【连载】CB Predictor操作手册(Crystal Ball Predictor 水晶球预测)

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下面说回归方法，通常用的有三种方法

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Regression methods回归方法

CB Predictor uses one of three regression methods: standard regression, forward stepwise regression, and iterative stepwise regression.
CB Predictor使用三种回归方法中的一种：标准回归，逐步回归和迭代回归。

Standard regression标准回归

Standard regression performs multiple linear regression, generating regression coefficients for each independent variable you specify, no matter how significant.
标准回归是多元线性回归，根据要求对每个自变量生成回归系数，各系数没有轻重之分。

Forward stepwise regression逐步向前回归

Forward stepwise regression adds one independent variable at a time to the multiple linear regression equation, starting with the independent variable with the most significant probability of the correlation (partial F statistic). It then recalculates the partial F statistic for the remaining independent variables, taking the existing regression equation into consideration.
逐步回归是指在某个时间在多元线性方程中增加一个自变量，首先从相关性最大、最重要的自变量开始（部分F统计）。然后重新计算增加了自变量的部分f统计，同时考虑现有的回归方程。

CB Predictor Note: The resulting multiple linear regression equation will always have at least one independent variable.
注意：多元线性方程的至少要有一个以上自变量。

Forward stepwise regression continues to add independent variables until either:
•It runs out of independent variables.
•It reaches one of the selected stopping criteria in the Stepwise Options dialog.
•The number of included independent variables reaches one-third the number of data points in the series.
逐步回归中连续增加自变量直到：
    自变量全部增加完了
    根据逐步回归方法达到了停止的标准
    在系列中自变量的数量达到了1/3的数据点的数量。
There are two stopping criteria: 有两个停止标准：

R-squaredR平方

Stops the stepwise regression if the difference between a specified statistic (either R2 or adjusted R2) for the previous and new regression solutions is below a threshold value. When this happens, CB Predictor does not use the last independent variable.如果之前的统计和新的回归方法之间的偏差低于临界值的时候应该停止逐步回归。当这种情况发生的时候，CB Predictor不使用最后一个自变量。For example, the third step of a stepwise regression results in an R2 value of 0.81, and the fourth step adds another independent variable and results in an R2 value is 0.83. The difference between the R2 values is 0.02.If the Threshold value is 0.03, CB Predictor returns to the regression equation for the third step and stops the stepwise Regression例如，逐步回归结果的第三步R2的值是0.81，第四步加另一个独立变量后R2的值是0.83。两者之间的R2值差值是0.0 2。     如果差值为0.03，CB Predictor将返回到第三步回归方程，并停止逐步回归。

F-test significanceF值

Stops the stepwise regression if the probability of the F statistic for a new solution is above a maximum value.如果新方案的F值是最大的则停止逐步回归。For example, if you set the maximum probability to 0.05 and the F statistic for the fourth step of a stepwise regression results in a probability of 0.08, CB Predictor returns to the regression equation for the third step and stops the stepwise regression.例如，如果设置的最大概率值是0.05，逐步回归结果第四步F统计值是0.08，CB Predictor返回到第三步回归方程，并停止逐步回归

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Iterative stepwise regression迭代回归

Iterative stepwise regression adds or removes one independent variable at a time to or from the multiple linear regression equation.
迭代回归是指在某个时间点从多元线性回归方程中增加或去除一个自变量。
To perform iterative stepwise regression, CB Predictor:迭代回归的情况是：

1.Calculates the partial F statistic for each independent variable.
1、对每个自变量计算其部分F值。

2.Adds the independent variable with the most significant correlation (partial F statistic).
2、增加相关性最明显的自变量（部分F值）

3.Checks the partial F statistic of the independent variables in the regression equation to see if any became insignificant (have a probability below the minimum) with the addition of the latest independent variable.
3、检查回归方程中的每个自变量的部分F值，看它们是否会因为增加了一个自变量而变的没有相关性（低于最小值）。

4.Removes the least significant of any insignificant independent variables one at a time.
4、在某个时间点去除相关性最小的自变量。

5.Repeat step 3 until no insignificant variables remain in the regression equation.
5、重复第三步，直到回归方程中没有没有相关性的自变量。

6.Repeat steps 1 through 5 until:
•The model runs out of independent variables.
•The regression reaches one of the stopping criteria (see the previous section for information on how the stopping criteria work).
•The same independent variable is added and then removed
6、重复第一到第五步，直到：
        使用完了所有的自变量
        达到了停止回归的标准
        同一个进行了自变量增加、删除。

CB Predictor Note: The resulting equation will always have at least one independent variable.
CB Predictor注意：方程最后至少要包含一个自变量

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回归统计涉及了几个统计参数，如R方等.....

