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Boundless Lecture Slides

Boundless Lecture Slides. Available on the Boundless Teaching Platform. Free to share, print, make copies and changes. Get yours at www.boundless.com. Using Boundless Presentations. Boundless Teaching Platform

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Boundless Lecture Slides

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  1. Boundless Lecture Slides Available on the Boundless Teaching Platform Free to share, print, make copies and changes. Get yours at www.boundless.com

  2. Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com

  3. About Boundless • Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com. Free to share, print, make copies and changes. Get yours at www.boundless.com

  4. Correlation Correlation and Regression More About Correlation Regression The Regression Line ] R.M.S. Error for Regression Correlation and Regression Free to share, print, make copies and changes. Get yours at www.boundless.com

  5. Multiple Regression Correlation and Regression(continued) ] Correlation and Regression Free to share, print, make copies and changes. Get yours at www.boundless.com

  6. Correlation and Regression > Correlation Correlation • An Intuitive Approach to Relationships • Scatter Diagram • Coefficient of Correlation • Coefficient of Determination • Line of Best Fit • Other Types of Correlation Coefficients • Variation and Prediction Intervals • Rank Correlation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/correlation-44/

  7. Correlation and Regression > More About Correlation More About Correlation • Ecological Fallacy • Correlation is Not Causation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/more-about-correlation-45/

  8. Correlation and Regression > Regression Regression • Predictions and Probabilistic Models • A Graph of Averages • The Regression Method • The Regression Fallacy Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/regression-46/

  9. Correlation and Regression > The Regression Line The Regression Line • Slope and Intercept • Two Regression Lines • Least-Squares Regression • Model Assumptions • Making Inferences About the Slope • Regression Toward the Mean: Estimation and Prediction Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/the-regression-line-47/

  10. Correlation and Regression > R.M.S. Error for Regression R.M.S. Error for Regression • Computing R.M.S. Error • Plotting the Residuals • Homogeneity and Heterogeneity Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/r-m-s-error-for-regression-48/

  11. Correlation and Regression > Multiple Regression Multiple Regression • Multiple Regression Models • Estimating and Making Inferences About the Slope • Evaluating Model Utility • Using the Model for Estimation and Prediction • Interaction Models • Polynomial Regression • Qualitative Variable Models • Models with Both Quantitative and Qualitative Variables • Comparing Nested Models • Stepwise Regression • Checking the Model and Assumptions • Some Pitfalls: Estimability, Multicollinearity, and Extrapolation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/correlation-and-regression-11/multiple-regression-49/

  12. Appendix Free to share, print, make copies and changes. Get yours at www.boundless.com

  13. Correlation and Regression Key terms • Akaike information criteriona measure of the relative quality of a statistical model, for a given set of data, that deals with the trade-off between the complexity of the model and the goodness of fit of the model • ANCOVA modelAnalysis of covariance; a general linear model which blends ANOVA and regression; evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV), while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates. • ANOVA ModelAnalysis of variance model; used to analyze the differences between group means and their associated procedures in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. • ANOVA ModelAnalysis of variance; used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups), in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. • Bayesian information criteriona criterion for model selection among a finite set of models that is based, in part, on the likelihood function • bivariate distributiongives the probability that both of two random variables fall in a particular range or discrete set of values specified for that variable • Bonferroni pointhow significant the best spurious variable should be based on chance alone • Cartesian coordinateThe coordinates of a point measured from an origin along a horizontal axis from left to right (the -axis) and along a vertical axis from bottom to top (the -axis). • collinearitythe condition of lying in the same straight line • concomitantHappening at the same time as something else, especially because one thing is related to or causes the other (i.e., concurrent). • concordanceAgreement, accordance, or consonance. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. Free to share, print, make copies and changes. Get yours at www.boundless.com

