AP STATISTICS Unit 3: Describing Relationships
Enduring understanding (Big Idea): Students will understand relationships between two variables including how to describe, analyze, model, and use them.
Also that association does not necessarily mean causation. Moreover, for linear relationships how to make predictions and determine what can be explained.
Essential Questions:
1. What is a relationship between two or more variables? How can
5. What are confounding and "other" variables
we examine it?
6. If the overall pattern of a bivariate observations is regular, how can we
2. What type of variables impact association studies? How are they
describe it by a smooth curve that is a mathematical model
displayed?
7. Why are residual plots used to determine linearity in the association of
3. Where are the individuals in a graphical representation of
bivariate data?
bivariate data?
8. What is the distinction between association and causation?
4. What are the differences between Independent/Dependant
9. What is the distinction between association and independence?
variables and Explanatory/Response Variables?
BY THE END OF THIS UNIT:
Students will know:
(See the AP Statistics Course Description page 7 for full details)
I. Exploring Data: Describing patterns and departures from patterns (20%–30%)
D Exploring Bivariate Data: 1 Analyzing patterns in scatterplots, 2 Correlation and
linearity, 3 Least-squares regression line, 4 Residual plots, outliers and influential
points, 5 See Unit #12
Vocabulary: Coefficient of Determination, Correlation r (correlation coefficient),
Direction, Explanatory Variable, Extrapolation, Form, Influential Observations,
Least-squares Regression Line (LSRL), Linear, Negative and Positive
Association, Regression Line, Residual, Residual Plot, Response variable,
Scatterplots, Strength
Unit Resources:
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Fathom http://www.keycurriculum.com/products/fathom
Use Applets from: http://www.whfreeman.com/tps4e
o http://www.rossmanchance.com/applets/
o http://teachers.dadeschools.net/akoski/statsSyllabus1.htm
Download the chapter glossary at (below) and give copies to your kids.
o http://bcs.whfreeman.com/tps4e/#628644__666335__
Learning Tasks: homework - see page 3-6 & 7 of the Teacher's Edition
Performance Task: end the chapter with a "FRAPPY" (see Formative Assessments and
Problem Task suggestions below)
Project: "Characterizing Students III"
Unit Review Game: Jeopardy and Millionaire (PowerPoints)
http://www.apstatsmonkey.com/StatsMonkey/TPS3e.html
Students will be able to…
1.
identify explanatory and response variables in situations where one
variable helps explain what influences the other and know its importance
2. make a scatterplot to display the relationship between two quantitative
variables and describe its overall direction, form and strength
3. recognize outliers in a scatterplot & explain influence on correlation r
4. know basic properties of correlation and how to calculate & interpret it
5. interpret the slope & y intercept of a least-squares regression line (LSRL)
6. use the LSRL for predication and know the dangers of extrapolation
7. find the slope of the LSRL from the means of the variables
8. calculate & interpret residuals & their plots & determine data's linearity
9. use residual's standard deviation s & r2 to determine the fit of the LSRL
10. identify LSRL and s in a computer output
11. explain why association does not necessarily imply causation
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 3: Describing Relationships
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on two categorical and quantitative variables (S-ID)
Standards:
S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted
to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear…models; b.
Informally assess the fit of a function by plotting and analyzing residuals; c. Fit a linear function for a scatter plot that suggests a linear association.
NCSCOC 4.01 Analyze bivariate data. a) Recognize and analyze correlation and linearity; b)Determine the least squares regression line, and c) Create residual
plots and identify outliers and influential points to analyze data.
http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
AP Stats ID1 & 2 Exploring Bivariate Data: 1 Analyzing patterns in scatterplots, 2 Correlation and linearity
Concepts and Skills to Master (on paper and with technology)
 explanatory and response variables
 displaying relationships: scatterplots
 interpreting scatterplots
Section 3.1
[Scatterplots and Correlation]
 measuring linear association: correlations
 facts about correlation
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Previous Skills and concepts in this course from Chapter 1 through Chapter 2
Academic Vocabulary
Correlation r (correlation coefficient), Direction, Explanatory variable, Form, Linear association, Negative association, Positive Association, Response
variable, Scatterplots, Strength
Suggested Instructional Strategies






Rely on the Teachers' Edition and the Platinum Resource Binder
The text is excellent and students should have their book (and their calculator) at each
class. The challenge is how to inspire kids to read and study it. There should be class
discussions during each class using material from the book and using the calculator.
Consider assigning the next class' material as a prereading. Especially focus on the boxes
labeled "AP Exam Common Error" in the margins (and also in Appendix A)
With all students on their calculators and you on your projection calculator do
Technology Corner 3.1 on page 149 using calculator (or other Technology)
Do Activity on page 152 (continued)
Have a Class Discussion of Section 3.1's "Summary" on page 157
The College Board has posted tremendously helpful material
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use:
Resources
 Textbook Correlation:
Section 3.1 (pages 140 - 163)
 Most of the PowerPoint slides on the Instructor's
CD are very helpful.
 Use resources at
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.
html
 Monitor the AP Statistics List Serve [see Electronic
Discussion Groups on
http://apcentral.collegeboard.com/apc/public/course
s/teachers_corner/2151.html ] soon to be an AP
community see
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 3: Describing Relationships

http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for FR look for AP Index 11_12.xls
for MC look for MC_Index.xls - Daren Starnes
Sample Formative Assessment Tasks
Skill-based tasks