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Regression statistics回归统计

Once CB Predictor finds the regression equation, it calculates several statistics to help you evaluate the regression. See Appendix E, “Regression Statistic Formulas” for more information on the formulas CB Predictor uses to calculate these statistics.
一旦CB Predictor得到回归方程，它会帮助你计算各种统计数据来对回归进行评。附录E中“回归统计公式”有关于CB Predictor计算统计的更多内容。

R2

Coefficient of determination. This statistic indicates the percentage of the variability of the dependent variable that the regression equation explains.
R2是一个决定系数。它能表示在回归方程中因变量受到多大影响的百分比的情况。

For example, an R2 of 0.36 indicates that the regression equation accounts for 36% of the variability of the dependent variable.
例如，在回归方程中R2的值是0.36的话，就意味者自变量对因变量有36%的影响力。

Adjusted R2调整 R2

Corrects R2 to account for the degrees of freedom in the data. In other words, the more data points you have, the more universal the regression equation is. However, if you have only the same number of data points as variables, the R2 might appear deceivingly high. This statistic corrects for that.

调整后的R2是在数据自由度方面对R2进行修改，换句话说，你如果有更多的数据点，回归方程就越广泛。但是，如果你只有相同的数据点，R2会出现很高的假象。这种统计方法可以对此进行纠正。

For example, the R2 for one equation might be very high, indicating that the equation accounted for almost all the error in the data. However, this value might be inflated if the number of data points was insufficient to calculate a universal regression equation.

例如，在一个方程中的R2可能非常高，这表明方程能计算出几乎所有的误差值。但是如果数据点的数量不足以用来进行回归方程计算时，这个值也可能非常大。

SSE

Sum of square deviations. The least squares technique for estimating regression coefficients minimizes this statistic, which measures the error not eliminated by the regression line.
平方差的总和。用最小的计算方法来估计回归系数的最小值，从而来度量回归线中没有去除的偏差。

For any line drawn through a scatter plot of data, there are a number of different ways to determine which line fits the data best. One method is to compare the fit of lines is to calculate the SSE (sum of the squared errors) for each line. The lower the SSE, the better the fit of the line to the data.
任何图线都可以通过散点图形成，但是有一些不同的方法去决定那条直线表明最好的数据。其中一中比较线性好坏的方法就是SSE。SSE越低，表示图线和数据越适合。

F statistic

Tests the significance of the regression equation as measured by R2. If this value is significant, it means that the regression equation does account for some of the variability of the dependent variable.
通过度量R2来测试回归方程的影响力。如果这个值关联性大，则表示回归方程中自变量的可变性越大。

t statistic

Tests the significance of the relationship between the coefficients of the dependent variable and the individual independent variable, in the presence of the other independent variables. If this value is significant, it means that the independent variable does contribute to the dependent variable.
测试自变量系数和单独的因变量或其他的因变量之间关系的重要性。如果这个值是重要的，那表示因变量受自变量的影响大。

p

Indicates the probability of your calculated F or t statistic being as large as it is (or larger) by chance. A low p value is good and means that the F statistic is not coincidental and, therefore, is significant. A significant F statistic means that the relationship between the dependent variable and the combination of independent variables is significant.
表示计算F的可能性或者统计的数据越来越大。P值越低表示越好，并意味着F统计的可能性越高，因此更有意义。一个有效的F值表示自变量和相关的因变量之间的关系越明显。

Generally, you want your p to be less than 0.05.
一般来说，P值最好小于0.05

Durbin-Watson

Detects autocorrelation at lag 1. This means that each time-series value influences the next value. This is the most common type of autocorrelation.For the formula, see page 138.
The value of this statistic can be any value between 0 and 4. Values indicate slow-moving, none, or fast-moving autocorrelation, as shown in Table 2.2.
缺陷自相关是1。这表示每个时间序列值会对下一个值有影响。这是一般情况下的自相关。这种统计的值可以是0-4之间的任何数值，数值表示移动快慢的情况。

Table 2.2 Interpreting the Durbin Watson statistic

Durbin-Watson statistic统计	Means含义
Less than 1 小于1	The errors are positively correlated. An increase in one period follows an increase in the previous period.误差是正相关。一个周期增加下一个周期也会随着增加。
22	No autocorrelation.不相关
More than 3大于3	The errors are negatively correlated. An increase in one period follows an decrease in the previous period.误差是负相关。一个周期的增加下一个周期会随之减少。

Avoid using independent variables that have errors with a strong positive or negative correlation, since this can lead to an incorrect forecast for the dependent variable.

