Using Minitab for Regression Analysis: An extended exampleThe following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to generate the statistical measures discussed in Anderson Sweeney and Williams. The data here have already been input, and stored in C1 and C2. The scatter plot below is similar to A, S, & W Figure 14.3 on page 559. You can find additional discussion of scatter plots in the Minitab Handbook on pages 158-63.This is formed using GRAPH > SCATTERPLOT > SIMPLEThere seems to be a strong positive relationship between these two variables. One way to measure the strength of the relationship is with the correlation coefficient. For discussion see A, S & W, pages 110-12, 572-3 or the Minitab Handbook, pages 296-97. In Minitab 14 you can compute a correlation by clicking on STAT > BASIC STATISTICS > CORRELATION. Minitab uses formula (3.12) on page 110 of A, S & W to do the calculation.MTB > Correlation 'Fertilizer' 'Crop Yield'.Correlations: Fertilizer, Crop YieldPearson correlation of Fertilizer and Crop Yield = 0.920P-Value = 0.003We can overlay a fitted line on our scatter plot. We can obtain the plot either with or without the estimated regression equation. To produce a plot with the estimated equation, use STAT > REGRESSION > FITTED LINE PLOT, and selecting the Linear alternative (See Minitab Handbook, pp. 320-21).Or this simpler picture from GRAPH > SCATTERPLOT > WITH REGRESSIONTo estimate a regression line, the command in Minitab is “Regress,” which we access by clicking on STAT > REGRESSION > REGRESSION. We fill it in as shown, with the Y variable entered into “Response:” and the X variable entered into “Predictors:”To predict, we click on the box labeled Options… and insert the X value (the value of Fertilizer) for which we would like to predict. Here, I chose to predict for X=550.By clicking on the box labeled Storage…, I can ask Minitab to store some information for me to use later: the residuals, the standardized residuals, the leverages, and the fitted values. If you are uncertain about what these terms mean, you can consult ASW. Residuals are defined in ASW by equation (14.28); standardized residuals by equation (14.32); leverages by equation (14.33); and fitted values the values of ˆy defined by equation (14.3).When you click on OK > OK and Minitab executes the command, the following code appears in the session window. If you examine it you will see that Minitab begins by labeling the columns in which it will store the residuals (“RESI1”), the standardized residuals (“SRES1”), the leverages (“HI1”), and the fitted values (“FITS1”). The main command, the “Regress” command, instructs Minitab to regress the Y variable ‘Crop Yield’ on one X variable, named ‘Fertilizer.’ Then Minitab uses various subcommands to store the residuals, standardized residuals, leverages, and fitted values. The subcommand “predict” is asking for a prediction when X=550, and the final subcommand asks Minitab to suppress some optional output.Here is the computer output.MTB > Name c3 "RESI1" c4 "SRES1" c5 "HI1" c6 "FITS1"MTB > Regress 'Crop Yield' 1 'Fertilizer';SUBC> Residuals 'RESI1';SUBC> SResiduals 'SRES1';SUBC> Hi 'HI1';SUBC> Fits 'FITS1';SUBC> Constant;SUBC> Predict 550;SUBC> Brief 2.Below the code you find your results:Regression Analysis: Crop Yield versus FertilizerThe regression equation isCrop Yield = 36.4 + 0.0589 FertilizerPredictor Coef SE Coef T PConstant 36.429 5.038 7.23 0.001Fertilizer 0.05893 0.01127 5.23 0.003S = 5.96118 R-Sq = 84.5% R-Sq(adj) = 81.5%Analysis of VarianceSource DF SS MS F PRegression 1 972.32 972.32 27.36 0.003Residual Error 5 177.68 35.54Total 6 1150.00Predicted Values for New ObservationsNewObs Fit SE Fit 95% CI 95% PI1 68.84 2.82 (61.60, 76.08) (51.89, 85.79)Values of Predictors for New ObservationsNewObs Fertilizer1 550b, computed using formula (14.6), is the number 36.429 found The estimated