CHECK YOUR UNDERSTANDING (textbook pages 144, 149, and 154)
Use assessments at http://www.stats4stem.org/
Use Released Multiple Choice questions (see the last Suggested Instructional Strategy
above for a link to the list of MC questions) The column "% correct " shows the global
performance on the AP Exam for that question. Add a column to the spreadsheet to keep
a record of the questions you used and when used.
https://epl.collegeboard.org/epl/login.do
Problem Tasks


Students in groups should discuss and write down the
solution of an AP Exam Free Response question, then
compare it to the model solution, and [selected
group(s)] should present their solutions to the class
describing what they learned from their discussions
See the last Suggested Instructional Strategy above for
a list of released free response questions you can use
(Do not use 2002 #4 until the end of Chapter 3.) Add
a column to the spreadsheet to keep a record of the
questions you used and when used.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 3: Describing Relationships
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variables (S-ID)
Standards
S.ID.6a,b,c Represent data on two quantitative variables on a scatter plot, …. a. Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. Use given functions or choose a function suggested by the context. Emphasize linear…models; b. Informally assess the fit of a
function by plotting and analyzing residuals; c. Fit a linear function for a scatter plot that suggests a linear association.
NCSCOC 4.01b,c Analyze bivariate data. … b)Determine the least squares regression line, and c) Create residual plots and identify outliers and influential
points to analyze data. http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
AP Stats ID3,4 …Exploring Bivariate Data: 3 Least-squares regression line, 4 Residual plots, outliers and influential points
Concepts and Skills to Master (on paper and with technology)





interpreting a regression line
prediction
residuals and a least-squares regression line
calculating the equation of the least-squares line
how well the line fits the data: residual points
Section 3.2



[Least-Square Regression]
how well the line fits the data: the role of r2 in regression
interpreting computer regression output
correlation and regression wisdom
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Previous Skills and concepts in this course from Chapter 1 through Section 3.1
Academic Vocabulary
Coefficient of Determination, Extrapolation, Influential Observations, Least-squares Regression Line (LSRL), Regression Line, Residual,
Residual Plot
Suggested Instructional Strategies
Resources
 Rely on the Teachers' Edition and the Platinum Resource Binder
 Textbook Correlation: Chapter 3 Section 2
 The text is excellent and students should have their book (and their calculator) at
(Pages 164 - 190)
each class. The challenge is how to inspire kids to read and study it. There should
 Most of the PowerPoint slides on the Instructor's CD are
be class discussions during each class using material from the book and using the
very helpful.
calculator. Consider assigning the next class' material as a prereading. Especially
 Use resources at
focus on the boxes labeled "AP Exam Common Error" in the margins (and also in
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.html
Appendix A)

Monitor the AP Statistics List Serve [see Electronic
 With all students on their calculators and you on your projection calculator do
Discussion Groups on
Technology Corners 3.2 on pages 170 and 178 (or other Technology)
http://apcentral.collegeboard.com/apc/public/courses/teach
 Do the Activity on page 170
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 3: Describing Relationships




Do the Data Exploration on page 174
Have a class discussion of Section 3.2's "Summary" on page 190
Have a class discussion of the Chapter 3 Review on page 198
The College Board has posted tremendously helpful material
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
 Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html, for FR look for AP
Index 11_12.xls and for MC look for MC_Index.xls - Daren Starnes
Sample Formative Assessment Tasks
Skill-based task
 CHECK YOUR UNDERSTANDING (textbook pages 167, 171, 176, and 181)
 Use assessments at http://www.stats4stem.org/
 Use Quizzes at http://bcs.whfreeman.com/tps4e/#628644__630756__
 Do the Chapter 3 AP Statistics Practice Test on page 200


Use ARTIST SCALE - Bivariate Quantitative Data
http://ore.gen.umn.edu/artist/tests/index.html
Use Released Multiple Choice questions (see the last Suggested Instructional
Strategy above for a link to the list of MC questions) The column "% correct "
shows the global performance on the AP Exam for that question. Add a column to
the spreadsheet to keep a record of the questions you used and when used.
ers_corner/2151.html ] soon to be an AP community see
https://epl.collegeboard.org/epl/login.do
Problem Task
At the End of Unit 3 do FRAPPY #3 [which uses 2002 #4]:
http://apstatsmonkey.com/StatsMonkey/TPS3e_files/Frappy3.p
df (Or as an alternate, see the last Suggested Instructional Strategy
above for a list of free response questions that you could alternately
use as your FRAPPY. Go to
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for the FR questions. Look for the link AP Index 11_12.xls. Add a
column to the spreadsheet and keep a record of the questions you
used and when used.)
To Use Frappies: On the first page at
http://apstatsmonkey.com/StatsMonkey/FRAPPYs.html click on the
FRAPPY Presentation to learn about them and how to use them as
Formative Assessments. (Click on the Frappy Presentation to
Advance to a new slide. You may also download handout notes
using the link to the right)
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.