Home » Data visualisatie technieken: complexe informatie helder in beeld
Data visualisatie technieken: complexe informatie helder in beeld
Data Visualization Techniques From Basics to Big Data with SAS Visual Analytics
Een foto zegt meer dan duizend woorden. Dit geldt ook voor het presenteren van data. Hoe maak je complexe data visueel inzichtelijk? Door de combinatie van geavanceerde analysetechnieken en een eenvoudige visuele interface stelt SAS Visual Analytics de gebruiker in staat enorme hoeveelheden data snel en gemakkelijk visueel aantrekkelijk te presenteren. Dit schept een nooit eerder vertoonde mogelijkheid om snel ingewikkelde problemen op te lossen, risico’s te verkleinen en de besluitvorming binnen uw organisatie te verbeteren.
Bedrijf:SAS Institute BV
Maand / jaar:januari 2013
Onderwerpen: Business Intelligence
Vakgebieden: Business intelligence
SamenvattingEen foto zegt meer dan duizend woorden. Dit geldt ook voor het presenteren van data. Hoe maak je complexe data visueel inzichtelijk? Door de combinatie van geavanceerde analysetechnieken en een eenvoudige visuele interface stelt SAS Visual Analytics de gebruiker in staat enorme hoeveelheden data snel en gemakkelijk visueel aantrekkelijk te presenteren. Dit schept een nooit eerder vertoonde mogelijkheid om snel ingewikkelde problemen op te lossen, risico’s te verkleinen en de besluitvorming binnen uw organisatie te verbeteren.
Uw data op de beste manier in beeld brengen
De vijf meest gebruikte grafieken
Big data visualiseren
Eenvoudig visualiseren met autocharting
Data Visualization Techniques From Basics to Big Data with SAS® Visual Analytics WHITE PAPER SAS White Paper Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Generating the Best Visualizations for Your Data . . . . . . . . . . . . . . . . 2 The Basics: Charting 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Line Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Bar Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bubble Plots A Scatter Plot Variation . . . . . . . . . . . . . . . . . . . . . . . . . 6 Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Visualizing Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Large Data Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Different Varieties of Data (Semistructured and Unstructured) . . . . . . 10 Visualization Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Filtering Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Data Visualization Made Easy with Autocharting . . . . . . . . . . . . . . . . 14 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Content for this paper, Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics, was provided by: Justin Choy, Principal Product Manager for SAS Business Intelligence Solutions; Varsha Chawla, Senior Solutions Architect; and Lisa Whitman, Senior Training and Development Specialist. The information originally appeared in papers presented at SAS Global Forum 2012 and SAS Global Forum 2011. Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Introduction A picture is worth a thousand words especially when you are trying to understand and gain insights from data . It is especially relevant when you are trying to find relationships among thousands or even millions of variables and determine their relative importance . Organizations of all kinds generate huge amounts of data each minute, hour and day . Everyone including executives, departmental decision makers, call center workers, and employees on production lines hopes to learn things from collected data that can help them make better decisions, take smarter actions and operate more efficiently . If your data has billions of rows, one of the best ways to discern important relationships is through advanced analysis and high-performance data visualization . If sophisticated analyses can be performed quickly, even immediately, and results presented in ways that showcase patterns and allow querying and exploration, people across all levels in your organization can make faster, more effective decisions . To create meaningful visuals of your data, there are some tips and techniques you should consider . Data size and column composition play an important role when selecting graphs to represent your data . This paper discusses some of the basic issues concerning data visualization and provides suggestions for addressing those issues . In addition, big data brings a unique set of challenges for creating visualizations . This paper covers some of those challenges and potential solutions as well . If you are working with large data, one challenge is how to display results of data exploration and analysis in a way that is not overwhelming . You may need a new way to look at the data that collapses and condenses the results in an intuitive fashion but still displays graphs and charts that decision makers are accustomed to seeing . You may also need to make the results available quickly via mobile devices, and provide users with the ability to easily explore data on their own in real time . SAS® Visual Analytics is a new business intelligence solution that uses intelligent autocharting to help business analysts and nontechnical users visualize data . It creates the best possible visual based on the data that is selected . SAS Visual Analytics uses high-performance analytic technologies to explore huge volumes of data very quickly to find patterns and trends, identify opportunities for further analysis, and provide results to information consumers . The heart and soul of SAS Visual Analytics is the SAS® LASRTM Analytic Server, which delivers game-changing abilities to execute and accelerate analytic computations on massive amounts of data, in-memory with unprecedented performance . The combination of high-performance analytics and an easy-to-use data exploration interface enables different types of users to create and interact with graphs so they can understand and derive value from massive amounts of data faster than ever . This creates an unprecedented ability to solve difficult problems, improve business performance and mitigate risk rapidly and confidently . 