Applet Exercise How can you improve your understanding of what the method of

Chapter 11, Problem 11.2

(choose chapter or problem)

Applet Exercise How can you improve your understanding of what the method of least-squares actually does? Access the applet Fitting a Line Using Least Squares (at www.thomsonedu. com/statistics/wackerly). The data that appear on the first graph is from Example 11.1. a What are the slope and intercept of the blue horizontal line? (See the equation above the graph.) What is the sum of the squares of the vertical deviations between the points on the horizontal line and the observed values of the ys? Does the horizontal line fit the data well? Click the button Display/Hide Error Squares. Notice that the areas of the yellow boxes are equal to the squares of the associated deviations. How does SSE compare to the sum of the areas of the yellow boxes? b Click the button Display/Hide Error Squares so that the yellow boxes disappear. Place the cursor on right end of the blue line. Click and hold the mouse button and drag the line so that the slope of the blue line becomes negative. What do you notice about the lengths of the vertical red lines? Did SSE increase of decrease? Does the line with negative slope appear to fit the data well? c Drag the line so that the slope is near 0.8. What happens as you move the slope closer to 0.7? Did SSE increase or decrease? When the blue line is moved, it is actually pivoting around a fixed point. What are the coordinates of that pivot point? Are the coordinates of the pivot point consistent with the result you derive in Exercise 11.1? d Drag the blue line until you obtain a line that visually fits the data well. What are the slope and intercept of the line that you visually fit to the data? What is the value of SSE for the line that you visually fit to the data? Click the button Find Best Model to obtain the least-squares line. How does the value of SSE compare to the SSE associated with the line that you visually fit to the data? How do the slope and intercept of the line that you visually fit to the data compare to slope and intercept of the least-squares line?