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The Practice of Statistics, 5 th Edition 1 How Faithful is the Old Faithful?
The Practice of Statistics, 5th Edition 1
How Faithful is the
Old Faithful?
The Practice of Statistics, 5th Edition 2
Who Has Been Eating My Cookies?????????
• Someone has been steeling the cookie
I bought for your class
• A teacher from the highschool department?
• SCI stats team: help me identify the prime
suspect in “the case of the missing cookie”
The Practice of Statistics, 5th Edition 3
The Practice of Statistics, 5th Edition 4
Activity: CSI Stats
“The Case of the Missing Cookies”
• Collect Height and Hand Span of each member of your group in cm
We are going to use the Hand Print span information to predict the prime’s suspect height
• Record data on the table (hand span (cm) vs height cm)
• Make a graph with the class data on to a group white board. Example below:
Describe what you see:
What does the graph tell you about the relationship?
Summarize your observations in a sentence or two.
???Which highschool teacher is believed to be the
“prime suspect?
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates, Moore
Bedford Freeman Worth Publishers
CHAPTER 3 Describing Relationships 3.1
Scatterplots and Correlation
The Practice of Statistics, 5th Edition 6
Scatterplots and Correlation – Learning Objectives
Define Explanatory and Response variables in situations where one
variable helps to explain or influences the other
Make a scatterplot to display the relationship between two quantitative
variables.
Describe the direction, form, and strength of a relationship displayed in
a scatterplot and identify outliers in a scatterplot.
Interpret the correlation.
Understand the basic properties of correlation, including the influence of
outliers on the correlation
Use technology to calculate correlation.
Explain why association does not imply causation.
The Practice of Statistics, 5th Edition 7
Explanatory and Response Variables
Most statistical studies examine data on more than one variable. In
many of these settings, the two variables play different roles.
• In the case of The Missing Cookie?
A response variable measures an outcome of a study.
An explanatory variable may help explain or influence
changes in a response variable.
The Practice of Statistics, 5th Edition 8
Example1. : Weight and Height Tim wants to know if there is a relationship between height and weight. Kelly
wants to know if she can predict a student’s weight from his or her height.
Information about height is easier to obtain than information about weight!
Problem: For each student, identify the explanatory and response variables, if
possible.
Ex 2: Linking SAT Math and Critical Reading Scores
The Practice of Statistics, 5th Edition 9
The Practice of Statistics, 5th Edition 10
Scatterplots and How to Make them
Scatterplot:
Relationship between quantitative variables on the same individual
Explanatory variable on the x-axis, and response on the y-axis
Each individual data appears as a dot on the graph
1. Decide which variable should go on each axis.
• Remember, the EXplanatory variable goes on the X-axis!
2. Label and scale your axes.
3. Plot individual data values.
How to Make a Scatterplot
The Practice of Statistics, 5th Edition 11
Track and Field Day
Each member of a small statistics class ran a 40-yard sprint and then
did a long jump (with a running start). The table below shows the sprint
time (in seconds) and the long-jump distance (in inches)
Problem: Make a scatterplot of the relationship between the sprint time
and long-jump distance.
Describe what you see.
Sprint time (s) 5.41 5.05 7.01 7.17 6.73 5.68 5.78 6.31 6.44 6.50 6.80 7.25 Long-jump distance (in) 171 184 90 65 78 130 173 143 92 139 120 110
The Practice of Statistics, 5th Edition 12
Describing Scatterplots
To describe a scatterplot, follow the basic strategy of data analysis from
Chapters 1 and 2. Look for patterns and important departures from
those patterns.
As in any graph of data, look for the overall pattern and for
striking departures from that pattern.
• You can describe the overall pattern of a scatterplot by the
direction, form, and strength of the relationship.
• An important kind of departure is an outlier, an individual
value that falls outside the overall pattern of the relationship.
How to Examine a Scatterplot
DOFS!!!!
The Practice of Statistics, 5th Edition 13
Describing Scatterplots
Two variables have a :
• positive association when above-average values of one tend to
accompany above-average values of the other and when below-
average values also tend to occur together.
• negative association when above-average values of one tend to
accompany below-average values of the other.
Describe the scatterplot.
Direction
Form
Strength
There is a moderately strong,
negative, curved relationship between
the percent of students in a state who
take the SAT and the mean SAT math
score.
Further, there are two distinct clusters
of states and two possible outliers that
fall outside the overall pattern.
The Practice of Statistics, 5th Edition 14
Example: Describing a scatterplot
Form: There seems to be a linear pattern in the graph (that is, the overall
pattern follows a straight line).
Strength: Because the points do not vary much from the linear pattern,
the relationship is fairly strong. There do not appear to be any values that
depart from the linear pattern, so there are no outliers.
Direction: In general, it appears that
teams that score more points per
game have more wins and teams
that score fewer points per game
have fewer wins. We say that there
is a positive association between
points per game and wins.
The Practice of Statistics, 5th Edition 15
1. Describe the Track and Field Day Scatterplot
2.
The Practice of Statistics, 5th Edition 16
In Class-Work and Homework
• Hand back the Quiz
• Time Permitting: “Religions and Babies”
http://www.ted.com/talks/hans_rosling_religions_and_babies
Scatterplot that relates Income and Babies per Woman
• Calculator Activity Scatterplots on the calculator
• Homework: page 159 #1-13 ALL
• Quiz Next Class (please come see me if you have any questions!!!)