1 SAS White Paper Generating the Best Visualizations for Your Data There are some basic concepts that can help you generate the best visuals for your data: · Understandthedatayouaretryingtovisualize,includingitssizeandcardinality. · Determinewhatyouaretryingtovisualizeandwhatkindofinformationyouwant to convey . · Knowyouraudienceandunderstandhowitprocessesvisualinformation. · Useavisualthatconveystheinformationinthebestandsimplestformforyour audience . What Is Data Cardinality? Cardinality is the uniqueness of data values contained in a column . High cardinality means there is a large percentage of totally unique values (e .g ., bank account numbers, because each item should be unique) . Low cardinality means a column of data contains a large percentage of repeat values (as might be seen in a "gender" column) . The Basics: Charting 101 For those who need help knowing which graph type to use when, here is a quick guide to help determine which chart type (or graph) is the most appropriate for your data . Line Graphs A line graph, or line chart, shows the relationship of one variable to another . They are most often used to track changes or trends over time (see Figure 1) . Line charts are also useful when comparing multiple items over the same time period (see Figure 2) . The stacking lines are used to compare the trend or individual values for several variables . You may want to use line graphs when the change in a variable or variables clearly needs to be displayed and/or when trending or rate-of-change information is of value . It is also important to note that you shouldn't pick a line chart merely because you have data points . Rather, the number of data points that you are working with may dictate the best visual to use . For example, if you only have 10 data points to display, the easiest way to understand those 10 points might be to simply list them in a particular order using a table . When deciding to use a line chart, you should consider whether the relationship between data points needs to be conveyed . If it does, and the values on the X axis are continuous, a simple line chart may be what you need . 2 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Figure 1: Line graphs show the relationship of one variable to another. Figure 2: Multiple category line graphs compare multiple items over the same time period. 3 SAS White Paper Bar Charts Bar charts are most commonly used for comparing the quantities of different categories or groups (see Figure 3) . Values of a category are represented using the bars, and they can be configured with either vertical or horizontal bars with the length or height of each bar representing the value . When values are distinct enough that differences in the bars can be detected by the human eye, you can use a simple bar chart . However, when the values (bars) are very close together or there are large numbers of values (bars) that need to be displayed, it becomes more difficult to compare bars to each other . To help provide visual variance, bars can have different colors . The colors can be used to indicate such things as a particular status or range . Coloring the bars works best when most bars are in a different range or status . When all bars are in the same range or status, the color becomes irrelevant, and it is most visually helpful to keep the color consistent or have no coloring at all . Another form of a bar chart is called the progressive bar chart, or waterfall chart . A waterfall chart shows how the initial value of a measure increases or decreases during a series of operations or transactions . The first bar begins at the initial value, and each subsequent bar begins where the previous bar ends . The length and direction of a bar indicates the magnitude and type (positive or negative, for example) of the operation or transaction . The resulting chart is a stepped cascade that shows how the transactions or operations lead to the final value of the measure . Bar charts can be configured with either vertical or horizontal bars with the length or height of each bar representing the value. Figure 3: Bar graphs are most commonly used to compare quantities of different categories. 