STATWAY STUDENT HANDOUT | 2

Lesson 3.1.2

Developing an Intuitive Sense of Form, Direction,
and Strength of the Relationship Between Two Measurements

STATWAY™ STUDENT HANDOUT

Lesson 3.1.2

Developing an Intuitive Sense of Form, Direction,
and Strength of the Relationship Between Two Measurements

STUDENT NAME / DATE

INTRODUCTION

In this lesson, you will compare and contrast a variety of scatterplots with the goal of thinking about how to describe relationships you see in the data. At the end of the lesson, you will discuss ways that statisticians describe these relationships.

Try These

1 Match each description for a set of measurements (A and B) to a scatterplot, and briefly explain your reasoning.

Scatterplot 1 Scatterplot 2

A x = city miles per gallons and y = highway miles per gallon for 10 cars

i. What does a dot represent?

B x = sodium (milligrams/serving) and y = Consumer Reports quality rating for 10 salted peanut butters

i What does a dot represent?

2 These scatterplots show body measurements for 34 adults who are physically active. Some measurements are a girth, which is a measure of length around a body part. Match each description (A, B, and C) to a scatterplot. Briefly explain your reasoning.

Scatterplot 1 Scatterplot 2 Scatterplot 3

A x = forearm girth (centimeters), y = bicep girth (cm). The bicep is above the elbow.

i What does a dot represent?

B x = calf girth (cm), y = bicep girth (cm). The calf is below the knee.

i What does a dot represent?

C x = age (years), y = bicep girth (cm)

i What does a dot represent?

3 Match each description of a set of measurements (A to F) to a scatterplot. Briefly explain your reasoning.

Scatterplot 1 Scatterplot 2 Scatterplot 3

Scatterplot 4 Scatterplot 5 Scatterplot 6

A x = month number (January = 1) and y = rainfall (inches) in Napa, California. Napa has several months of drought each summer.

i What does each dot represent?

B x = month number (January = 1) and y = average temperature in Boston, Massachusetts. Boston has cold winters and hot summers.

i What does each dot represent?

C x = year (from 1970) in five-year increments and y = Medicare expenditures ($). The yearly increase in Medicare costs has been getting bigger over time.

i What does each dot represent?

D x = average temperature (°C) each month and y = average temperature (°F) each month in San Francisco, California.

i What does each dot represent?

E x = chest girth (cm) and y = shoulder girth (cm) for a sample of men

i What does each dot represent?

F x = engine displacement (in liters) and y = city miles per gallon for a sample of cars. Engine displacement is roughly a measurement of the size of the engine. Larger engines use more gas.

i What does each dot represent?

Take It Home

1  Match each description of a set of measurements (A, B, and C) to a scatterplot. Then describe what a dot represents in each graph.

A x = average outdoor temperature and y = heating costs for a residence for 10 winter days

B x = height (inches) and y = shoe size for 10 adults

C x = height (inches) and y = score on an intelligence test for 10 teenagers

2 Lines have been added to some of the scatterplots used in the Lesson 3.1.1 to summarize the relationship between the ingredient and the Consumer Reports rating for breakfast cereals. You will learn more about summary lines in future lessons.

A Which ingredients (sugar, protein, and/or fat) are negatively associated with ratings?

B Which is more strongly associated with ratings: sugar or fat?

C How is the idea of strength related to whether an ingredient is a good predictor of ratings?

3 Suppose you gathered the following information from students at a local high school:

§  GPA (grade point average),

§  Average weekly hours spent working at a job,

§  Average weekly hours spent doing homework,

§  Average hours of sleep a night,

§  Hourly wage,

§  Height,

§  Weight,

§  Length of the left foot,

§  Age of the oldest child in the student’s immediate family,

§  Number of children in the student’s immediate family,

§  Gender,

§  Race, and

§  Age.

A From this list of variables, choose:

i Two of these variables that you think will show a positive linear association,


ii Two of these variables you think will show a negative linear association, and


iii Two of these variables you think will not show an association in a scatterplot.


You may use the same variable for more than one comparison.
Briefly explain your reasoning for each pair.

B Sketch a scatterplot with 12 students to illustrate each of the three relationships described in part A. You will have three scatterplots showing imaginary data to illustrate the association. If there is an association, sketch a line to highlight the association. For each scatterplot, label the axes of each graph with the name of the variable. Scale the graph with realistic numbers for the variable.

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This lesson is part of STATWAY™, A Pathway Through College Statistics, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. Version 1.0, A Pathway Through Statistics, Statway™ was created by the Charles A. Dana Center at the University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version 1.5 and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is an open-resource research and development community that seeks
to harvest the wisdom of its diverse participants in systematic and disciplined inquiries to improve developmental mathematics instruction. For more information on the Statway Networked Improvement Community, please visit carnegiefoundation.org. For the most recent version of instructional materials, visit Statway.org/kernel.

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A Pathway through statistics, version 1.5, STATWAY™ - STUDENT HANDOUT