EXERCISES FOR CHAPTER 91. a. Use the regression equation given for Figure 9.1 to predict Y for new cases, with Xnew = 0, 2, 5, and 12.
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.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. ||Which of these predictions is most/least reliable?|
|2. ||Will all predictions for new cases lie on the regression line?|
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. ||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).|
|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.|
Questia, a part of Gale, Cengage Learning. www.questia.com
Book title: Empirical Direction in Design and Analysis.
Contributors: Norman H. Anderson - Author.
Publisher: Lawrence Erlbaum Associates.
Place of publication: Mahwah, NJ.
Publication year: 2001.
Page number: 282.
This material is protected by copyright and, with the exception of fair use, may
not be further copied, distributed or transmitted in any form or by any means.