4 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Scatter Plots A scatter plot (or X-Y plot) is a two-dimensional plot that shows the joint variation of two data items . In a scatter plot, each marker (symbols such as dots, squares and plus signs) represents an observation . The marker position indicates the value for each observation . Scatter plots also support grouping . When you assign more than two measures, a scatter plot matrix is produced . A scatter plot matrix is a series of scatter plots that displays every possible pairing of the measures that are assigned to the visualization . Scatter plots are useful for examining the relationship, or correlations, between X and Y variables . Variables are said to be correlated if they have a dependency on, or are somehow influenced by, each other . For example, "profit" is often related to "revenue" and the relationship that exists might be that as revenue increases profit also increases (a positive correlation) . A scatter plot is a good way to visualize these relationships in the data . In a scatter plot, you can also apply statistical analysis with correlation and regression . Correlation identifies the degree of statistical correlation between the variables in the plot . Regression plots a model of the relationship between the variables in the plot . Once you have plotted all of the data points using a scatter plot, you are able to visually determine whether data points are related . Scatter plots can help you gain a sense of how spread out the data might be or how closely related the data points are, as well as quickly identify patterns present in the distribution of the data (see Figure 4) . Scatter plots are helpful when you have many data points . If you are working with a small set of data points, a bar chart or table may be a more effective way to display the information . Scatter plots can help you gain a sense of how spread out the data might be or how closely related the data points are. They can also quickly identify patterns present in the distribution of the data. Figure 4: A scatter plot is a good way to visualize relationships in data. 5 SAS White Paper Bubble Plots A Scatter Plot Variation A bubble plot is a variation of a scatter plot in which the markers are replaced with bubbles . In a bubble plot, each bubble represents an observation . The location of the bubble represents the value for two measured axes; the size of the bubble represents the value for a third measure . A bubble plot is useful for data sets with dozens to hundreds of values or when the values differ by several orders of magnitude . You can also use a bubble plot when you want specific values to be visually represented by different bubble sizes . Animated bubble plots are a good way to display changing data over time . Pie Charts There is much debate around the value and usefulness of pie charts . Pie charts are used to compare the parts of a whole . However, they can be difficult to interpret because the human eye has a hard time estimating areas and comparing visual angles . Another challenge with using a pie chart for analysis is that it is very difficult to truly compare slices of the pie that are similar in size but not located next to each other . For these reasons, pie charts are not often used in data analysis . If you do use pie charts, they are most effective when there are limited components and when text and percentages are included to describe the content . By providing additional information, users do not have to guess the meaning and value of each slice . If you choose to use a pie chart, then the slices should be a percentage of the whole (see Figure 5) . When designing reports or dashboards, another consideration for the efficacy of a pie chart is the amount of space the pie chart requires in the sizing of the report . Because of the round shape, pie charts require extra real estate, so they may be less than ideal when developing dashboards for small screens or mobile devices . Other charts may provide a more effective way of representing the same information in less space (see Figure 6) . Pie charts are most effective when there are limited components and when text and percentages are included to describe the content. 6 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Figure 5: The use of pie charts is a much debated subject in the data visualization world. Figure 6: Alternatives to pie charts include line charts and bar charts. 7 SAS White Paper Of course there are other chart types that you can choose from to present data and analytical results . The selection of these chart types will usually depend upon the number of categories and measures (or dimensions) you have to visualize . By following the tips outlined in the introduction and understanding the examples, you may need to try different types of visuals and test them with your audience to make sure the correct information is being conveyed . Visualizing Big Data Big data brings new challenges to visualization because there are large volumes, different varieties and varying velocities that must be taken into account . The cardinality of the columns you are trying to visualize should also be considered . One of the most common definitions of big data is data that is of such volume, variety and velocity that an organization must move beyond its comfort zone technologically to derive intelligence for effective decisions . · Volumereferstothesizeofthedata. · Varietydescribeswhetherthedataisstructured,semistructuredorunstructured. · Velocityisthespeedatwhichdatapoursinandhowfrequentlyitchanges. Building upon basic graphing and visualization techniques, SAS Visual Analytics has taken an innovative approach to addressing the challenges associated with visualizing bigdata.Usinginnovative,in-memorycapabilitiescombinedwithSASAnalyticsand data discovery, SAS provides new