error. That is, the point estimate of $31.56 \mathrm{mpg}$, which is the average of the sample of 50 randomly selected mileages, will probably not exactly equal the population mean, which is the average mileage that would be obtained by all cars. Therefore, although the estimate $31.56$ provides some evidence that the population mean is at least 31 and thus that the automaker should get the tax credit, it does not provide definitive evidence. To obtain more definitive evidence, we employ what is called statistical modeling. We introduce this concept in the next subsection.

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|The Sample and Inference

30.8+31.7+⋯+31.4=1578

## 广义线性模型代考

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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。