Lesson 5.
For this lesson, we will do the latter part of Chapter 4 in Moore and the first part of Chapter 5. Test 1 covers through the end of Chapter 4.
Correlation
On page 99, we learn why we need to get a numerical measure of how close the points are to a straight line. Our eyes can deceive us. Which one of the two graphs on page 89 looks closest to linear to you? You might be interested to know that, in my classes, opinions are quite divided about this question. Do you see why that’s interesting?
Now, before you read much of the chapter, look at some pictures, and do some things, as described below.
Before turning to page 100, take my advice: Do not try to compute the correlation coefficient for a set of data using the formula. Now turn the page and look at the formula. It is a pretty intimidating-looking formula. It is shown here just so that you see that it uses the standardized values of the observations. Just read about how the formula works and then use MINITAB to compute it. DO NOT DO 8b. You will never have to compute it step-by-step in this class. Use MINITAB for 8c.
Now look at the figures on p. 102. Focus on learning to glance at a dataset and estimate the correlation coefficient. These pictures are a good place to start.
In the e-book find the applet for this section - right beside Example 4.7. You'll begin with a blank graph and "Add data." Click to add points to the plot. See if you can duplicate the graphs on p. 92 -- or at least make something like them. Change them a bit and see how that changes the correlation coefficient. Keep this applet open as you go through the reading and use it to make illustrations for yourself of the statements you're reading.
Now, use MINITAB to do problem 8a and 8c. Use Graph > Scatterplot for part a. Use Stat > Basic Statistics > Correlation for part c.
Now read pages 99-103. Keep the applet beside Example 4.7 open as you go through the reading and use it to make illustrations for yourself of the statements you're reading. In the "Facts" on page 101, you can use the applet to explore Fact 3 and Fact 4. In the "Cautions" on page 103, definitely use the applet to explore Caution 3. (You an also find this applet under "Resources > Applets > Chapter 4.)
Do problems 4.9 and 4.11. Do these make sense to you? If so, go on to 4.12-4.21. If not, use the StatTutor for more explanations. Ask questions on the Discussion Board.
Now do the homework at the end of Chapter 4.
The Regression Line
There's a lot of information about the regression line in this lesson and it's important to DO some things as well as read. So print out the worksheet listed in the table below and get out your calculator. Then "lightly" read pages 115-118. In a classroom I skim over this in about five minutes, and then have the class look at the formulas on p. 120 and start on the worksheet.
| What | Read about it | Do it | Preliminary material |
| Look at a scatterplot and "by eye" guess where the best line to approximate the data is. | Watch it being done : In StatsPortal, under Applets, choose "Correlation and Regression," which is an applet for Chapter 4. You can put points on the plot and, if you check the option "Show least-squares line" you can see how the line moves as you put points in different places. (This applet also appears in the e-book beside Example 4.7.) |
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By hand, find the equation of the best line to fit the data. |
p. 120 |
Do 1 - 7 |
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| Use that equation to predict. Use two such predictions to draw the line. |
p. 117 | same worksheet Do 8 - 9 |
How to plug in points and graph a line: |
| Use the predicted values to find the "errors" or "residuals." | p. 119 | same worksheet |
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| Interpret the slope and intercept of that best line. | p. 117 Read additional examples. |
same worksheet Finish it. |
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| Using MINITAB, find the equation of the best line to fit the data. | p. 121. Also MINITAB Manual. Stat > Regression > Regression |
problem 5.3 | |
Now that you see how to find the equation of the best line to fit the data, you may want to re-read p. 115-120 so that you can get a better feeling for how it all fits together.
Now do problems 5.1 (and finish 5.3 if you haven't yet done so.)
Last updated May 23, 2007 . Mary Parker