For the accompanying data

set, (a) draw a scatter diagram of the

data, (b) compute the correlation

coefficient, and

(c) determine whether there is a linear relation between x and y.

**x**

22

66

11

77

99

**y**

88

77

66

99

55

n

3

0.997

4

0.950

5

0.878

6

0.811

7

0.754

8

0.707

9

0.666

10

0.632

11

0.602

12

0.576

13

0.553

14

0.532

15

0.514

16

0.497

17

0.482

18

0.468

19

0.456

20

0.444

21

0.433

22

0.423

23

0.413

24

0.404

25

0.396

26

0.388

27

0.381

28

0.374

29

0.367

30

0.361

A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ModifyingAbove y with caret equals negative 0.0505 x plus 2.9315y=−0.0505x+2.9315.

(a) Predict the grade-point average of a student who plays video games 8 hours per week.

An author of a book discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation ModifyingAbove y with caretyequals=2.942.94xnegative 0.4871−0.4871. Complete parts (a) through (d).

(d) A certain team had an on-base percentage of 0.3260.326 and a winning percentage of 0.5480.548. What is the residual for that team? How would you interpret this residual?