  14. Correlation and Regression • convergent cross mappingA statistical test that (like the Granger Causality test) tests whether one variable predicts another; unlike most other tests that establish a coefficient of correlation, but not a cause-and-effect relationship. • correlationOne of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship. • correlationOne of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship. • correlation coefficientAny of the several measures indicating the strength and direction of a linear relationship between two random variables. • covarianceA measure of how much two random variables change together. • covarianceA measure of how much two random variables change together. • covarianceA measure of how much two random variables change together. • covarianceA measure of how much two random variables change together. • covariatea variable that is possibly predictive of the outcome under study • credible intervalAn interval in the domain of a posterior probability distribution used for interval estimation. • dependent variablein an equation, the variable whose value depends on one or more variables in the equation • ecological correlationA correlation between two variables that are group parameters, in contrast to a correlation between two variables that describe individuals. Free to share, print, make copies and changes. Get yours at www.boundless.com

  15. Correlation and Regression • exogeneitya condition in linear regression wherein the variable is independent of all other response values • extrapolationa calculation of an estimate of the value of some function outside the range of known values • extrapolationa calculation of an estimate of the value of some function outside the range of known values • extrapolationa calculation of an estimate of the value of some function outside the range of known values • Granger causality testA statistical hypothesis test for determining whether one time series is useful in forecasting another. • graph of averagesa plot of the average values of one variable (say ) for small ranges of values of the other variable (say ), against the value of the second variable () at the midpoints of the ranges • heteroscedasticityThe property of a series of random variables of not every variable having the same finite variance. • heteroscedasticityThe property of a series of random variables of not every variable having the same finite variance. • homoscedasticif all random variables in a sequence or vector have the same finite variance • homoscedasticif all random variables in a sequence or vector have the same finite variance • homoscedasticityA property of a set of random variables where each variable has the same finite variance. • homoscedasticityA property of a set of random variables where each variable has the same finite variance. Free to share, print, make copies and changes. Get yours at www.boundless.com

  16. Correlation and Regression • independent variablein an equation, any variable whose value is not dependent on any other in the equation • interaction variableA variable constructed from an original set of variables to try to represent either all of the interaction present or some part of it. • interceptthe coordinate of the point at which a curve intersects an axis • interceptthe coordinate of the point at which a curve intersects an axis • interpolationthe process of estimating the value of a function at a point from its values at nearby points • interpolationthe process of estimating the value of a function at a point from its values at nearby points • interpolationthe process of estimating the value of a function at a point from its values at nearby points • Kendall's rank correlation coefficientA statistic used to measure the association between two measured quantities; specifically, it measures the similarity of the orderings of the data when ranked by each of the quantities. • least squaresa standard approach to find the equation of regression that minimizes the sum of the squares of the errors made in the results of every single equation • least squares regressiona statistical technique, based on fitting a straight line to the observed data. It is used for estimating changes in a dependent variable which is in a linear relationship with one or more independent variables • MulticollinearityStatistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a non-trivial degree of accuracy. • Multicollinearitya phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, so that the coefficient estimates may change erratically in response to small changes in the model or data Free to share, print, make copies and changes. Get yours at www.boundless.com

  17. Correlation and Regression • multiple regressionregression model used to find an equation that best predicts the variable as a linear function of multiple variables • multiple regressionregression model used to find an equation that best predicts the variable as a linear function of multiple variables • multiple regressionregression model used to find an equation that best predicts the variable as a linear function of multiple variables • nested modelstatistical model of parameters that vary at more than one level • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • orthogonalstatistically independent, with reference to variates • p-valueThe probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. • partial regression coefficienta value indicating the effect of each independent variable on the dependent variable with the influence of all the remaining variables held constant. Each coefficient is the slope between the dependent variable and each of the independent variables • polynomial regressiona higher order form of linear regression in which the relationship between the independent variable and the dependent variable is modeled as an th order polynomial • post hoc fallacyflawed logic that assumes just because A occurred before B, then A must have caused B to happen • qualitative variableAlso known as categorical variable; has no natural sense of ordering; takes on names or labels. • random effect modelA kind of hierarchical linear model assuming that the dataset being analyzed consists of a hierarchy of different populations whose differences relate to that hierarchy. Free to share, print, make copies and changes. Get yours at www.boundless.com