techniques based on core fundamentals of data analysis and presentation of results . Large Data Volumes One challenge when working with big data is how to display results of data exploration and analysis in a way that is meaningful and not overwhelming . You may need a new way to look at the data that collapses and condenses the results in an intuitive fashion but still displays graphs and charts that decision makers are accustomed to seeing . You may also need to make the results available quickly via mobile devices, and provide users with the ability to easily explore data on their own in real time . When working with massive amounts of data, it can be difficult to immediately grasp what visual might be the best to use . Autocharting takes a look at all of the data you are trying to examine and then, based on the amount of data and the type of data, it presents the most appropriate visualization technique . SAS Visual Analytics uses intelligent autocharting to help business analysts and nontechnical users easily visualize their data . With this functionality, they can build hierarchies on the fly, interactively explore the data and display data in many different ways to answer specific questions or solve specific problems without having to rely on constant assistance from IT to provide new views of information . In addition, the "what does it mean" balloons in SAS Visual Analytics provide explanations of complex analytic functions that have been performed, and identify and explain the relationships between the variables that are displayed (see Figure 7) . One challenge when working with big data is how to display results of data exploration and analysis in a way that is meaningful and not overwhelming. 8 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics This makes analytics and the creation of data visualizations easy, even by those with nontechnical or limited analytic backgrounds . Data volume can become an issue because traditional architectures and software may not be able to process huge amounts of data in a timely manner, thus requiring you to make compromises and aggregate the details you want to visualize . Even the most common descriptive statistics calculations can become complicated when you are dealing with big data and don't want to be restricted by column limits, storage constraints and limited support for different data types . One SAS solution to these issues is an in-memory engine that speeds the task of data exploration and a visual interface that clearly displays the results in a simple visualization (as provided by SAS Visual Analytics) . For example, what if you have a billion rows in a data set and want to create a scatter plot on two measures? The user trying to view a billion points in a scatter plot will have a hard time seeing so many data points . And the application creating the visual may not be able to plot a billion points in a timely or effective manner . One potential solution is to use binning (the grouping together of data) on both axes so that you can effectively visualize the big data (see Figure 7) . Figure 7: SAS Visual Analytics provides autocharting and "what does it mean" balloons to help nontechnical users create and understand data visualizations. The "what does it mean" balloon (bottom right corner) explains that the correlation shown in this binned box plot indicates a strong linear relationship between unit reliability and unit lifespan. Box plots are another example of how the volume of data can affect how a visual is shown . A box plot is a graphical display of five statistics (the minimum, lower quartile, median, upper quartile and maximum) that summarize the distribution of a set of data . The lower quartile (25th percentile) is represented by the lower edge of the box, and the upper quartile (75th percentile) is represented by the upper edge of the box . The median (50th percentile) is represented by a central line that divides the box into sections . Extreme values are represented by whiskers that extend out from the edges of the box . 9 SAS White Paper Usually,thesedisplaywellwhenusingbigdata(seeFigure8).Often,boxplotsareused to understand the outliers in the data . Generally speaking, the number of outliers in the data can be represented by 1 to 5 percent of the data . With traditionally sized data sets, viewing 1 to 5 percent of the data is not necessarily hard to do . However, when you are working with massive amounts of data, viewing 1 to 5 percent of the data is rather challenging . For example, if you were working with a billion rows of data, the outliers would represent 10 million data points and visualizing 10 million data points would be difficult.InFigure8,wehaveonecategoryandtwomeasures.Tovisualizeoutlierscould mean plotting 20 million outlier points . If you bin the results and show a box plot with whiskers, you can view the distribution of the data and see the outliers all calculated on big data . While visualizing structured data is fairly simple, semistructured or unstructured data requires new visualization techniques, Figure 8: A box plot on big data quickly compares the distribution of data points within a category. such as word clouds or network diagrams. Different Varieties of Data (Semistructured and Unstructured) Variety brings challenges because while visualizing structured data is fairly simple, semistructured or unstructured data requires new visualization techniques . A word cloud visual can be used on unstructured data as an interesting way to display high- or low-frequency words (see Figure 9) . In word clouds, the size of the word represents the word's frequency within a body of text . Another visualization technique that can be used for semistructured or unstructured data is the network diagram, which can, for example, show the relationship of someone tweeting and that person's followers (see Figure 10) . Note: Word clouds and network diagrams are visualization techniques that are currently available in SAS solutions such as SAS Text Miner and SAS Social Media Analytics . 