应该避免自变量有明显的正相关或者负相关，这样会导致因变量预测不准确。

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Historical data statistics历史数据统计

CB Predictor automatically calculates the following statistics for historical data series:
CB Predictor会自动计算历史数据的下列统计值：

mean均值
The mean of a set of values is found by adding the values and dividing their sum by the number of values. The term “average” usually refers to the mean. For example, 5.2 is the mean or average of 1, 3, 6, 7, and 9.
平均值是指一系列数据通过增加数据或者减少数据的和，通常称为平均值。例如5.2就是数据1.3.6.7.9的平均值。

standard deviation标准方差
The standard deviation is the square root of the variance for a distribution. Like the variance, it is a measure of dispersion about the mean and is useful for describing the “average” deviation.
标准方差是一个分布的偏差的平方根。

For example, you can calculate the standard deviation of the values 1, 3, 6, 7, and 9 by finding the square root of the variance that is calculated in the variance example below.
The standard deviation, denoted as , is calculated from the variance as follows:
例如，你可以对1.3.6.7.9这组数字计算它们的标准方程，在下面的例子中可以看出如何用方差计算方差的平方根。
    标准偏差，计算如下：
S=√10.2＝3.19

where the variance is a measure of the dispersion, or spread, of a set of values about the mean. When values are close to the mean, the variance is small. When values are widely scattered about the mean, the variance is larger.
偏差是对一系列数值的平均值进行分散，或离散计算。当这个值接近平均值，差异很小。当这个值越远离平均值，差异越大。

To calculate the variance of a set of values:
计算数值的误差值：

1.Find the mean or average.
1、找到数据的平均值。

2.For each value, calculate the difference between the value and the mean.
2、对每一个值，计算其和平均值之间的差值。

3.Square these differences.
3、对这些差值进行平均。

4.Divide by n-1, where n is the number of differences.
4、除以n-1，n是表示有多少个数据。

For example, suppose your values are 1, 3, 6, 7, and 9. The mean is 5.2. The variance, denoted by , is calculated as follows:
例如，1.3.6.7.9这组数据，它们的均值是5.2，方差的计算方法如下：

S^2=[(1-5.2)^2+(3-5.2)^2+(6-5.2)^2+(7-5.2)^2+(9-5.2)^2]/(5-1)=40.8/4=10.2

minimum最小值
The minimum is the smallest value in the data range.
最小值是指在一组数据中最小的一个数值。

Maximum最大值
The maximum is the largest value in the data range.
最大值是指在一组数据中最大的一个数值。

Ljung-Box statistic Ljung-Box 统计
Measures whether a set of autocorrelations is significantly different from a set of autocorrelations that are all zero. See page 139 for the formula.
对自相关是0和自相关明显的差异进行度量。

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下次进入手册的第三章，用CB Predictor进行预测{:8_307:}

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:dabin期待ing

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Chapter 3              
Forecasting with CB Predictor
用CB Predictor进行预测

In this chapter
•Overview
•Creating a spreadsheet with historical data
•Loading and starting CB Predictor
•Guidelines for using CB Predictor
•Analyzing the results
•Customizing reports and charts
在这一章中
•概述
•用历史数据创建一个电子表格
•加载和启动CB Predictor
•使用CB Predictor指南
•分析结果
•自定义报告和图表

This chapter contains detailed procedures for using CB Predictor. It describes how to forecast using both time-series forecasting methods and multiple linear regression. It also describes all the settings you can choose for your results.
本章对CB Predictor的使用步骤进行了详细描述。它对时间序列和多元线性回归的预测都进行了描述，同时对选择结果的设置进行了描述。

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Overview概述

When you use CB Predictor for the first time, there are several things you need to do:
当你第一次使用CB Predictor时，需要注意以下几方面的事情：

