HW 6 - Part III

Why did I use the teaching tool at http://cyberk.com/1.0, when I gave the lecture on the topic Simple Linear Regression.

The World Wide Web(WWW) has opened up a new medium for education. There are a lot of WWW locations that provide various forms of information for statistics education in electronic form. For example, electronic textbooks, teachware tools and other course materials are availabe at some WWW sites.

In most of the electronic forms, hypertext documents are designed for user interaction. In the context of learning statistics, the student can view demos, cut and paste sample command into the program, try out suggestions, quickly find the definitions for new words, and follow up on related concepts. For example, in HTML, help for concepts and keywords can be linked inside the document, so that simply clicking on the word allows the user to easily find definitions for unfamiliar concepts.

The most impressive thing is dynamic graph which is siginificantly different from the classic textbook and teaching method. Using Lisp-stat and Java, a series of dynamic graphics have been created to help students to learn introductory statistical concepts. The goal of these Web-based demonstrations is to present statistical ideas in vivid and direct manner. This is done by visualizing concepts that are difficult to communicate using dtraditional methods and by eliminating extraneous steps. Adding the interactive components would stimulate student interests by providing a 'hands on' learning experience. Many topics can be presented using colorful graphics that can be manipulated in real-time. The dynamic Web environment provides a powerful tool for introductory statistics courses.

After reading some papers on Web-based teaching, referring electronic textbooks and teaching tools given in class, and considering the topic Linear Regression, I experimented with several tools and textbooks before I decided to choose which one as a tool for my lecture.

1. I tried Web-enhanced introductory statistics courses at West Virginia at http://www.stat.wvu.edu/srs. A series of Web-based statistical modules and infrastructure component are available. Each module covers a statistical topic and contains links to images, examples, applets and exercises. If lectures notes are simply transferred to the Web as static pages, the gain will be minimal. West Virginia University created a dynamic Web environment for teaching. I chose the topic regression in the inferential statistical module. In the basic principle, a plot of some points are shown. If I click on the model for regression, then the regression line is drawn immediately. If I drag some points to different places, the changed regression line will be given too. This applet can let students do the interactivity by adding or changing the points by themselves and then see how the regression line change. This advantage can help students to visualize how the points affect the regression line. But this page does not explain the reason and the criterion for drawing this regression line, just giving the regression line automatically once the points are placed. I would like to show why this kind of line is chosen as the regression line, so I did not use this applets in my lecture.
   
   
2. I located an applet at http://www.stat.sc.edu/~west/javahtml/Regression.html. This applet is similar to the above one. It is designed to teach students the effects of leverage points on a regression line. Students may add points to the plot by clicking the mouse button. The different thing is that it has a summary on how the points affect the regression analysis. This should be more helpful. As I said in the part one, there is no criterion explained about the regression line, so I did not use it in my lecture.
   
   
3. I experienced with Hyperstat electronic textbook at http://davidmlane.com/hyperstat. It contains many contents. There are 18 chapters. All the chapters have the same organization and features. I clicked the chapter 15, prediction. Just like our classic textbooks, the chapter was divided into several sections. The contents are discussed step by step in detail. It is well organized. In the section 1, the text is complete in explaining the basic concepts. As I read the text, it seems that I was reading a printed textbook except that some description of concepts is accessible easily by just clicking the key words. From this text I can understand what the regression line is, how the related estimates are computed, and what is the criterion. Inside Hyperstat textbook, the text is not significantly different from what one encounters in a classical printed textbook. While such information is certainly useful and easily accessible, it is static in that it cannot respond to user input.

   It is helpful that there are a lot of links of references related to the chapter, including Analysis tools, Instructional Demos, and Text. I am interested in the Demos, so I clicked some of them. In the Demo Regression by Eye, if I click New Data button and Draw regression line button, the different regression lines will appear with the different sets of points in the picture. At the same time, the correlation and the minimun MSE are shown. This Demo helps students to visualize how the spread shape of the points determine the correlation and the regression line. In the Demo Linear Regression, there is an applet that let us mark and change the locations of some ponts, and then the equation and graph of the regresson line, and residuals will be given accordingly. Of course, these interactivity will be more effective and impressive than the classic static textbook.

   Since these links are outside the hyper textbook and sometimes it can not be open, it is a little bit inconvenient. I prefer the interactivities and demonstrations are within the text, so I didn't use it in my lecture.
   
   

4. I located a statistical applet at http://ww3.whfreeman.com/test/statistics/CorrelationRegression.html. The definition of the Least-Square regression line is given first. In the following picture, if we add any point and click the least-square line button, the regression line will be shown immediately. The funny thing is that we can draw any line in the picture and later we can put it in the trash. Students may draw the guessed regression line according to the points, and then compare it with the accurate regression line. The Mean X and Mean Y lines are also available. I think this applet is too simple to explain everything clear about Simple Linear Regression.
   
