1. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-1 (p. 522) The relationship between exam grade and time needed to complete the exam. Notice the general trend in these data: Students who finish the exam early tend to have better grades.

2. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-2 (p. 523) The same set of n = 6 pairs of scores (X and Y values) is shown in a table and in a scatterplot. Notice that the scatterplot allows you to see the relationship between X and Y.

3. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-3 (p. 524) Examples of positive and negative relationships. (a) Beer sales are positively related to temperature. (b) Coffee sales are negatively related to temperature.

4. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-4 (p. 525) Examples of relationships that are not linear: (a) relationship between reaction time and age; (b) relationship between mood and drug dose.

5. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-5 (p. 525) Examples of different values for linear correlations: (a) shows a strong positive relationship, approximately +0.90; (b) shows a relatively weak negative correlation, approximately –0.40; (c) shows a perfect negative correlation, –1.00; (d) shows no linear trend, 0.00.

6. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-6 (p. 530) Scatterplot of the data from Example 16.3.

7. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-7 (p. 533) Hypothetical data showing the logical relationship between the number of churches and the number of serious crimes for a sample of U.S. cities.

8. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-8 (p. 534) (a) In this example, the full range of X and Y values shows a strong, positive correlation, but the restricted range of scores produces a correlation near zero. (b) An example in which the full range of X and Y values shows a correlation near zero, but the scores in the restricted range produce a strong, positive correlation.

9. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-9 (p. 535) A demonstration of how one extreme data point (an outlier) can influence the value of a correlation.

10. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-10 (p. 536) Three sets of data showing three different degrees of linear relationship.

11. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-11 (p. 538) A demonstration of regression toward the mean. The figure shows a scatterplot for a set of data with a less-than-perfect correlation. Notice that the highest scores on variable 1 (extreme right- hand points) are not the highest scores on variable 2, but are displaced downward toward the mean. Also, the lowest scores on variable 1 (extreme left-hand points) are not the lowest scores on variable 2, but are displaced upward toward the mean.

12. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-12 (p. 539) A scatterplot of a population of X and Y values with a near-zero correlation. However, a small sample of n = 3 data points from this population shows a relatively strong, positive correlation. Data points in the sample are circled.

13. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Table 1 (p. 541)

14. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-14 (p. 542) Hypothetical data showing the relationship between practice and performance. Although this relationship is not linear, there is a consistent positive relationship. An increase in performance tends to accompany an increase in practice.

15. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Tables 16-1 and 16-2 (p. 543)

16. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-14 (p. 543) Scatterplots showing (a) the scores and (b) the ranks for the data in Example 16.8. Notice that there is a consistent, positive relationship between the X and Y scores, although it is not a linear relationship. Also notice that the scatterplot of the ranks shows a perfect linear relationship.

17. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-17 (p. 545) Scatterplots showing (a) the scores and (b) the ranks for the data in Example 16.9.

18. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-16 (p. 553) Hypothetical data showing the relationship between SAT scores and GPA with a regression line drawn through the data points. The regression line defines a precise, one-to-one relationship between each X value (SAT score) and its corresponding Y value (GPA).

19. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-17 (p. 555) Relationship between total cost and number of hours playing tennis. The tennis club charges a $25 membership fee plus $5 per hour. The relationship is described by a linear equation: Total cost = $5 (number of hours) + $25 Y = bX + a.

20. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-18 (p. 556) The distance between the actual data point (Y) and the predicted point on the line (Ŷ) is defined as Y – Ŷ. The goal of regression is to find the equation for the line that minimized these distances.

21. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-19 (p. 558) The scatterplot for the data in Example 16.14 is shown with the best-fitting straight line. The predicted Y values (Ŷ) are on the regression line. Unless the correlation is perfect (+1.00 or –1.00), there will be some error between the actual Y values and the predicted Y values. The larger the correlation is, the less the error will be.

22. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-20 (p. 560) (a) Scatterplot showing data points that perfectly fit the regression equation Ŷ = 1.6X – 2. Note that the correlation is r = 1.00. (b) Scatterplot for the data from Example 16.14 Notice that there is error between the actual data points and the predicted Y values of the regression line.

23. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-21 (p. 562) A set of 9 data points (X and Y values) with a correlation of 0.80. The colored lines in part (a) show deviations from the mean for Y. For these data, SS Y = 240. In part (b) the colored lines show deviations from the regression line. For these data, SS error = 86.4 The regression line reduces SS value by r 2 = 0.64 or 64%.

24. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-22 (p. 563) A set of 9 data point (X and Y values) with a correlation of 0.30. The colored lines in part (a) show deviations from the mean for Y. For these data, SS y = 240. In part (b) the colored lines show deviations from the regression line. For these data, SS error = 218.4. The regression line reduces the SS value by r 2 = 0.99 or only 9%.

25. Statistics for the Behavioral Sciences, Sixth Edition by Frederick J. Gravetter and Larry B. Wallnau Copyright © 2004 by Wadsworth Publishing, a division of Thomson Learning. All rights reserved. Figure 16-23 (p. 569) The scatterplot for the data of Demonstration 16.1. An envelope is drawn around the points to estimate the magnitude of the correlation. A line is drawn through the middle of the envelope to roughly estimate the Y-intercept for the regression equation.