1.Create an Excel spreadsheet with your historical data.
1、建立一个有历史数据的excel电子表格

2.Start CB Predictor.
2、打开CB Predictor

3.Run CB Predictor.
3、运行CB Predictor

4.Analyze your results.
4、对结果进行分析

5.Customize your results.
5、对结果进行设置。

This chapter describes how to complete each of these steps to make forecasting your historical data an easy task.
本章描述了怎样完成对历史数据进行预测的每一个步骤。

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Creating a spreadsheet with historical data
用历史数据创建一个电子表格

Before using CB Predictor, you must create an Excel spreadsheet with your historical data. Creating a spreadsheet for use with CB Predictor is easy. The spreadsheet must include:
在使用CB Predictor之前，你必须先建立一张有历史数据的excel电子表格。这张电子表格必须包括：

•Optionally, a descriptive spreadsheet title.
对电子表格标题进行描述。

•Optionally, a date (or other time period, such as Q2-2004) column or row, either at the top or along the left side of your data. If you format your dates as Excel dates, CB Predictor’s Intelligent Input can find the dates, extend them with the forecasted values, and use them as labels on charts.
有一组数据按列或者行进行排列，如果对数据继续排列，CB Predictor会自动的选择输入的数据，并且会输出预测值。

•Historical data, spaced equal time periods apart, in columns or rows adjacent to the date column or row. You can use CB Predictor to simultaneously forecast from one to 10,000 adjacent historical data series.
历史数据必须是同一时间段的数据，按列或者行排列，你可以使用CB Predictor同时对相近的1-10000的历史数据进行预测。

Excel Note: Excel only has 256 possible columns, compared to 16,000 or 65,000 possible rows (depending on your version). So, if you have a large number of historical data points, organize your data in columns. If you have a large number of data series, organize your data in rows.
注意：EXCEL表只有256列，16000或65000行（根据软件的不同版本）。所以，如果你的历史数据比较多，需要对历史数据进行整理。

To produce a reasonable forecast, you should have at least 6 historical data values. To use seasonal forecasting methods, you need at least two complete cycles of data.
为了得到一个合理的预测值，你需要至少有6个以上的历史数据。如果使用季节性预测方法，你不要至少有两个以上完整周期的数据。

•Optionally, headings for each data column or row, such as SKU 23442, Gas Usage, or Interest Rate.
对每行或每列的数据输入标题。

The Toledo Gas spreadsheet has all these components.
托莱多气体电子表格的所有内容：


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Loading and starting CB Predictor
加载和启动CB Predictor

If you have Crystal Ball Professional or Premium Edition, CB Predictor is loaded when you start Crystal Ball.

如果你有CB Predictor的专业版或高级版，CB Predictor会在你启动Crystal Ball的时候同时启动
To start CB Predictor, use one of these:

•In the menubar, choose Run > CB Predictor, or
•Type Alt-r, p.

When you start CB Predictor, the CB Predictor dialog, or wizard, appears as shown in Figure 3.2. It has four tabs, arranged from left to right in the typical order of their use. For descriptions of each setting on each tab, see Appendix A, “The CB Predictor Wizard.”
开始CB Predictor，在菜单中点击Run>CB Predictor，或者点击Alt-r，p
当开始CB Predictor，CB Predictor对话框或者向导会出现，如图3.2.从左到右它有四个表格。

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Loading and starting CB Predictor
加载和启动CB Predictor

If you have Crystal Ball Professional or Premium Edition, CB Predictor is loaded when you start Crystal Ball.

如果你有CB Predictor的专业版或高级版，CB Predictor会在你启动Crystal Ball的时候同时启动
To start CB Predictor, use one of these:

•In the menubar, choose Run > CB Predictor, or
•Type Alt-r, p.