  18. Correlation and Regression • rank correlation coefficientA measure of the degree of similarity between two rankings that can be used to assess the significance of the relation between them. • regressionAn analytic method to measure the association of one or more independent variables with a dependent variable. • regression fallacyflawed logic that ascribes cause where none exists • residualThe difference between the observed value and the estimated function value. • root-mean-square error(RMS error) A frequently used measure of the differences between values predicted by a model or an estimator and the values actually observed. • scatter plotA type of display using Cartesian coordinates to display values for two variables for a set of data. • significance levelA measure of how likely it is to draw a false conclusion in a statistical test, when the results are really just random variations. • Simpson's paradoxThat the association of two variables for one subset of a population may be similar to the association of those variables in another subset, but different from the association of the variables in the total population. • slopethe ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical. • slopethe ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical. • Spearman's rank correlation coefficientA nonparametric measure of statistical dependence between two variables that assesses how well the relationship between two variables can be described using a monotonic function. • spurious variablea mathematical relationship in which two events or variables have no direct causal connection, yet it may be wrongly inferred that they do, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "confounding factor" or "lurking variable") Free to share, print, make copies and changes. Get yours at www.boundless.com

  19. Correlation and Regression • standard partial regression coefficientthe number of standard deviations that would change for every one standard deviation change in , if all the other variables could be kept constant • statistical powerthe probability that a statistical test will reject a false null hypothesis, that is, that it will not make a type II error, producing a false negative • sum of squared errorsa mathematical approach to determining the dispersion of data points; found by squaring the distance between each data point and the line of best fit and then summing all of the squares • tautologyA statement that is true for all values of its variables. • trendthe long-term movement in time series data after other components have been accounted for • trend lineA line on a graph, drawn through points that vary widely, that shows the general trend of a real-world function (often generated using linear regression). Free to share, print, make copies and changes. Get yours at www.boundless.com

  20. Correlation and Regression Correlation This graph shows a positive correlation between world population and total carbon emissions. Free to share, print, make copies and changes. Get yours at www.boundless.com Flickr."Correlation between Population Growth and Emissions Growth Chart | Flickr - Photo Sharing!."CC BY-SAhttp://www.flickr.com/photos/mplemmon/3202552975/View on Boundless.com

  21. Correlation and Regression Alternate Correlation Coefficient This equivalent expression gives the correlation coefficient as the mean of the products of the standard scores. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Pearson product-moment correlation coefficient."GNU FDLhttp://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficientView on Boundless.com

  22. Correlation and Regression Coefficient of Determination This equation gives the most general form of the coefficient of determination. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Coefficient of determination."GNU FDLhttp://en.wikipedia.org/wiki/Coefficient_of_determinationView on Boundless.com

  23. Correlation and Regression Concordance Correlation Coefficient Equation for The Concordance Correlation Coefficient. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Concordance correlation coefficient."GNU FDLhttp://en.wikipedia.org/wiki/Concordance_correlation_coefficientView on Boundless.com

  24. Correlation and Regression Greenhouse Effect The greenhouse effect is a well-known cause-and-effect relationship. While well-established, this relationship is still susceptible to logical fallacy due to the complexity of the system. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Greenhouse Effect."CC BY-SAhttp://commons.wikimedia.org/wiki/File:Greenhouse_Effect.pngView on Boundless.com

  25. Correlation and Regression Simpson's Paradox Simpson's paradox for continuous data: a positive trend appears for two separate groups (blue and red), a negative trend (black, dashed) appears when the data are combined. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Simpson's paradox continuous."Public domainhttp://commons.wikimedia.org/wiki/File:Simpson's_paradox_continuous.svgView on Boundless.com

