Are you looking to understand the power of regression analysis and how it can help you better understand relationships between variables? In this tutorial, I will show you how to do simple linear and multiple regression analyses with SigmaPlot. SigmaPlot includes many statistical methods and 100s of regression equations to choose from, and you can add your own customized regression equation if needed. This tutorial hopefully will make you better understand how regression analysis works and how you can apply it to your research.
Regression analysis has four main uses: description, estimation, prediction, and control. It describes the relationship between dependent and independent variables, allows for estimation of the dependent variable based on observed independent variables, predicts outcomes and changes in the dependent variable based on their relationship, and controls the effect of one or more independent variables while examining the relationship between one independent variable and the dependent variable.
Finding the best subset of data for regression analysis is an important step in ensuring the accuracy and robustness of your results. In our case, we have three subsets, the three independent variables: Square footage, number of bedrooms, and age. Which of these correlates with the price the most, and are they all relevant to our study?
And the Best Subset report shows that we do not get a better regression model by including the number of bedrooms variable. R-square is equal for using 2 vs 3 independent variables, but Adjusted R-square is higher for using only the two variables, Square footage and Age.
SigmaPlot will create a scatter plot of your data with your regression fit line and 95% confidence and prediction bands if you choose this. If you chose SigmaPlot to create a report, you would also find your Regression report sheet with all statistical test results for your analysis.
Use the sigmaoptions command to create a SigmaOptions object to customize your sigma plot appearance. You can also use the command to override the plot preference settings in the MATLAB session in which you create the sigma plots.
plotoptions = sigmaoptions returns a default set of plot options for use with the sigmaplot command. You can use these options to customize sigma plot appearance using the command line. This syntax is useful when you want to write a script to generate plots that look the same regardless of the preference settings of the MATLAB session in which you run the script.
You can use the same option set to create multiple sigma plots with the same customization. Depending on your own toolbox preferences, the plot you obtain might look different from this plot. Only the properties that you set explicitly, in this example Grid and FreqUnits, override the toolbox preferences.
I tried to work this out and figured out the JMP is usung 2 sigma to calculate the limits and also the value of sigma it esimates for this purpose is different from the values I cacluated abouve. I am unable to understand this.
This is a common question and is answered in the JMP course on Statistical Process Control. I assume you are creating an Individual and Moving Range chart. You need to understand how Individual and Moving Range charts are created. They use an ESTIMATE of the standard deviation for the control limits. The standard deviation can be estimated in several ways. Because these charts were created before calculators, a moving range is typically used, not the sample standard deviation, s.
I'm not sure I'm in the position to say which is the "best way" but from my experience in the manufacturing environment for 30 years as I understand it the IR-MR charts were desirable since they were easy to calculate and easy to train the operations how to calculate much more so than a standard deviation calculation. You have to realize that very often control charts were kept on the production floor with graph paper and operations would fill in the data accordingly. The key I believe is to choose a technique and utilize the value of that technique and respond to the "voice of the process" when there is an out of control signal.
If I may weigh in.... The I-mR chart is the "Swiss Army Knife" of Process Behavior Charts. It is very useful for almost any data set and is robust. It is NOT dependent on the distribution of the data; i.e., the data does not need to be normally distributed. The use of the standard deviation of the data to calculate upper and lower control limits is almost always WRONG. The reason is this: Your data is time-ordered; otherwise a control chart is useless. The stanadard deviation calculation gives the same result regardless of the order of the data. The moving range gives a time-ordered dispersion statistic, and IS time order dependent. The moving range multiplied by 2.66 gives an estimate of 3-sigma for the data. As LouV says, Wheeler's book is excellent. You can find many of Wheeler's articles at www.qualitydigest.com. I also suggest you look at the work of Davis Balestracci.
The link above is a LinkedIn thread on whether control charts require normal data or not. Though this is not the exact topic of your question, there were a couple things that I, as someone who is certainly not a statistical expert, found personally useful for putting things into perspective and may help you as well:
There is a larger discussion here as well. For me the control charts were the "Voice of the Process" thus a smoke detector so to speak of when a "stable" process may be migrating off course due to special cause. It is very wasteful to chase common cause variability which is all too prevalent. Then of course there are specifications which in a perfect world are set based upon "fitness for use" and performance which is an entirely another discussion worth having but not enough room here to expound upon. Our quality system was founded upon specification built around fitness for use which were derived via Design of Experiments and understanding the various fingerprint impurities in a process and their impact on the penultimate specification, customer use. So often material specifications are set under the guideline that higher quality is better however many times certain "impurities" are synergistic and beneficial to the performance of the final product or process and just blindly optimizing a process for specification does not always give the best performing product/process. I just wanted to add this to the discussion since process/product understanding is the key and control charts are an integral part of that understanding but not the entire story. However, that being said, an excursion into a special cause is not necessarily a bad thing but rather an opportunity to learn about ones process/product since you may find out that the excursion provided a process/product that performs better in your customers hands so the key is to evaluate the impact of the excursion and gain process knowledge from it which is the scientific method.
However if I include these new points which have gone out of the 3 sigma limit into the sigma calculation, the new sigma appears to be Ok. Can I therefore say that my process is in control or is this a fraud ?
A clustered heat map is a visualization of numeric data assigned to the levels of two categorical variables. This type of data can be displayed in a table where the rows refer to the levels of one variable and the columns refer to the levels of the other variable. The data table is typed into a SigmaPlot worksheet.
A heat map for this two-way data is constructed as a rectangular array of solid colors. The dimensions of the array and the positions of its individual color cells match the arrangement of the heat map data in the worksheet. The methods of assigning colors to data values are discussed below.
Heat maps assist in visualizing variations in the density of values in the data table. Put another way, heat maps are used to identify clusters of data.
The primary benefit of heat maps is that they make complicated data simpler to understand than the output of many other graphical or numerical techniques. One of the original applications of heat maps that is frequently used is to examine population density in a city or region. Heat maps are used by professionals in a variety of different fields:
Worksheet data for a heat map is arranged in a number of columns. One column is for column labels and another column is for row labels. These labels appear on the axes for the heat map. You are allowed to create a heat map without providing labels.
The data to be selected for the heat map must be entered in adjoining columns. The number of rows of data can vary among the columns. When the heat map is created, the number of rows in the heat map equals the maximum number of rows in the selected data. Non-numeric data is allowed in the data table, but will be treated as missing values. The color assigned to a missing value is transparent.
One more column is needed for a color palette that will be used to generate the heat map colors. The palette is created by the user by using the Insert Graphic Cells dialog, the transform language, or manually by typing in a color code.
The colors assigned to the worksheet data depend on whether a discrete or continuous color scale is selected. The scales are based on the palette in the color column. For discrete color scales, the color column often uses an existing color scheme of 7 to 10 colors. For continuous color scales, the color column often contains only two or three colors, but can contain more.
Examples of heat map data are accessed from the Macro Data button in the Samples Files group on the Help tab of the SigmaPlot ribbon. When the button is pressed, the Macro Data Sets notebook opens in the Notebook Manager and heat map examples are provided in three sections.
The Create Heat Map macro is accessed by pressing the Heat Map button in the Graphing Tools group on the Tools tab of the SigmaPlot ribbon. When running the macro, a dialog box appears for setting options to create a heat map. The settings are:
7fc3f7cf58