Download Quiz #5 - Department of Mathematics | Illinois State University

MAT 312
Quiz #5 (Test #2 Prep)
Name _______________
10 points
Calculator Used _______________
Impact on Course Grade: approximately 2%
(1) through (7): 1 pt each, no partial credit; (8) 3 pts
Score _______________
Multiple Choice: For questions (1) through (7), choose the one best response and circle the letter of that
response.
1.
A least-squares linear regression line maximizes the sum of the squared residual values.
(A) True
(B) False
(C) It cannot be determined.
2.
Among the following statistics, which one is most likely being used to help make the following
claim:
"Based on the sample, we are 95% sure that the average speed of all drivers on this highway is
between 63 and 69 miles per hour"?
A) 5-number summary
B) median C) midspread
D) mode
E) standard deviation
3.
A median-median line is to be generated from a scatter plot of data. Given the scatter plot, what is
the first step in creating the median-median line?
A)
B)
C)
D)
E)
F)
Calculate the slope of the median-median line.
Determine the ordered pairs corresponding to the summary points (M1, M2, M3).
Draw an ellipse around the points of the scatter plot.
Partition the data into three groups with, if possible, an equal number of points in each group.
None of the statements (A) through (D) correctly identify the first step.
More than one of the steps in statements (A) through (D) could be completed first.
4.
A box-and-whiskers plot is a visual representation best suited for _?_ data.
A) basketball
B) lots of
C) qualitative
D) quantitative
E) time-sensitive
The following data set is used for questions 5 through 7.
Table 1: Raises and Job Performance Ratings for University Administrators
Administrator ID #
Annual Salary Raise (y)
Job Rating: 5-point Scale (x)
1
$18,000
2.76
2
16,700
1.52
3
15,787
4.40
4
10,608
3.10
5
10,268
3.83
6
9,795
2.84
7
9,513
2.10
8
8,459
2.38
9
6,099
3.59
10
4,557
4.11
11
3,741
3.14
12
3,718
3.64
13
3,652
3.36
14
3,227
2.92
15
2,808
3.00
A faculty group sought to determine whether job rating (call it x) is a useful linear predictor of annual
salary raise (call it y). The group used least-squares linear regression to determine a prediction equation:
y = –1782.83x + 14012.17
5.
A)
B)
C)
D)
E)
F)
Which one of the following statements is most correct?
The prediction equation assures us that the actual raises for the 15 administrators fall in a perfect
straight line.
The prediction equation suggests that for the mean job rating an administrator would get the mean
salary increase.
The prediction equation suggests that if we know an administrator's job rating, we can determine
his or her exact salary raise.
The prediction equation suggests that, on the average, administrators have a poor job rating.
None of the statements (A) through (D) are correct.
More than one of the statements (A) through (D) is correct.
6.
Which one of the following statements about the prediction line y = –1782.83x + 14012.17 is least
correct?
A)
If the linear model is accepted as valid, the equation could be used to predict an administrator raise
from an administrator's job rating.
The equation can be used to state the actual raise for an administrator by knowing his or her job
rating.
The equation produces predicted raises with an average residual (average error) of 0.
The equation produces predicted raises with the sum of the squared residuals minimized.
B)
C)
D)
7. Which statement best interprets the meaning of the slope of the prediction equation?
A)
B)
C)
D)
For an administrator with a job rating of 1.00, we can estimate his or her raise to be $1782.83.
For a $1 salary raise, we can estimate that the administrator job rating will decrease by 1782.83.
For a 1-point increase in an administrator job rating, we can estimate a salary decrease of
$1782.83.
For a 1-point increase in an administrator job rating, we can estimate a salary increase of
$1782.83.
Respond to Question #8 with the requested information.
8. Here are weight-loss results for nine people who were part of a low-carb diet program.
Participant ID # Number of Weeks on the Diet (x) Total Weight Loss in Pounds (y)
1
2
3
4
5
6
7
8
9
10
4
8
5
12
7
5
9
6
19
18
8
16
26
12
12
29
15
a. On the grid above, create a scatter plot for these data. Represent weeks on the diet on the horizontal
axis (x) and weight loss in pounds on the vertical axis (y).
b. Suppose that we want to create a median-median line for these data. Begin that process by finding the
three summary points used to help determine the equation of the line. DO NOT go beyond this step! You
must identify these ordered pairs on the scatter plot and also list them here.
(i) M1: __________
(ii) M2:
__________
(iii) M3:
__________