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# \$1.00Regression and Correlation

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Wrapping your head around correlation coefficients can be difficult.  It is also important to understand how outliers can impact regression.  So with that in mind I have found a number of applets to demonstrate visually these concepts.  Regression and correlation are some of the most useful concepts you will learn in this course.

Go and explore the following four applets about “Regression.”< /div>
1. Correlation:http://www.stat.tamu.edu/~west/applets/rplot.html. This website allows you to change the r value (correlation coefficient) and watch how the data changes. The best way to do this is to click on the slider under the r and slowly move it in both directions. You will see that negative r's correspond to lines with a negative slope and positive r's correspond to lines with a positive slope.
2. Regression by eye:http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html. This site will allow you to draw a line through the shown data. It will give you the MSE for your line. If you click on “Show Minimum MSE,” it will give you the smallest MSE for the best fit line. You can also guess the r value for the data. If you click the box next to “Draw regression line,” the best fit line will appear.
3. Regression:http://www.stattucino.com/berrie/dsl/regression/regression.html. When you click on the area of the applet, a point will be plotted. Once you have plotted two points, a line will appear with its corresponding r value. As you add additional points by clicking, the line will adjust to include those points as will the r term.
4. Regression applet:http://www.stat.sc.edu/~west/javahtml/Regression.html. At this site, you will see five data points and the best fit line for those points. Under the graph is the equation for the best fit line as well as the r value. When you click elsewhere on the graph, the best fit line that includes the new point is plotted in red. Additionally, the new regression line and r appear in red under the original. This is a great applet to use for experimenting with the concept of influential points/outliers. You will notice that for a point near the line, the changes are minimal. For a point farther away from the line, the regression line and r values significantly change.
• Discuss which activity had the greatest impact on you and why.
• Identify what was easy and what was challenging with the applets.