Guessing a regression line. In the Correlation and Regression applet, click onAPPLETthe

Chapter 0, Problem 5.55

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Guessing a regression line. In the Correlation and Regression applet, click onAPPLETthe scatterplot to create a group of 15 to 20 points from lower left to upper rightwith a clear positive straight-line pattern (correlation around 0.7). Click theDraw line button and use the mouse (right-click and drag) to draw a linethrough the middle of the cloud of points from lower left to upper right. Note thethermometer above the plot. The red portion is the sum of the squared verticaldistances from the points in the plot to the least-squares line. The green portion isthe extra sum of squares for your lineit shows by how much your line missesthe smallest possible sum of squares.(a) You drew a line by eye through the middle of the pattern. Yet the right-handpart of the bar is probably almost entirely green. What does that tell you?(b) Now click the Show least-squares line box. Is the slope of the least-squaresline smaller (the new line is less steep) or larger (line is steeper) than that of yourline? If you repeat this exercise several times, you will consistently get the sameresult. The least-squares line minimizes the vertical distances of the points fromthe line. It is not the line through the middle of the cloud of points. This is onereason why it is hard to draw a good regression line by eye.