The following 20 observations are for two quantitative variables, x and y.

Observationxy

1

−21

24

2

−32

49

3

2

10

4

29

−16

5

−13

12

6

23

−26

7

−12

29

8

−22

37

9

15

−3

10

3

−3   Observationxy

11

−36

48

12

36

−27

13

11

−18

14

−32

33

15

22

−14

16

−3

16

17

−15

20

18

12

19

19

−19

−9

20

−7

−20

(a)

Develop a scatter diagram for the relationship between x and y.

A scatter diagram has 20 points.

The horizontal axis is labeled x and ranges from −40 to 40.

The vertical axis is labeled y and ranges from −40 to 60.

The points plotted from x values of −36 to 36 are evenly scattered between y values of −27 to 49.   A scatter diagram has 20 points.

The horizontal axis is labeled x and ranges from −40 to 40.

The vertical axis is labeled y and ranges from −40 to 60.

The points are plotted diagonally from top left to bottom right. The points are somewhat scattered.   A scatter diagram has 20 points.

The horizontal axis is labeled x and ranges from −40 to 40.

The vertical axis is labeled y and ranges from −40 to 60.

The points are plotted such that for each point the value of the x coordinate is same as the value of the y coordinate.   A scatter diagram has 20 points.

The horizontal axis is labeled x and ranges from −40 to 40.

The vertical axis is labeled y and ranges from −40 to 60.

The points are plotted diagonally from bottom left to top right. The points are somewhat scattered.

(b)

What is the relationship, if any, between x and y?

There is a positive relationship between x and y because y increases as x increases.There is a negative relationship between x and y because y decreases as x increases.    There is no relationship between x and y.There is a positive relationship between x and y because y decreases as x increases.There is a negative relationship between x and y because y increases as x increases.