  26. Correlation and Regression Francis Galton A picture of Sir Francis Galton, who coined the use of the word "regression. " Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Francis Galton 1850s."CC BY-SAhttp://en.wikipedia.org/wiki/File:Francis_Galton_1850s.jpgView on Boundless.com

  27. Correlation and Regression Vertical Strips Drawing vertical strips on top of a scatter plot will result in the -values included in this strip forming a new data set. Free to share, print, make copies and changes. Get yours at www.boundless.com Blogspot.CC BY-SAhttp://1.bp.blogspot.com/-F54hUuZ3aWQ/T8FJ_vCbDfI/AAAAAAAAA1A/GsuMTPu_2uo/s1600/20091215_regressionAssumptions_1c.pngView on Boundless.com

  28. Correlation and Regression Multiple Regression This image shows data points and their linear regression. Multiple regression is the same idea as single regression, except we deal with more than one independent variables predicting the dependent variable. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Linear regression."CC BY-SAhttp://en.wikipedia.org/wiki/File:Linear_regression.svgView on Boundless.com

  29. Correlation and Regression Polynomial Regression A cubic polynomial regression fit to a simulated data set. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Polyreg scheffe."CC BY-SAhttp://en.wikipedia.org/wiki/File:Polyreg_scheffe.svgView on Boundless.com

  30. Correlation and Regression Linear Regression Random data points and their linear regression. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Linear regression."CC BY-SAhttp://en.wikipedia.org/wiki/File:Linear_regression.svgView on Boundless.com

  31. Correlation and Regression ANCOVA Model Graph showing the regression results of an ANCOVA model example: Public school teacher's salary (Y) in relation to state expenditure per pupil on public schools. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Ancova graph."CC BY-SAhttps://en.wikipedia.org/wiki/File:Ancova_graph.jpgView on Boundless.com

  32. Correlation and Regression Regression Line Equation An equation where y is the dependent variable, x is the independent variable, m is the slope, and b is the intercept. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikibooks."Statistics Ground Zero/Regression."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics_Ground_Zero/RegressionView on Boundless.com

  33. Correlation and Regression Matrix Correlation Plot This figure shows a very nice scatterplot matrix, with histograms, kernel density overlays, absolute correlations, and significance asterisks (0.05, 0.01, 0.001). Free to share, print, make copies and changes. Get yours at www.boundless.com Blogspot."Getting Genetics Done: More on Exploring Correlations in R."CC BY-SAhttp://gettinggeneticsdone.blogspot.com/2012/08/more-on-exploring-correlations-in-r.htmlView on Boundless.com

  34. Correlation and Regression Sir Francis Galton Sir Frances Galton first observed the phenomenon of regression towards the mean in genetics research. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Sir Francis Galton."GNU FDLhttp://en.wikipedia.org/wiki/Sir_Francis_GaltonView on Boundless.com

  35. Correlation and Regression Best Fit Line This shows how the scatter plots form a best fit line, implying there may be correlation. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Mihai Nica, Principles of Business Statistics. June 11, 2013."CC BY 3.0http://cnx.org/content/m17090/latest/?collection=col10874/latestView on Boundless.com

  36. Correlation and Regression ANOVA Model Graph showing the regression results of the ANOVA model example: Average annual salaries of public school teachers in 3 regions of a country. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Anova graph."CC BY-SAhttps://en.wikipedia.org/wiki/File:Anova_graph.jpgView on Boundless.com

  37. Correlation and Regression Regression Line Equation An equation where y is the dependent variable, x is the independent variable, m is the slope, and b is the intercept. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikibooks."Statistics Ground Zero/Regression."CC BY-SA 3.0http://en.wikibooks.org/wiki/Statistics_Ground_Zero/RegressionView on Boundless.com

  38. Correlation and Regression Correlation Coefficient This is the formula for calculating the coefficient of correlation. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Irene Mary Duranczyk, Suzanne Loch, and Janet Stottlemyer, Bivariate Descriptive Statistics: Correlation Coefficient and Coefficient of Determination. May 21, 2013."CC BY 3.0http://cnx.org/content/m46185/latest/View on Boundless.com