When you start CB Predictor, the CB Predictor dialog, or wizard, appears as shown in Figure 3.2. It has four tabs, arranged from left to right in the typical order of their use. For descriptions of each setting on each tab, see Appendix A, “The CB Predictor Wizard.”
开始CB Predictor，在菜单中点击Run>CB Predictor，或者点击Alt-r，p
当开始CB Predictor，CB Predictor对话框或者向导会出现，如图3.2.从左到右它有四个表格。

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Guidelines for using CB Predictor CB Predictor使用指南

After you create your Excel spreadsheet with historical data, forecasting data using CB Predictor follows a 10-step process:
将历史数据放入到Excel电子表格中后，按照以下的10个步骤用CB Predictor对历史数据进行预测：

1.Select a cell range with your historical data to forecast.
1、选择历史数据中的其中一个单元格来进行预测。

2.Specify your data arrangement.
2、指定数据的排列方式，

3.View a graph of your historical data to identify any seasonality (data cycles) or trend and to see summary statistics.
3、查看历史数据确认数据的季节性或者趋势和概要统计。

4.Identify your time periods, whether your data have seasonality, and, if so, how long your season is.
4、确认时间周期，看数据是否有季节性，如果有，周期是多长。

5.Set whether you want to use multiple linear regression to forecast any variables.
5、设定对预测变量是否需要使用多元线性回归方法。

6.Select the time-series forecast methods to try for each variable.
6、对每一个因素选择时间序列预测方法

7.Enter the number of periods you want to forecast.
7、输入你想要预测的周期数

8.Select a confidence interval to calculate or display with your forecasted values.
8、选择一个置信区间来计算或者显示预测值。

9.Select the results you want.
9、选择你需要的结果

10.Preview and run the forecast, creating your results.
10、评审和运行预测，得到你的结果。

CB Predictor leads you through these steps using the CB Predictor wizard, but you can also go directly to any of these steps to change methods or select different settings and reforecast data.
CB Predictor使用向导引导每个步骤，但是你也可以直接到其中的任何一个步骤去选择不同的预测结果。

Also, many of these steps might be done automatically by CB Predictor. For example, CB Predictor’s Intelligent Input can find and select your data, their arrangement, and the data units. And, you can skip many other steps if the settings are already what you want. For example, all the time-series forecasting methods are selected by default, and that is probably how most users will leave them.
同时，许多步骤CB Predictor会自动执行，例如，CB Predictor自动选择你要输入的数据，数据排列，和数据单位。你可以通过设置你想要的跳过一些步骤。

Selecting historical data选择历史数据

When you select your historical data, you must identify the Excel cells that contain the data, including dates and headers, and set settings to identify dates, headers, and orientation in the data.
当你选择了历史数据，你必须确认excel单元格包括了这些数据，包括数值和标题等。

To produce a reasonable forecast, you should have a minimum number of historical data points. CB Predictor imposes several requirements defining a minimum number of points to use to create a forecast. The bare minimum is 5. However, other limitations include:
为了得到一个合理的结果，你需要有历史数据的最小值。CB Predictor

•Single moving average requires that the number of historical data points is twice the number of points to forecast.
一次移动平均要求历史数据的数量是需要预测的数据点数量的两倍。

•Double moving average requires that the number of historical data points be three times the number of points to forecast (or at least 6, whichever is higher).
二次移动平均要求历史数据的数量是需要预测的数据点数量的三倍（或者至少是6个）

•To use seasonal methods, you must have at least two seasons (complete cycles) of historical data.
使用季节性方法，你必须有至少两个季节（完整周期）的历史数据

•For multiple linear regression, the number of historical data points must be three times the number of independent variables (counting the included constant as an independent variable).
对于多元线性回归，历史数据点的数量必须是自变量数量的三倍以上

•To lag an independent variable in multiple linear regression, the number of historical data points must be three times the lag.
在多元线性回归中要对一个自变量进行滞后，历史数据的数量必须是滞后次数的三倍。

If your data has empty cells in the middle of a data series, CB Predictor returns an error. CB Predictor treats zeros in data series as data values. If you are trying to forecast several data series at once, your data series do not have to start at the same time period. However, all the data series must end at the same time period.
如果你的数据系列中有空的单元格，CB Predictor会提示错误。CB Predictor会把它默认为是0。如果你想一次预测更多的数据，你的数据系列中不需要都是同一个时间开始的数据，但是需要是在同一个时间结束的数据。

When you initially open a spreadsheet, there are three ways to select the historical data to forecast:
当你开始打开一个电子表格时，有三种方法去选择对历史数据进行预测：