   
5. I explored the Berkeley electronic textbook at http://www.stat.berkeley.edu/users/stark/sticiGui/text/index.htm. In this text index, Home, text, Glossary, problems, calculator, tools, review, and grades are availale. Under the Glossary, there are 27 chapters. It contain so many topics and contents that it is useful at the undergraduate, graduate and even higher level. I chose the chapter 5 Regression, and went to the part of Regression line. In the picture for the example, both the SD line and regression line are drawn. That help students to compare the two kinds of lines. The data set and the unvariate statistics are also available. Following this picture, some exercises are given. Students can get the feedback immediately after typing the answer. This is pretty good. Then, the detailed explanation about the related concepts, the criterion, estimate computations are given clearly. Some following exercises are given again to check if students understand the concepts and computations well, and the solutions are attached. The special cases of the regression line are dicussed further, followed by the examples, exercises and solutions. This part is complete for simple linear regression.

   I would like to watch some dynamic graph, so I clicked the tools in the index and located at an applet for Correlation and Regression. We can use the slider to change the correlation and the number of data. The regression line and the residual plot can be shown. Points can be added or cleared. It is fun and helpful to play in this applet.

   Because the text for simple linear regression is a little more complicated in this textbook, so I didn't choose it for my introductory statistical lecture.
   
   

6. I located the sufstat textbook at http://surfstat.newcastle.edu.au/surfstat/mail/surfstat.html. All the material I can find inside the textbook about the linear regression is the text just as in the classic printed textbook. There is no dynamic graph available, so I didn't use it in my lecture.
   
   
7. I chose the teaching tool at http://cyberk.com/1.0/D-2/indes.html, in my lecture. In each unit, there are Think First, Three Keys, Practice, Resources, Feedback and Calculator. The reason why I chose this teaching tool is that it has a lot of interactivities and dynamic graphics in examples and exercises. Since I only have 18 minutes to talk about the Simple Linear Regression, I just used the Basics for my lecture. In this page, the linear model equation is written. How to fit a best straight line if the data are given? What criterion can we use? In order to talk about these problems, I used the first interactivity example. In this picture, the points are marked already. Our goal is to select a straight line that best fit the data. Two sliders can be moved to adjust the straight line. Following the picture, X & Y, a+bX, Residuals and Square of the Residuals are listed in the table. The Sum of Square of the Residuals (SSR), Estimate of intercept a, and Estimate of slope b are shown on the top of the picture. I explain the relationship between the value in the table and the corresponding coordinate of the points or length of the line segment. The different color for the points and lines make everything clear. The best line should get as close to the points as possible, so the absolute values of the residuals (the lengths of the vertical red line segments) should be as small as possible. Considering all the residuals, one criterion (Least Square) comes out. It is to select the straight line such that the SSR is smallest. Then according to the value of the SSR on the top of the picture to adjust the line untill the SSR is minimum. This line is called least square line, and the estimates are call Least Square estimates. I think this interactivity is impressive and effective, because it demonstrate how the regression line is obtained vividly. Then one exercise was practiced by fellow students in class to find the least square line, with slider to adjust the lines to get the smallest SSR. The feedback is given immediately. Using this electronic teaching tool is absolutely much more effective than the classic pure 'chalk and textbook' method. In this lecture, students can visualize the whole dynamic process of the graph and play it by themselves. I just talked the Basics 1 and 2 in detail. Actually, Basics 3 gives the formulas to compute the estimates of the regression line by the Least square criterion. If I had more time, I would compare these two methods.

These are the reasons why I chose the http://Cyberk.com/1.0 but not the others.

References:

A.J.Rossini and Rosenberger. (1994), Teaching Statistics and Computing via Multimedia through the Would Wide Web, Feature Article, Statistical Computing & Graphics, vol.5 No.3, 10-13.

R.Webster West and R. Todd Ogdent. (1998), Interactive Demonstrations for Statistics Education on the World Wide Web. Journal of Statistics Education v.6,n.3. http://www.amstat.org/publications/jse/v6n3/west.html

Jan de Leeuw. (1997), The UCLA Statistics Textbook and Modules, Isi Bulletin, Book 2, 55-58.

E. James Harner and William C. Wojciechowski. (1998), A Web-enhanced Introductory Statistics Course, Computing Science and Statistics, V.29,n.1,316-326.

Robin H. Lock. (1997), Internet Resources for Teaching Statistics, Computing Science and Statistics, V.29,N.2, 339-343.