### 统计代写|商业分析作业代写Statistical Modelling for Business代考| Contingency Tables (Optional)

• 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|The Brokerage Firm Case: Studying Client Satisfaction

Previous sections in this chapter have presented methods for summarizing data for a single variable. Often, however, we wish to use statistics to study possible relationships between several variables. In this section we present a simple way to study the relationship between two variables. Crosstabulation is a process that classifies data on two dimensions. This process results in a table that is called a contingency table. Such a table consists of rows and columns – the rows classify the data according to one dimension and the columns classify the data according to a second dimension. Together, the rows and columns represent all possibilities (or contingencies).An investment broker sells several kinds of investment products-a stock fund, a bond fund, and a tax-deferred annuity. The broker wishes to study whether client satisfaction with its products and services depends on the type of investment product purchased. To do this, 100 of the broker’s clients are randomly selected from the population of clients who have

purchased shares in exactly one of the funds. The broker records the fund type purchased by each client and has one of its investment counselors personally contact the client. When contacted, the client is asked to rate his or her level of satisfaction with the purchased fund as high, medium, or low. The resulting data are given in Table 2.16.

Looking at the raw data in Table $2.16$, it is difficult to see whether the level of client satisfaction varies depending on the fund type. We can look at the data in an organized way by constructing a contingency table. A crosstabulation of fund type versus level of client satisfaction is shown in Table $2.17$. The classification categories for the two variables are defined along the left and top margins of the table. The three row labels-bond fund, stock fund, and tax deferred annuity-define the three fund categories and are given in the left table margin. The three column labels-high, medium, and low-define the three levels of client satisfaction and are given along the top table margin. Each row and column combination, that is, each fund type and level of satisfaction combination, defines what we call a “cell” in the table. Because each of the randomly selected clients has invested in exactly one fund type and has reported exactly one level of satisfaction, each client can be placed in a particular cell in the contingency table. For example, because client number 1 in Table $2.16$ has invested in the bond fund and reports a high level of client satisfaction, client number 1 can be placed in the upper left cell of the table (the cell defined by the Bond Fund row and High Satisfaction column).

## 统计代写|商业分析作业代写Statistical Modelling for Business代考|column percentages

One good way to investigate relationships such as these is to compute row percentages and column percentages. We compute row percentages by dividing each cell’s freguency by its corresponding row total and by expressing the resulting fraction as a percentage. For instance, the row percentage for the upper left-hand cell (bond fund and high level of satisfaction) in Table $2.17$ is $(15 / 30) \times 100 \%=50 \%$. Similarly, column percentages are computed by dividing each cell’s frequency by its corresponding column total and by expressing the resulting fraction as a percentage. For example, the column percentage for the upper left-hand cell in Table $2.17$ is $(15 / 40) \times 100 \%=37.5 \%$. Table $2.18$ summarizes all of the row percentages for the different fund types in Table 2.17. We see that each row in Table $2.18$ gives a percentage frequency distribution of level of client satisfaction given a particular fund type.
For example, the first row in Table $2.18$ gives a percent frequency distribution of client satisfaction for investors who have purchased shares in the bond fund. We see that 50 percent of bond fund investors report high satisfaction, while 40 percent of these investors report medium satisfaction, and only 10 percent report low satisfaction. The other mows in Tahle $2.18$ provide. Гepcent freynency distrikutions of client satisfaction for stock fund and annuity parchasers
All three percent frequency distributions of client satisfaction-for the bond fund, the stock fund, and the tax deferred annuity-are illustrated using bar charts in Figure $2.23$. In this figure, the bar heights for each chart are the respective row percentages in Table $2.18$. For example, these distributions tell us that 80 percent of stock fund investors report high satisfaction, while $97.5$ percent of tax deferred annuity purchasers report medium or low satisfaction. Looking at the entire table of row percentages (or the bar charts in Figure 2.23), we might conclude that stock fund investors are highly satisfied, that bond fund investors are quite satisfied (but, somewhat less so than stock fund investors), and that tax-deferred-annuity purchasers are less satisfied than either stock fund or bond fund investors. In general, row percentages and column percentages help us to quantify relationships such as these.

In the investment example, we have cross-tabulated two qualitative variables. We can also cross-tabulate a quantitative variable versus a qualitative variable or two quantitative variables against each other. If we are cross-tabulating a quantitative variable, we often define categories by using appropriate ranges. For example, if we wished to cross-tabulate level of education (grade school, high school, college, graduate school) versus income, we might define income classes $\$ 0-\$50,000, \$ 50,001-\$100,000, \$ 100,001-\$150,000$, and above $\$ 150,000$. ## 统计代写|商业分析作业代写Statistical Modelling for Business代考|Scatter Plots We often study relationships between variables by using graphical methods. A simple graph that can be used to study the relationship between two variables is called a scatter plot. As an example, suppose that a marketing manager wishes to investigate the relationship between the sales volume (in thousands of units) of a product and the amount spent (in units of$\$10,000$ ) on advertising the product. To do this, the marketing manager randomly selects 10 sales regions having equal sales potential. The manager assigns a different level of advertising expenditure for January 2016 to each sales region as shown in Table 2.20. At the end of the month, the sales volume for each region is recorded as also shown in Table $2.20$.

A scatter plot of these data is given in Figure 2.24. To construct this plot, we place the variable advertising expenditure (denoted $x$ ) on the horizontal axis and we place the variable sales volume (denoted $y$ ) on the vertical axis. For the first sales region, advertising expenditure equals 5 and sales volume equals 89 . We plot the point with coordinates $x=5$ and $y=89$ on the scatter plot to represent this sales region. Points for the other sales regions are plotted similarly. The scatter plot shows that there is a positive relationship between advertising expenditure and sales volumethat is, higher values of sales volume are associated with higher levels of advertising expenditure.
We have drawn a straight line through the plotted points of the scatter plot to represent the relationship between advertising expenditure and sales volume. We often do this when the relationship between two variables appears to be a straight line, or linear, relationship. Of course, the relationship between $x$ and $y$ in Figure $2.24$ is not perfectly linear-not all of the points in the scatter plot are exactly on the line. Nevertheless, because the relationship between $x$ and $y$ appears to be approximately linear, it seems reasonable to represent the general relationship between these variables using a straight line. In future chapters we will explain ways to quantify such a relationship that is, describe such a relationship numerically. Moreover, not all linear relationships between two variables $x$ and $y$ are positive linear relationships (that is, have a positive slope). For example, Table $2.21$ on the next page gives the average hourly outdoor temperature $(x)$ in a city during a week and the city’s natural gas consumption (y) during the week for each of the previous eight weeks. The temperature readings are expressed in degrees Fahrenheit and the natural gas consumptions are expressed in millions of cubic feet of natural gas. The scatter plot in Figure $2.25$ shows that there is a

negative linear relationship between $x$ and $y$-that is, as average hourly temperature in the city increases, the city’s natural gas consumption decreases in a linear fashion. Finally, not all relationships are linear. In Chapter 14 we will consider how to represent and quantify curved relationships, and, as illustrated in Figure $2.26$, there are situations in which two variables $x$ and $y$ do not appear to have any relationship.

To conclude this section, recall from Chapter 1 that a time series plot (also called a runs plot) is a plot of individual process measurements versus time. This implies that a time series plot is a scatter plot, where values of a process variable are plotted on the vertical axis versus corresponding values of time on the horizontal axis.

## 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。