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Empirical Direction in Design and Analysis

By: Norman H. Anderson | Book details

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Page 282
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EXERCISES FOR CHAPTER 9
1. a. Use the regression equation given for Figure 9.1 to predict Y for new cases, with Xnew = 0, 2, 5, and 12.
1. Which of these predictions is most/least reliable?
2. Will all predictions for new cases lie on the regression line?
2. Justify the statement: “In Figure 9.1, visual inspection indicates that the regression line should pass through the Y values of 3, 4, 5, and 6 for the four successive values of X.”3. a. Use hand calculation to show that the standard deviation, or error half-bar, for b1 for the data of Table 9.1 is.063. Use calculations given in the text.b. Find the 95% confidence interval for b1.4 a. Graph these data and find the linear regression by visual inspection.
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b. How is this example related to Figure 9.1 in the text?5. Under Unequal Variance in Section 9.1.4, verify that the Y values of 3 ± 10 would yield b1 values of −4 and 6.6. Graph Y = b0 + b1X over the range from −10 to 10 for:
1. b0 = 0; b1 = −2, −1, 0, 1, and 2.
2. b0 = −2, −1, 0, l, and 2; b1 = 1.
3. Explain the pattern in (a) and in (b).
7. If Galton had studied the relation between heights of mothers and daughters, what do you guess he would have found?8. Do-it-yourself example of subgrouping artifact in correlation. (No calculation is needed or wanted; a graph will suffice.)
1. Consider two subgroups of three cases each. Make up simple artificial data with zero correlation within each subgroup, but a positive correlation for the group as a whole.
2. Show similarly how a substantial positive correlation within each of two subgroups could vanish in the group as a whole.

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