Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Determine which scatterplot shows the strongest linear correlation.
1)
A)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2)
The variables height and weight could reasonably be expected to have a positive linear
correlation coefficient, since taller people tend to be heavier, on average, than shorter
people. Give an example of a pair of variables which you would expect to have a negative
linear correlation coefficient and explain why. Then give an example of a pair of variables
whose linear correlation coefficient is likely to be close to zero.
2)
3)
Explain why having a high linear correlation does not imply causality. Give an example to
support your answer.
3)
4)
For a certain linear equation, as x increases from 3 to 4, the y–value increases from 17 to 22.
The y–value corresponding to an x–value of 9 is 47. What is the y–value corresponding to
an x–value of 10? Explain how you solved this problem.
4)
Solve the problem.
5)
For a compact car, a car–rental company charges $28.50 per day plus $0.15 per mile. For a
one–day rental, let x denote the number of miles driven and let y denote the total cost.
Obtain the equation that expresses y in terms of x. Construct a table of values using the
x–values 70, 140, and 220 miles. Draw the graph of the equation by plotting the points from
the table and connecting them with a straight line. Use the graph to estimate visually the
cost of driving the car 190 miles.
5)
2
Provide an appropriate response.
6)
^
A set of data consists of the number of years that applicants for foreign service jobs have
studied German and the grades that they receive on a proficiency test. The following
regression equation is obtained: y= 31.6 + 10.9x, where x represents the number of years of
study and y represents the grade on the test. What does the slope of the regression line
represent in terms of grade on the test?
6)
Solve the problem.
7)
For a day’s work, Chris is paid $50 to cover expenses plus $16 per hour. Let x denote the
number of hours Chris works in a day and let y denote Chris’s total salary for the day.
Obtain the equation that expresses y in terms of x. Construct a table of values using the
x–values 2, 4, and 8 hours. Draw the graph of the equation by plotting the points from the
table and connecting them with a straight line. Use the graph to estimate visually Chris’s
salary for the day if he works 6 hours.
7)
3
Provide an appropriate response.
8)
For each of 200 randomly selected cities, Pete compared data for the number of churches in
the city (x) and the number of homicides in the past decade (y). He calculated the linear
correlation coefficient and was surprised to find a strong positive linear correlation for the
two variables. Does this suggest that when a city builds new churches this will tend to
cause an increase in the number of homicides? Why do you think that a strong positive
linear correlation coefficient was obtained?
8)
9)
A regression equation is obtained for the following set of data.
x 2 4 6 9 10 12
y 28 33 39 45 47 52
For what range of x–values would it be reasonable to use the regression equation to predict
the y–value corresponding to a given x–value? Why?
9)
10)
Create a scatterplot that shows a perfect positive linear correlation between x and y. How
would the scatterplot change if the correlation showed each of the following?
(a) a strong positive linear correlation;
(b) a weak positive linear correlation;
(c) no linear correlation.
10)
11)
For a particular regression analysis, it is found that SST =909.9 and SSE =827.2. Does the
regression equation appear to be useful for making predictions? How can you tell?
11)
12)
Explain how to obtain the straight–line graph of the linear equation y = 3 – 4x. Be sure to
specify which x–values you would use and what the corresponding points on the line are.
Would this method work for an equation whose graph is not a straight line? Why or why
not?
12)
13)
What is the relationship between the linear correlation coefficient and the usefulness of the
regression equation for making predictions?
13)
14)
Describe what scatterplots are, and discuss their importance.
14)
15)
Define the terms “predictor variable” and “response variable.” Give an example of each.
15)
16)
^
A set of data consists of the number of years that applicants for foreign service jobs have
studied German and the grades that they receive on a proficiency test. The following
regression equation is obtained:
y= 31.6 + 10.9x, where x represents the number of years of study and y represents the
grade on the test. Identify the predictor and response variables.
16)
17)
A regression equation is obtained for a set of data. After examining a scatterplot, the
researcher notices a data point that is potentially an influential observation. How could the
researcher confirm that this data point is indeed an influential observation? How should
the researcher proceed if the data point is found to be an influential observation?
17)
18)
When performing regression analysis, how can you evaluate how useful the regression
equation is for making predictions?
18)
Solve the problem.
19)
Anne is running a 400–meter race. She runs at a constant speed of 7.5 meters per second. If
you let y denote her distance in meters from the finish line x seconds after the start of the
race, y = 400 – 7.5x. Determine b0 and b1 for this linear equation. Find Anne’s distance
from the finish line 10, 24, and 43 seconds after the race begins. Use these three points to
graph the linear equation y = 400 – 7.5x. Use the graph to estimate visually Anne‘s distance
from the finish line 32 seconds after the start of the race.