10 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Figure 9: In this word cloud, the size of the word represents the frequency of use within a body of text. Figure 10: Network diagrams can be used to show the relationship of someone tweeting and that person's followers. 11 SAS White Paper Visualization Velocity Velocity for big data is all about the speed at which data is coming into the organization, which can be difficult to manage . The ability to access and process varying velocities of data quickly is critical . For visualizations, this translates into how quickly you can look at, visualize and explore the massive amounts of data . A correlation matrix combines big data and fast response times to quickly identify which variables among the millions or billions are related . It also shows how strong the relationship is between the variables . SAS Visual Analytics makes it easy to assess relationships among large numbers of variables . You simply select a group of variables and drop them into the visualization pane . The intelligent autocharting function displays a color-coded correlation matrix that quickly identifies strong and weak relationships between the variables . Darker boxes indicate a stronger correlation; lighter boxes indicate a weaker correlation . If you hover over a box, a summary of the relationship is shown . You can double-click on a box in the matrix for further details . The example below visualizes 45 correlation calculations on slightly more than 1 .1 billion rows of data (Figure 11) . This graph shows the correlation values, and returns results in two to six seconds using the SAS LASR Analytic Server . Previously, this type of calculation would have taken many hours but now can be done in seconds . By using box plots and correlation matrices, SAS Visual Analytics can help speed up your analytics life cycle because analytical modelers can perform variable reductions more quickly and effectively . A correlation matrix combines big data and fast response times to quickly identify which variables among the millions or billions are related. It also shows how strong the relationship is between the variables. Figure 11: In this autocharted correlation matrix, darker boxes indicate a stronger correlation; lighter boxes indicate a weaker correlation. You can double-click on a box for further details. 12 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics Cardinality becomes a concern in big data because the data may have many unique values per column . The example in Figure 12 shows only 105 unique product descriptions . With big data, we may have more than a million unique values . As you can see from the example, even when viewing 105 bars the viewer cannot see the labels for each of the bars, and the graph is becoming less meaningful . Imagine if you had a million bars! It would be impossible to see them . Figure 12: High cardinality in a bar chart with big data may be difficult to understand. SAS has adopted a method for dealing with high cardinality in SAS Visual Analytics bar charts that provide an overview bar that zooms into the bar chart and provides a way for the user to scroll through the entire chart . The level of zoom can also be controlled . If you compare Figure 12 to Figure 13, it is easy to see that Figure 13 shows the information more clearly . 13 SAS White Paper Figure 13: This overview axis bar chart shows the high cardinality in this big data more clearly. You can easily scroll through the entire chart. Filtering Big Data When working with massive amounts of data, being able to quickly and easily filter your data is important but can be challenging . What if you only want to view data for a certain region, product line or some other variable? SAS Visual Analytics has filtering capabilities that make it easy to refine the information you see . Simply add a measure to the filter pane or select one that's already there, and then select or deselect the items on which to filter . But what if the filter isn't meaningful or it skews the data in undesirable ways? One way to better understand the composition of your data and help filter the data is to use histograms . Histograms provide a visual distribution of the data and provide cues for how the data will change if you filter on a particular measure . Histograms save time by giving you an idea of the effect the filter will have on the data before you apply it . Rather than relying on trial and error or instinct, you can use the histogram to help you decide what areas to focus on . Data Visualization Made Easy with Autocharting In SAS Visual Analytics, intelligent autocharting produces the best visual based on what data you drag and drop onto the visual palette . It is important to note that autocharting may not always create the exact visualization you had in mind . In that case, you also can select a specific visual to build . However, when you are first exploring a new data set, autocharts are useful because they provide a quick view of the data . You then have the ability to switch to another specific visual as desired . For example, with autocharting, when a single measure is selected, distribution of that measure is shown (Figure 14) . 