•Use CB Predictor’s Intelligent Input.
使用CB Predictor自动选择

•Select your data before you start the wizard.
在开始向导之前选择你的数据

•Select your data after you start the wizard.
在选择数据后再开启向导

Automatic data selection数据自动选取

The easiest way to select data is to select one cell somewhere in your continuous data range before you start the CB Predictor wizard. When you start the wizard, CB Predictor’s Intelligent Input searches for all the adjacent cells with numbers, dates, and headers and makes some other assumptions about your input data, such as whether your data are in rows or columns. This often completes most of the fields and settings on the Input Data tab.
这是最简单的方法，在打开CB Predictor向导前在数据中选择其中的一个数据。当你打开向导，CB Predictor自动选择所有数据的单元格，包括数据、标题和对数据的说明。

Manual data selection before starting CB Predictor

在用 CB Predictor之前选择数据的方法

The second way to select your historical data is to highlight the data range (including headers and dates) before you start CB Predictor.
第二种方法是在开始CB Predictor之前选择历史数据（包括标题和数据）

Manual data selection within CB Predictor用 CB Predictor选择数据的方法

The third way to select historical data is to start CB Predictor with no data, date, or header cells selected. The Input Data tab of the wizard appears with the Range field blank. At this point, you must select your historical data manually.
第三种方法是先CB Predictor，然后选择历史数据。

To select historical data manually from the Input Data tab:
在数据输入表中选择历史数据的方法是：

1.Start CB Predictor.
The Input Data tab of the wizard dialog appears. For more information on this dialog, see “Input Data tab” on page 100.
1、开始CB Predictor，输入数据的向导对话框出现。

2.Under Step 1, in the Range field, either type a range name (if defined), enter the range of cells with the historical data, including any headers (e.g., A4:B42), or:
2、第一步之后，在范围表格中，选择历史上历史数据，包括标题等（如，A4:B2），或者

a. Click Select.
The Select Range dialog replaces the wizard dialog.
a．点击select，出现选择数据范围的对话框

b. Select the cells with the historical data, including any cells with headers and dates.
b，选择历史数据的单元格，包括所有的标题和数据。

c. Click OK to return to the wizard dialog.
The selected range appears in the Range field.
c、点击ok，选择的数据范围出现在范围框中。

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Specifying data arrangement对数据进行排列

No matter which selection method you use, you must also specify your data arrangement to help CB Predictor identify whether you have dates and headers adjacent to your data series and whether your data are in rows or columns. If you used the Intelligent Input to select your data, these settings should already be set correctly.
无论你使用那种选择数据的方法，你还必须指定你的数据的安排，以帮助CB预测确定数据序列是否有日期和标题，以及是否是按要求进行行或列排列。如果使用数据是用智能输入的，这些设置都应该已经正确设置。

To set arrangement settings, use the Input Data tab of the CB Predictor wizard as shown in Figure 3.2 on page 64
排列设置，参考第64页的表3.2 CB预测显示卡的方法输入数据：

1.Under Step 2 of the wizard, if your historical data is in:
•Rows, select Data In Rows
•Columns, select Data In Columns
1、如果历史数据是如下情况，根据向导的第二步：
  行，选择数据以行排列
  列，选择数据以列排列

2.If you have headers (titles) at the top of your columns or to the left of your rows, select the First Row (Column) Has Headers setting.
2、如果你在每列的开头或者每行的左边都有标题，选择第一行（列）作为标题

3.If your first column or row lists the dates or time periods for your data series, select the First Column (Row) Has Dates setting.
3、如果你的第一行或列的时间有日期或者时间周期，则选择第一行（列）作为日期设置。

Viewing your historical data查看历史数据

As you progress through the wizard, you need to know if your data are seasonal (increase and decrease in a regular cycle) and, if so, what the season or cycle is. If you don’t already have a feel for the behavior of your data, you might want to view your selected historical data before you continue.
在使用向导卡的时候，需要知道数据是否是有周期性的（增加或者减少是有一定的规律的），如果是，是按怎样的周期或者规律。如果在之前对数据的情况不是很了解，你可能要在下一步操作之前先查看你的数据。

To view a graph of your historical data: 查看图表中的历史数据：

1.Under Step 3 of the CB Predictor wizard (on the Input Data tab), click View Data.
1、在CB Predictor的第三步向导卡（输入数据表格），点击查看数据

The View Historical Data dialog appears as shown in Figure 3.3.
如图3.3，查看历史数据对话框会显示出来。




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译者权归“思步网（www.step365.com）”及“lanj（西北偏北）”共同所有，未经许可，请勿转载