Refer to Figure 13 of this section. The least-squares line for these data is the line y

Chapter 5, Problem 20

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Refer to Figure 13 of this section. The least-squares line for these data is the line y = mx that fits the data best, in that the sum of the squares of the vertical distances between the line and the data points is minimal. We want to minimize the sumIn vector notation, to minimize the sum means to find the scalar m such that\\mx 3>||2is minimal. Arguing geometrically, explain how you can find m. Use the accompanying sketch, which is not drawn to scale.Find m numerically, and explain the relationship between m and the correlation coefficient r. You may find the following information helpful:x -y = 4182.9, ||i|| % 198.53, \\y\\ ^ 21.539.To check whether your solution m is reasonable, draw the line y = mx in Figure 13. (A more thorough discussion of least-squares approximations will follow in Section 5.4.)

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