intercept,immediately under the column heading Coef. The estimated slope,b, computed using1formula (14.7), is .05893, also under the column heading Coef. The estimated line is rewritten for your convenience at the top of the output. For further discussion, you may wish to consult page 560 of A, S, & W or pp. 297-306 of the Minitab Handbook. The Sum of Squares due to error, formula (14.8) of the text, is the number 177.68 in the column headed "SS." The total Sum of Squares, formula (14.9), is the number 1150.00 immediately below it. Finally, the Sum of Squares Due to the Regression, formula (14.10), is 972.32 at the top of the column. The Coefficient of Determination, r2, given by formula (14.12), is printed in the middle of the output, as R-Sq =84.5%. Note that SSR/SST = 972.32/1150 = .845, which is where R-Sq comes from. The Mean Squared Error, or s2 given by formula (14.15), is under the heading MS. It is 35.54 = 177.68/5 and its square root, the standard error of the estimate, formula (14.16), is s=5.961. Theb, given by formula (14.18), is in the column headed by estimated standard deviation of1“SE Coef” and is equal to 0.01127. Just above this is the estimated standard deviation of b, a formula missing from ASW, but equal in this instance to 5.038. The test statistic for 0b, given by formula (14.19) is in the column headed by “t-ratio” and is equal to 5.23.1The corresponding test statistic forb, another formula missing from ASW, is just abovethat ofb and is equal to 7.23. The F statistic given by formula (14.21) is given on the1output, under the heading “F” and is equal to 27.36 = 972.32/35.54.Finally, the last thing on the output is a prediction generated by the “predict” subcommand, which requested a prediction for a value of fertilizer = 550. The predicted level of crop yield is 68.84, and the Confidence interval Estimate of E(Y p), computed using formulas (14.23, 14.24), is given by the “95% C.I.” and is (61.60, 76.08). The Prediction Interval Estimate of Y p, computed using formulas (14.26, 14.27), is given by the “95% P.I.” and is (51.89, 85.79).Figures 14.11, 14.12, and 14.13, pp. 600-2 of A, S & W, show how to examine the assumptions of the model by examining plots of the residuals. In the following discussion, I will show how to make the graphs from scratch. However, this is not really necessary, because the process can be automated. As an example of the automated procedure, click on Graphs… and then fill in the following information to get plots of residuals against both fitted values and Fertilizer.Of course, once the residuals, etc., are stored you can equally well create graphs of them yourself, using GRAPH > SCATTERPLOT > SIMPLE. These two plots, showing residuals plotted against X and against fitted values, are just like Figures 14.11 and 14.13 in the book. They are displayed on the same page so that you will notice that they are identical, except for the units on the X-axis, just as 14.11 and 14.13 are. These plots differ when there is more than one explanatory variable – that is, in multiple regression. However, when there is only one explanatory variable – simple regression – predicted y is just a linear transformation of x and the graphs are redundant.Standardized residuals, computed using equation (14.32), are also of interest. Once standardized residuals and raw residuals have been calculated by Minitab, you can print them out in the session window using the following command found under MANIP > DISPLAY DATA.This gives rise to the following output.Data DisplayCropRow Fertilizer Yield RESI1 SRES11 100 40 -2.3214 -0.532052 200 50 1.7857 0.354443 300 50 -4.1071 -0.760194 400 70 10.0000 1.811935 500 65 -0.8929 -0.165266 600 65 -6.7857 -1.346877 700 80 2.3214 0.53205Standardized residuals can then be plotted and examined for evidence that regression assumptions are being violated, as in Figure 14.14 of ASW.Finally, in