1.	Suppose the children of a primary school are surveyed.  What type of association would you expect between their ages and their height? 	

2.	Suppose the babies in a nursery are surveyed.  What type of association would you expect between a child's age and the average number of hours the child sleeps in a day?	

3.	What are two variables associated with professional baseball players that are most likely positively associated?	

4.	What are two variables associated with professional baseball players that are most likely negatively associated?	

5.	Suppose the regression line for a scatterplot passes through the points (0,10) and (5,20).  What y value is predicted to be related to the value x = 2 ?	

6.	Suppose the regression line for a scatterplot passes through the points (0,30) and (5,20).  What y value is predicted to be related to the value x = 2?	

7.	Suppose the regression line for a scatterplot passes through the points (0,10) and (5,20).  What type of association exists between the variables?	

8.	Suppose the regression line for a scatterplot passes through the points (0,30) and (5,20).  What type of association exists between the variables?	

9.	Suppose the equation for a regression line is y = 4x + 6.  If x = 5, what is the predicted corresponding value for y?	

10.	Suppose the equation for a regression line is y = 4x + 6.  If y = 12, what is the predicted corresponding value for x?	

11.	Suppose the equation for a regression line is y = 18 – 3x.  If x = 4, what is the predicted corresponding value for y?	

12.	Suppose the equation for a regression line is y = 18 – 3x.  If y = 9, what is the predicted corresponding value for x?	

13.	Suppose the equation for a regression line has a positive slope.  What type of association exists between the variables?	

14.	What can you say about the slope of a regression line for variables that are negatively associated? 	

15.	If all the points of a scatterplot lie on a straight line, what can you say about the correlation of the data?	

16.	When the units of measurement are changed, what happens to the correlation of the data?	

17.	Is it possible for the correlation for a scatterplot to change dramatically when a single point is moved? 	

18.	If there is an association between two variables, is it reasonable to presume that changes in one variable will cause changes in the other variable?	

19.	Below are data on the age of ten cars and the amount spent on auto repairs in one year.  Make a scatterplot of the data.

Age (years)	
Auto repairs ($) 	

	
2	
	
120	

3	
	
175	

3	

160	

5	

	
250	

6	

	
	
325	

7	

	

380	

10	

	

	
500	

12	

	

	
	
615	

12	

	

	

630	

15	

	

	

	
770	

20.	Below are data on two related variables.  Make a scatterplot of the data.

X	
Y	

	
118	
	
66	

99	
	
50	

120	

73	

121	

	
69	

123	

	
	
72	

108	

	

65	

111	

	

	
62	

21.	Suppose that age and amount of time slept per day are gathered from people at a mall.  According to this data, young children and older adults tend to sleep more than older children and younger adults.  How could you describe the resulting scatterplot of this data, where x represents ages and y represents the amount of sleep per day?	

22.	Suppose the points of a scatterplot tend to follow the bell-shaped curve of the normal distribution.  What can you say about the feasibility of using a least-squares regression line to describe this data?	

23.	Below is the scatterplot for data collected on two variables.  Would a least-squares regression equation be useful in describing the relationship between the variables?  Why or why not?

24.	What type of association exists between the variables on the scatterplot below?

25.	Does the scatterplot below have an outlier? 

26.	A little-league manager keeps a record book showing the statistics for his players. The first few lines of the record book show:
 
Player  	
At Bats	
Hits	
Average	

Brett	
142	
37	
.261	

Mike 	
128	
32	
.250	

Carlos	
128	
35	
.273	

John	
123	
36	
.293	

What are the individuals and the variables in these data? 	

27.	The least-squares regression line is the “best” line in that it minimizes a certain sum. What is this sum?	

28.	Can outliers significantly impact the least-squares regression line?	

29.	Ten crickets were observed under various temperatures and the number of chirps each cricket made per second was recorded. The results are shown in the table below.
 
Temperature in degrees F	
70	
72	
74	
75	
81	
82	
83	
84	
89	
93	

Chirps per second	
15	
15	
15	
16	
17	
17	
16	
17	
19	
20	

Make a scatterplot. Is the association between these variables positive or negative?	

30.	Describe the form, direction, and strength of the relationship.
Time spent 
 studying (hours)	
1	
2	
5	
4	
6	
7	
8	
5	
2	
4	
3	
5	

Test score 
 (percentage)	
49	
57	
80	
70	
88	
91	
98	
80	
57	
72	
65	
82	

Answer Key

1.	The variables are most likely positively associated.	
2.	The variables are most likely negatively associated.	
3.	Answers will vary.  For example, batting average and salary	
4.	Answers will vary.  For example, number of hits allowed and salary for pitchers	
5.	14	
6.	26	
7.	A positive association	
8.	A negative association	
9.	26	
10.	3	
11.	6	
12.	3	
13.	A positive association	
14.	The slope is negative.	
15.	r = 1 or r = – 1.	
16.	The correlation does not change.	
17.	It is possible to change the value from positive to negative by moving a single outlier.	
18.	No.  Association does not imply causation.	
19.	
	
20.	
	
21.	The points follow a general “U” shape, higher at the ends and lower in the middle.	
22.	This will not be effective, as the data does not consistently show a linear relationship among the variables.	
23.	The least-squares regression line would not be useful to describe the relationship between the variables.  While there does appear to be a strong relationship between the variables, the relationship does not appear to be linear.	
24.	A positive correlation	
25.	The point (50, 100) appears to be an outlier.	
26.	The individuals are the players. The variables are at bats, hits, and average.	
27.	The sum of the squares of the vertical distances from each data point to the line.	
28.	Yes.  The removal or repositioning of a single outlier can dramatically change the least-squares regression line.	
29.	The association is positive.
	
30.	The form is a straight-line pattern. The direction is positive: As study time increases, test scores increase. The relationship is strong because the points all lie close to a line.