19)
7
20)
A car mechanic tells a client that it will cost $120 for parts plus $50 per hour for labor to fix
her car. Let x denote the number of hours of labor and let y denote the total cost to fix the
car. Obtain the equation that expresses y in terms of x. Construct a table of values using the
x–values 2, 3, and 5 hours. Draw the graph of the equation by plotting the points from the
table and connecting them with a straight line. Use the graph to estimate visually the total
cost of fixing the car if the number of hours of labor is 3.5.
20)
8
Provide an appropriate response.
21)
Give an example of a linear equation whose graph is a horizontal line.
21)
Solve the problem.
22)
A ball is thrown downward from a tall building with an initial velocity of 10 meters per
second (m/sec). According to the laws of physics, if you let y denote the velocity of the ball
after x seconds, y = 10 + 9.8x. Determine b0 and b1 for this linear equation. Determine the
velocity of the ball after 1, 2, 3, and 4 seconds. Use these four points to graph the linear
equation y = 10 + 9.8x. Use the graph to estimate visually the velocity of the ball after 2.5
seconds.
22)
9
Provide an appropriate response.
23)
^
For a particular regression analysis, the following regression equation is obtained:
y= 2.12 + 0.56x. Furthermore, the coefficient of determination is 0.043. How useful would
the regression equation be for making predictions? How can you tell?
23)
24)
Suppose data are collected for each of several randomly selected adults for height, in
inches, and number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph.
How would the value of the linear correlation coefficient, r, change if all of the heights
were converted to meters?
24)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or is
horizontal.
25)
The equation of the line is y =11 +20x.
25)
A)
Slopes downward
B)
Slopes upward
C)
Is horizontal
10
Determine the regression equation for the data. Round the final values to three significant digits, if necessary.
26)
x 1 3 5 7 9
y 143 116 100 98 90
26)
A)
^
y= – 140 + 6.2x
B)
^
y= – 151 + 6.8x
C)
^
y= 151 – 6.8x
D)
^
y= 140 – 6.2x
Is the data point, P, an outlier, a potential influential observation, both, or neither?
27)
27)
A)
Both
B)
Outlier
C)
Potential influential observation
D)
Neither
You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or is
horizontal.
28)
The y–intercept is 11 and the slope is 0.
28)
A)
Slopes downward
B)
Slopes upward
C)
Is horizontal
You are given information about a straight line. Use two points to graph the equation.
11
29)
The equation of the line is y = – 2– 0.25x.
29)
A)
B)
C)
D)
Determine the regression equation for the data. Round the final values to three significant digits, if necessary.
30)
Two different tests are designed to measure employee productivity (x) and dexterity (y). Several
employees were randomly selected and tested, and the results are given below.
x
y
23 25 28 21 21 25 26 30 34 36
49 53 59 42 47 53 55 63 67 75
30)
A)
^
y= 2.36 + 2.03x
B)
^
y= 75.3 – 0.329x
C)
^
y= 5.05 + 1.91x
D)
^
y= 10.7 + 1.53x
You are given information about a straight line. Use two points to graph the equation.
31)
The equation of the line is y = – 5.75 – x.
31)
A)
B)
13
C)
D)
You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or is
horizontal.
32)
The equation of the line is y = – 3+5.6x.
32)
A)
Is horizontal
B)
Slopes upward
C)
Slopes downward
B
Determine the y–intercept and slope of the linear equation.
33)
y =5.8 +2.5x
33)
A)
y–intercept =5.8, slope = – 2.5
B)
y–intercept =2.5, slope =5.8
C)
y–intercept =5.8, slope =2.5
D)
y–intercept =2.5, slope = – 5.8
C
Provide an appropriate response.
34)
True or false? In the context of regression analysis, the coefficient of determination is the proportion
of variation in the observed values of the response variable not explained by the regression
34)
A)
True
B)
False
B
A
Compute the coefficient of determination. Round your answer to four decimal places.
35)
^
The test scores (y) of 6 randomly selected students and the numbers of hours they prepared (x) are
as follows.
x 5 10 4 6 10 9
y 64 86 69 86 59 87
The regression equation is y= 1.06604x + 67.3491.
35)
A)
–0.2242
B)
0.6781
C)
0.0503
D)
0.2242
Provide an appropriate response.
36)
True or false? The straight–line graph of the linear equation y =b0+b1x is vertical if b1= 0.
36)
A)
True
B)
False
The regression equation for the given data points is provided. Graph the regression equation and the data points.
