Study Master, Chapter 3
McGraw-Hill Ryerson Mathematics of Data Management, pp. 212–213
1. Revenues at a golf course are compared to mean monthly temperatures and amounts of rainfall, as shown in the table below.
|
Monthly Revenue ($1000s) |
135 |
178 |
140 |
161 |
170 |
127 |
|
Mean Monthly Temperature |
15 |
25 |
29 |
26 |
19 |
14 |
|
Amount of Rainfall (cm) |
35 |
18 |
18 |
15 |
16 |
33 |
a) Create a scatter plot for revenue versus temperature and classify the linear correlation.
b) Determine the correlation coefficient.
c) Repeat parts a) and b) for monthly revenue versus amount of rainfall.
d) Which of these has a stronger linear correlation? Explain.
Use the information in the following table to answer questions 2 to 5.
These data, represent the number of applicants to a first-year university program over time. The last four values were projected numbers, estimated at the time the study was conducted.
|
Year |
1998 |
1999 |
2000 |
2001 |
2002 |
2003 |
2004 |
2005 |
2006 |
|
Number of Graduates |
114 |
125 |
133 |
144 |
180 |
215 |
198 |
191 |
203 |
2. a) Create a scatter plot and classify the linear correlation.
b) Determine the correlation coefficient. Use linear regression to find the best-fit line.
c) Do there appear to be any outliers? Explain.
3. In one particular year, a "double cohort" of students graduated from high school. This graduating class was comprised of those students leaving OAC for the last time plus a full complement of grade 12 graduates.
a) Is it evident from looking at the graph in question 2a) when this happened? Explain.
b) Explain how this hidden variable has distorted the trend of these data.
c) Is the effect of this hidden variable confined to just one year? Describe the "disturbance" that appears between 2002 and 2004, and explain why this might happen.
4. a) Repeat the analysis of question 2, with the outlying region of points from 2002 to 2004 removed.
b) Describe the effects on the linear model of removing this cluster of data.
5. a) Use both models developed in questions 2 and 4 to predict the number of applicants in 2010.
b) Which model do you think has provided a more reliable prediction? Explain.
Use the information in this table to answer questions 6 and 7.
The number of players required for a single-elimination tennis tournament depends on the number of rounds, as shown at the right |
Number of Rounds |
1 |
2 |
3 |
4 |
Number of Players |
2 |
4 |
8 |
16 |
6. a) Create a scatter plot, and perform a quadratic regression. Record the equation of the best-fit curve and the coefficient of determination.
b) Is this a good mathematical model for this situation? Explain.
c) Use this model to determine the number of players required for a 6-round tournament of this nature. Is this a reasonable answer? Explain.
Study Master, Chapter 3 [continued]
7. a) Determine a better mathematical model, using non-linear regression. Record the equation of the best-fit curve and the coefficient of determination.
b) Use this model to determine the number of players required for a 6-round tournament of this nature. Is this a reasonable answer? Explain.
c) Account for the discrepancies between these two models.
8. Explain each of the following types of cause and effect. Illustrate with an example.
a) common-cause factor b) accidental relationship
c) presumed relationship d) reverse cause and effect relationship
9. Claire, a high school student, claims that listening to loud music helps her study. To defend her argument, she compiles the following results for four recent tests and her study habits:
|
Test |
History |
English |
Mathematics |
Science |
|
Volume of Music While Studying (Dial Setting) |
0 |
1 |
2 |
1.5 |
|
Score (percent) |
48 |
59 |
72 |
70 |
a) Create a scatter plot for these data and classify the linear correlation.
b) Do these data support Claire’s claim? Explain.
c) To what extent has Claire established a cause and effect relationship?
d) Identify at least two extraneous variables.
e) Identify at least two types of bias that could be present in this study. Do you think that this bias could be intentional or unintentional? Explain.
f) Suggest ways that Claire might improve the validity of her study.
10. a) Explain the term "hidden variable."
b) Describe an example of a relationship between two variables that could be obscured by a hidden variable, and how the hidden variable could be recognized.
Study Guide
For help with a specific question or type of question, review the examples specified below.
|
Question(s) |
Section |
Refer to: |
|
1 a) |
3.1 |
Example 1 |
|
1 b) |
3.1 |
Examples 2, 3 |
|
1 c) |
3.1 |
Examples 1, 2, 3 |
|
1 d) |
3.1 |
Key Concepts |
|
2 a) |
3.1 |
Example 1 |
|
2 b) |
3.2 |
Example 2 |
|
2 c), 4, 5 |
3.2 |
Example 3 |
|
3 |
3.5 |
Example 3 |
|
6 |
3.3 |
Investigate and Inquire, Example 3 |
|
7 |
3.3 |
Investigate and Inquire, Examples 1, 2 |
|
8 |
3.4 |
Page 196, Example 1 |
|
9 a) |
3.1 |
Example 1 |
|
9 b), c) |
3.4 |
Key Concepts |
|
9 d) |
3.5 |
Example 2 |
|
9 e) |
3.5 |
Examples 1, 2 |
|
9 f) |
3.4 |
Example 2 |
|
10 |
3.5 |
Example 3 |