496 Regression by Eye 9.2 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 496 CHAPTER 9 Correlation and Regression The Regression by eye applet allows you to interactively estimate the regression line for a data set. When the applet loads, a data set consisting of 20 points is displayed. To add a point, click at the desired location or click Add point and enter the coordinates. To remove a point, click and drag it outside the axis area. All of the points on the plot can be removed by clicking Reset. You can move the green line on the plot by clicking and dragging the endpoints. Without looking at the intercept and slope of the regression line, move the line to try to minimize the sum of the squares of the residuals, also known as the sum of square error (SSE). Note that the regression line minimizes the SSE. The intercept, slope, and SSE for the green line and for the regression line are shown below the plot. Click Simulate to generate a new data set. EXPLORE Step 1 Move the endpoints of the green line to try to approximate the regression line. Step 2 Click Regression to show the line. DRAW CONCLUSIONS 1. Click Simulate to generate a new data set. Move the green line to try to approximate the regression line. Then click Regression to show the line. Repeat this five times. Describe your process for approximating the regression line. 2. On a blank plot, place 10 points so that they have a strong positive correlation. Record the equation of the regression line. Then, add a point in the upper-left corner of the plot and record the equation of the regression line. How does the regression line change? 3. Remove the point from the upper-left corner of the plot. Add 10 more points so that there is still a strong positive correlation. Record the equation of the regression line. Add a point in the upper-left corner of the plot and record the equation of the regression line. How does the regression line change? 4. Use the results of Exercises 2 and 3 to describe what happens to the slope of the regression line when an outlier is added as the sample size increases. APPLET Correlation by eye User Regression 5 x 10 10 0 475 12.9 -0.29 435.0525 15 20 5 10 15 y Simulate Sample size Add point Reset Info 20 Line Intercept Slope SSE
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