  39. Correlation and Regression Mean Squared Error This image gives the formula for calculating the MSE. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Mean squared error."GNU FDLhttp://en.wikipedia.org/wiki/Mean_squared_errorView on Boundless.com

  40. Correlation and Regression ICC Formula This equation gives the population ICC in the framework of the random effect model. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Intraclass correlation."GNU FDLhttp://en.wikipedia.org/wiki/Intraclass_correlationView on Boundless.com

  41. Correlation and Regression ANCOVA This pie chart shows the partitioning of variance within ANCOVA analysis. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."ANCOVA - Partitioning Variance."CC BY-SAhttp://en.wikipedia.org/wiki/File:ANCOVA_-_Partitioning_Variance.jpgView on Boundless.com

  42. Correlation and Regression High Residual These images depict the highest residual in our example. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikispaces."drunkdrivingstats - Regression and Residual Plot."CC BY-SAhttp://drunkdrivingstats.wikispaces.com/Regression+and+Residual+PlotView on Boundless.com

  43. Correlation and Regression Residual Histogram To the extent that a residual histogram matches the normal distribution, the residuals are normally distributed. Free to share, print, make copies and changes. Get yours at www.boundless.com Blogspot.CC BY-SAhttp://1.bp.blogspot.com/-pSYglMf65Uw/T8FJ_kv1sJI/AAAAAAAAA1Q/DzGttY98RQQ/s1600/20091215_regressionAssumptions_2a.pngView on Boundless.com

  44. Correlation and Regression Atlantic Beach Tiger Beetle This is the Atlantic beach tiger beetle (Cicindela dorsalis dorsalis), which is the subject of the multiple regression study in this atom. Free to share, print, make copies and changes. Get yours at www.boundless.com University of Delaware."Handbook of Biological Statistics: Multiple regression."License: Otherhttp://udel.edu/~mcdonald/statmultreg.htmlView on Boundless.com

  45. Correlation and Regression Interaction Model 1 A table showing no interaction between the two treatments — their effects are additive. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Interaction (statistics)."GNU FDLhttp://en.wikipedia.org/wiki/Interaction_(statistics)View on Boundless.com

  46. Correlation and Regression Interaction Model 2 A table showing an interaction between the treatments — their effects are not additive. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Interaction (statistics)."GNU FDLhttp://en.wikipedia.org/wiki/Interaction_(statistics)View on Boundless.com

  47. Correlation and Regression Example Graph This graph will be used in our example for drawing a trend line. Free to share, print, make copies and changes. Get yours at www.boundless.com Austrailian Bureau of Statistics."Error 404."CC BYhttp://www.abs.gov.au/websitedbs/a3121120.nsf/4a256353001af3ed4b2562bb00121564/64efcd94f3621967ca25761700052ab8!OpenDocumentView on Boundless.com

  48. Correlation and Regression Least Squares Regression Line Random data points and their linear regression. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Linear regression."CC BY-SAhttp://en.wikipedia.org/wiki/File:Linear_regression.svgView on Boundless.com

  49. Correlation and Regression Scatter Plot Patterns An illustration of the various patterns that scatter plots can visualize. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Irene Mary Duranczyk, Suzanne Loch, and Janet Stottlemyer, Bivariate Descriptive Statistics: Linear Regression and Correlation: Scatter Plots. May 20, 2013."CC BY 3.0http://cnx.org/content/m46171/latest/View on Boundless.com

  50. Correlation and Regression Extrapolation An example of extrapolation, where data outside the known range of values is predicted. The red points are assumed known and the extrapolation problem consists of giving a meaningful value to the blue box at . Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Extrapolation example."CC BY-SAhttp://en.wikipedia.org/wiki/File:Extrapolation_example.svgView on Boundless.com

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