37)
^
x 3 5 7 15 16
y 8 11 714 20
y= 5.1 + 0.75x
37)
15
A)
B)
C)
D)
Provide an appropriate response.
38)
True or false? In the context of regression analysis, if the regression sum of squares is large relative
to the error sum of squares, then the regression equation is useful for making predictions.
38)
A)
True
B)
False
Obtain the linear correlation coefficient for the data. Round your answer to three decimal places.
39)
x 62 53 64 52 52 54 58
y 158 176 151 164 164 174 162
39)
A)
0.754
B)
–0.775
C)
–0.081
D)
0.507
Determine the y–intercept and slope of the linear equation.
40)
y =10 +16x
40)
A)
y–intercept = – 16, slope = – 10
B)
y–intercept =16, slope =10
C)
y–intercept =10, slope =16
D)
y–intercept = – 10, slope = – 16
Determine the regression equation for the data. Round the final values to three significant digits, if necessary.
41)
Ten students in a graduate program were randomly selected. The following data represent their
grade point averages (GPAs) at the beginning of the year (x) versus their GPAs at the end of the year
(y).
x y
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
41)
A)
^
y= 4.91 + 0.0212x
B)
^
y= 2.51 + 0.329x
C)
^
y= 3.67 + 0.0313x
D)
^
y= 5.81 + 0.497x
C
C
Is the data point, P, an outlier, a potential influential observation, both, or neither?
42)
42)
A)
Both
B)
Outlier
C)
Neither
D)
Potential influential observation
Determine the y–intercept and slope of the linear equation.
43)
y = – 3.1 –2x
43)
A)
y–intercept = – 3.1, slope =2
B)
y–intercept =3.1, slope =2
C)
y–intercept = – 2, slope = – 3.1
D)
y–intercept = – 3.1, slope = – 2
D
Determine the regression equation for the data. Round the final values to three significant digits, if necessary.
44)
Managers rate employees according to job performance (x) and attitude (y). The results for several
randomly selected employees are given below.
x
y
59 63 65 69 58 77 76 69 70 64
72 67 78 82 75 87 92 83 87 78
44)
A)
^
y= 2.81 + 1.35x
B)
^
y= 92.3 – 0.669x
C)
^
y= 11.7 + 1.02x
D)
^
y= – 47.3 + 2.02x
C
18
B
The y–intercept and slope, respectively, of a straight line are given. Find the equation of the line.
45)
14 and 15
45)
A)
y =14x +15
B)
y =14 +15x
C)
y =15 –14x
D)
y +15x =14
Provide an appropriate response.
46)
For the linear equation y = – 4–4.6x, explain what the y–intercept and slope represent in terms of
the graph of the equation.
46)
A)
The y–intercept, b0= – 4.6, gives the y–value at which the straight line y = – 4–4.6x intersects
the y–axis. The slope, b1= – 4, indicates that the y–value decreases by 4 units for every
increase in x of 1 unit.
B)
The y–intercept, b0= – 4, gives the y–value at which the straight line y = – 4–4.6x intersects
the y–axis. The slope, b1=4.6, indicates that the y–value increases by 4.6 units for every
increase in x of 1 unit.
C)
The y–intercept, b0= – 4, gives the y–value at which the straight line y = – 4–4.6x intersects
the x–axis. The slope, b1= – 4.6, indicates that the x–value decreases by 4.6 units for every
increase in y of 1 unit.
D)
The y–intercept, b0= – 4, gives the y–value at which the straight line y = – 4–4.6x intersects
the y–axis. The slope, b1= – 4.6, indicates that the y–value decreases by 4.6 units for every
increase in x of 1 unit.
Solve the problem.
47)
A study was conducted to compare the average time spent in the lab each week versus course
grade for computer students. The results are recorded in the table below.
Number of hours spent in lab Grade (percent)
10 96
11 51
16 62
958
789
15 81
16 46
10 51
Determine the percentage of variation in the observed values of the response variable explained by
the regression..
47)
A)
11.2%
B)
33.5%
C)
0.112%
D)
0.335%
Compute the specified sum of squares.
48)
^
The data below consist of test scores (y) and hours of preparation (x) for 5 randomly selected
students. The regression equation is y= 44.8447 + 3.52427x.
x 5 2 9 6 10
y 64 48 72 73 80
SSE
48)
A)
599.200
B)
511.724
C)
87.4757
D)
96.1030
Solve the problem.
49)
The paired data below consist of the temperatures on randomly chosen days and the amount a
certain kind of plant grew (in millimeters):
x 62 76 50 51 71 46 51 44 79
y36 39 50 13 33 33 17 616
Find the SST.
49)
A)
243
B)
1864
C)
0
D)
1684