14 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics In SAS Visual Analytics, intelligent autocharting Figure 14: Autocharting in SAS Visual Analytics uses a bar chart to show the distribution of a single measure. produces the best visual based on what data you drag and drop onto the visual palette. When you are first exploring a new The addition of a second measure results in an autocharted scatter plot (Figure 15) . data set, autocharts are useful because they provide a quick view of the data. Figure 15: With autocharting, two measures result in a scatter plot. 15 SAS White Paper A category of data can be one of three types: standard, date or geographic . When the category type is standard, the visual will show a frequency count of data (see Figure 16) . If the category is a date, then a measure is also required and the visual will be a line graph (see Figures 1 and 2) . If the category is geographic, then a map will be displayed (see Figure 17) . Figure 16: When the category type of data is standard, SAS Visual Analytics displays a frequency count. Figure 17: If SAS Visual Analytics determines that the data category is geographic, a map frequency chart is used. 16 Data Visualization Techniques: From Basics to Big Data with SAS® Visual Analytics The autocharting in SAS Visual Analytics takes into account the cardinality of the data andadjuststhevisualsaccordingly.UsingthevisualinFigure18asanexample,the cardinality of the column "Product Description" was 105 . Autocharting checked the cardinality of the selected column and automatically provided the overview bar axis because the cardinality was deemed high . The overview axis is an option that can be turned on and off as required . Figure 18: Autocharting checked the cardinality of the selected column and automatically provided the overview axis, an option that can be turned on or off as desired. 17 SAS White Paper Conclusion Visualizing your data can be both fun and challenging . If you are working with big data, it is easier to understand information in a visual as compared to a large table with lots of rows and columns . However, with the many visually exciting choices available, it is possible that the visual creator may end up presenting the information using the wrong visualization . In some cases, there are specific visuals you should use for certain data . In other instances, your audience may dictate which visualization you present . In the latter scenario, showing your audience an alternative visual that conveys the data more clearly may provide just the information that's needed to truly understand the data . You can choose the most appropriate visualization by understanding the data and its composition, what information you are trying to convey visually to your audience, and how viewers process visual information . And products such as SAS Visual Analytics can help provide the best, fastest visualizations possible . Dealing with billions of records on a regular basis is just a reality of doing business today, and SAS understands that . SAS Visual Analytics allows you to explore all of your data using visual techniques combined with industry-leading analytics . Visualizations such as box plots and correlation matrices help you quickly understand the composition and relationships in your data . With SAS Visual Analytics, large numbers of users (including those with limited analytical and technical skills) can quickly view and interact with reports via the Web or mobile devices, while IT maintains control of the underlying data and security . The net effect is the ability to accelerate the analytics life cycle and to perform the process more often, with more data all the data, if that's what best serves the purpose . By using all data that is available, users can quickly view more options, make more precise decisions and succeed even faster than before . Visualizing your data can be both fun and challenging. If you are working with big data, it is easier to understand information in a visual as compared to a large table with lots of rows and columns. Dealing with billions of records on a regular basis is just a reality of doing business today, and SAS understands that. SAS® Visual Analytics allows you to explore all of your data using visual techniques combined with industry-leading analytics. 18 About SAS SAS is the leader in business analytics software and services, and the largest independent vendor in the business intelligence market . Through innovative solutions, SAS helps customers at more than 60,000 sites improve performance and deliver value by making better decisionsfaster.Since1976SAShasbeengivingcustomersaroundtheworldTHEPOWERTOKNOW® . SAS Institute Inc. World Headquarters +1 919 677 8000 To contact your local SAS office, please visit: sas.com/offices SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies. Copyright © 2012, SAS Institute Inc. All rights reserved. 106006_S93957_1012