统计代写|商业分析作业代写Statistical Modelling for Business代考|Graphically Summarizing Quantitative Data

• 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|Frequency distributions and histograms

Major consulting firms such as Accenture, Ernst \& Young Consulting, and Deloitte \& Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case a consulting firm has developed an electronic billing system for a Hamilton, Ohio, trucking company. The system sends invoices electronically to each customer’s computer and allows customers to easily check and correct errors. It is hoped that the new hilling system will substantially reduce the amount of time it takes customers to make payments. Typical payment times-measured from the date on an invoice to the date payment is received-using the trucking company’s old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days.
The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. Therefore, in order to assess the system’s effectiveness, the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system’s operation. The payment times for the 65 sample invoices are manually determined and are given in Table $2.4$. If this sample can be used to establish that the new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking companies.

Looking at the payment times in Table $2.4$, we can see that the shortest payment time is 10 days and that the longest payment timee is 29 days. Beyond that, it is pretty difficult to interpret the data in any meaningful way. To better understand the sample of 65 payment times, the consulting firm will form a frequency distribution of the data and will graph the distribution by constructing a histogram. Similar to the frequency distributions for qualitative data we studied in Section 2.1, the frequency distribution will divide the payment times into classes and will tell us how many of the payment times are in each class.

统计代写|商业分析作业代写Statistical Modelling for Business代考|Form Nonoverlapping Classes of Equal Width

Step 3: Form Nonoverlapping Classes of Equal Width We can form the classes of the frequency distribution by defining the boundaries of the classes. To find the first class boundary, we find the smallest payment time in Table $2.4$, which is 10 days. This value is the lower boundary of the first class. Adding the class length of 3 to this lower boundary, we obtain $10+3=13$, which is the upper boundary of the first class and the lower boundary of the second class. Similarly, the upper boundary of the second class and the lower boundary of the third class equals $13+3=16$. Continuing in this fashion, the lower boundaries of the remaining classes are $19,22,25$, and 28 . Adding the class length 3 to the lower boundary of the last class gives us the upper boundary of the last class, 31 . These boundaries define seven nonoverlapping classes for the frequency distribution. We summarize these classes in Table 2.6. For instance, the first class $-10$ days and less than 13 days-includes the payment times 10,11 , and 12 days; the second class $-13$ days and less than 16 days-includes the payment times 13 , 14 , and 15 days; and so forth. Notice that the largest observed payment time- 29 days-is contained in the last class. In cases where the largest measurement is not contained in the last class, we simply add another class. Generally speaking, the guidelines we have given for forming classes are not inflexible rules. Rather, they are inended to help us find reasunable classes. Finally, the method we have used for forming classes results in classes of equal length. Generally, forming classes of equal length will make it easier to appropriately interpret the frequency distribution.

统计代写|商业分析作业代写Statistical Modelling for Business代考|Graph the Histogram

Step 5: Graph the Histogram We can graphically portray the distribution of payment times by drawing a histogram. The histogram can be constructed using the frequency, relative frequency, or percent frequency distribution. To set up the histogram, we draw rectangles that correspond to the classes. The base of the rectangle corresponding to a class represents the payment times in the class. The height of the rectangle can represent the class frequency, relative frequency, or percent frequency.

We have drawn a frequency histogram of the 65 payment times in Figure 2.7. The first (leftmost) rectangle, or “bar,” of the histogram represents the payment times 10,11 , and 12 . Looking at Figure 2.7, we see that the base of this rectangle is drawn from the lower boundary (10) of the first class in the frequency distribution of payment times to the lower boundary (13) of the second class. The height of this rectangle tells us that the frequency of the first class is 3 . The second histogram rectangle represents payment times 13,14 , and 15 . Its base is drawn from the lower boundary (13) of the second class to the lower boundary (16) of the third class, and its height tells us that the frequency of the second class is 14 . The other histogram bars are constructed similarly. Notice that there are no gaps between the adjacent rectangles in the histogram. Here, although the payment times have been recorded to the nearest whole day, the fact that the histogram bars touch each other emphasizes that a payment time could (in theory) be any number on the horizontal axis. In general, histograms are drawn so that adjacent bars touch each other.

Looking at the frequency distribution in Table $2.7$ and the frequency histogram in Figure 2.7, we can describe the payment times:
1 None of the payment times exceeds the industry standard of 30 days. (Actually, all of the payment times are less than 30 -remember the largest payment time is 29 days.)
2 The payment times are concentrated between 13 and 24 days ( 57 of the 65 , or $(57 / 65) \times 100=87.69 \%$, of the payment times are in this range).

统计代写|商业分析作业代写Statistical Modelling for Business代考|Graph the Histogram

1 支付时间没有超过 30 天的行业标准。（实际上，所有的付款时间都少于 30 天——记住最大的付款时间是 29 天。）
2 付款时间集中在 13 到 24 天之间（65 天中的 57 天，或(57/65)×100=87.69%, 的付款时间在此范围内）。

广义线性模型代考

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MATLAB代写

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