Figure (14.15) of A, S & W, the authors show a normal probability plot for the standardized residuals. This is an attempt to check whether the errors are plausibly normally distributed. Here is the corresponding plot. The command “nscore c3 c8” computes the normal score of the standardized residuals in c3, and stores the result in c8, like Table 14.9 of A, S & W. For a description of the command, see the Minitab Handbook, pp. 240-2. In the latest version of Minitab, you can find the command in the menus by looking under STAT > BASIC STATISTICS > NORMALITY TEST.Since the plot below is approximately linear, the errors appear to be (approximately, at least) normally distributed.One way of detecting influential observations is to compute the leverage of the observations. This is discussed in the text on pages 609-11, and mentioned in the Minitab Handbook, p. 400. Below we display the leverage of each observation. These were computed using formula (14.33) in A, S & W. Minitab considers leverage noteworthy if it is greater than 3p/n, where p is the number of coefficients, including the constant. In this case 3p/n = 6/7 = .857, so none are noteworthy.MTB > print c1 c5Data DisplayRow Fertilizer HI11 100 0.4642862 200 0.2857143 300 0.1785714 400 0.1428575 500 0.1785716 600 0.2857147 700 0.464286。
minitab数据分析参考目录minitab数据分析参考 (1)引言 (2)背景介绍 (2)目的和意义 (2)Minitab软件简介 (3)Minitab软件概述 (3)Minitab软件的功能和特点 (4)数据分析基础 (5)数据收集和整理 (5)数据可视化 (6)数据摘要和描述统计 (7)常用的数据分析方法 (8)假设检验 (8)方差分析 (9)回归分析 (10)相关分析 (11)时间序列分析 (12)Minitab在数据分析中的应用 (13)数据导入和处理 (13)数据可视化分析 (14)假设检验的实施 (15)回归分析的实施 (16)其他常用分析方法的实施 (17)案例分析 (18)案例一：销售数据分析 (18)案例二：质量控制分析 (19)案例三：市场调研分析 (20)总结与展望 (21)主要内容总结 (21)存在的问题和不足 (22)未来发展方向 (23)引言背景介绍随着信息时代的到来，数据分析已经成为了各行各业中不可或缺的一部分。
在企业管理、市场营销、医学研究等领域，数据分析的应用越来越广泛。
而在数据分析的过程中，使用合适的工具和软件是至关重要的。
Minitab作为一款专业的统计分析软件，被广泛应用于各个领域的数据分析中。
Minitab软件由美国Minitab公司开发，是一款功能强大且易于使用的统计分析软件。
它提供了丰富的统计分析工具和图表，可以帮助用户对数据进行可视化分析、假设检验、回归分析、质量控制等多种统计分析操作。
Minitab软件的优势在于其简单直观的用户界面和强大的分析功能，使得用户可以轻松地进行数据分析，从而更好地理解数据背后的规律和趋势。
在过去的几十年里，Minitab软件已经成为了许多企业和学术机构中的首选工具。
无论是进行产品质量控制、市场调研、医学研究还是工程优化，Minitab都能够提供全面的数据分析解决方案。
其强大的统计分析功能和灵活的数据处理能力，使得用户能够更加高效地进行数据分析，从而为决策提供科学依据。
Minitab Statistical Software入门内容1简介4概述4案例4 Minitab用户界面4数据类型6打开并检查工作表6在下一章中72用图形表示数据8概述8创建、解释和编辑直方图8创建并解释散点图13在一个布局上排列多个图形16保存Minitab项目19在下一章中193分析数据20概述20对数据进行汇总摘要20比较两个或更多均值22保存项目28在下一章中284评估质量29概述29创建并解释控制图29创建并解释能力统计量33保存项目35在下一章中355设计实验36概述36创建设计的试验36查看设计39将数据输入到工作表40分析设计并解释结果40使用存储的模型进行其他分析44保存项目47在下一章中486重新执行分析49概述49使用会话命令执行分析49复制会话命令50使用exec文件重复进行分析51保存项目52在下一章中527导入和准备数据53概述53从不同来源导入数据53准备数据以进行分析55当数据值更改时57保存工作表57索引591.简介概述Minitab Statistical Software入门介绍了Minitab中一些最常用的功能和任务。
备注:本指南中某些功能仅在桌面应用中可用。
使用Web应用时在Windows计算机或Mac上，您可以打开桌面应用来访问Minitab提供的所有功能。
大部分统计分析都需要执行一系列步骤，这些步骤通常由背景知识或您要调查的主题领域来指导完成。
第2章到第5章介绍以下步骤：•利用图形研究数据并显示结果•进行统计分析•评估质量•设计试验在第6章和第7章中，您学习如何执行以下操作：•使用快捷方式自动执行将来的分析•将数据从不同文件类型导入到Minitab中，并准备数据以进行分析。
案例某家在网上销售图书的公司具有三个区域出货中心。
每个出货中心都用不同的计算机系统来输入和处理订单。
该公司想要确定最高效的计算机系统，并在每个出货中心使用该计算机系统。
在整个Minitab Statistical Software入门中，您学习了使用Minitab来分析来自出货中心的数据。
Minitab软件操作教程1. 介绍Minitab是一款流行且功能强大的统计软件包，广泛用于数据分析和质量管理。
它提供了丰富的统计方法和图表工具，帮助用户快速分析数据、发现趋势和模式，并做出有用的决策。
本教程将带你逐步了解Minitab软件的基本操作。
2. 安装和启动Minitab首先，您需要安装Minitab软件。
请按照官方网站上的说明进行安装，并确保您拥有有效的许可证。
安装完成后，您可以在开始菜单或应用程序目录中找到Minitab的快捷方式。
点击Minitab图标启动软件。
在Minitab启动界面上，您可以选择新建项目或打开现有项目。
如果您是第一次使用Minitab，选择新建项目开始。
3. 创建数据集在Minitab中，数据集是您将要分析的数据的集合。
要创建一个新的数据集，请选择“Worksheet”选项卡并点击“New Worksheet”。
您可以手动输入数据或从外部文件中导入数据。
如果您选择手动输入数据，请注意确保数据按照正确的格式分列。
如果您选择导入数据，请确保数据文件格式与Minitab兼容。
4. 数据分析Minitab提供了丰富的数据分析方法，可以帮助您探索数据、找出异常值、计算统计量和生成图表。
以下是一些常用的数据分析方法：描述性统计：•平均值：使用“Stat”->“Basic Statistics”->“Display Descriptive Statistics”计算数据列的平均值。
•方差和标准差：使用“Stat”->“Basic Statistics”->“Display Descriptive Statistics”计算数据列的方差和标准差。
•百分位数：使用“Stat”->“Basic Statistics”->“Descriptive Statistics”计算数据列的百分位数。
假设检验：•单样本T检验：使用“Stat”->“Basic Statistics”->“1-Sample t”执行单样本T检验，检验样本均值是否与给定值相等。
