Chapter 5Lesson 5.1a
Summarizing Bivariate Data
5.1a: Correlation
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Looking at Scatterplots
Scatterplots are the best way to start observingthe relationship and the ideal way to pictureassociations between two quantitative variables.
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Roles for Variables
It is important to determine which of the twoquantitative variables goes on the x-axis andwhich on the y-axis.
This determination is made based on the rolesplayed by the variables.
When the roles are clear, the explanatoryvariable goes on the x-axis, and the responsevariable goes on the y-axis.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Describing Scatterplots
When looking at scatterplots, we will look fordirection, form, strength, and unusual features.
1. Direction: Positive or Negative?
A pattern that runs from the upper left to thelower right is said to have a negative direction.
A trend running the other way has a positivedirection.
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1. Direction: Positive or Negative?
The graph shows apositive associationbetween the year since1900 and the % of peoplewho say they would votefor a woman president.
As the years have passed,the percentage who wouldvote for a woman hasincreased.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
1. Direction: Positive or Negative?
This graph shows anegative associationbetween peak periodfreeway speed and costper person of trafficdelays.
As the peak periodfreeway speed increases,the cost per person oftraffic delays decreases.
positivenegativenoIdentify as having a positive relationship,a negative relationship, or no relationship.
1.Heights of mothers and heights of theiradult daughters
++
2.Age of a car in years and its current value
3.Weight of a person and calories consumed
4.Height of a person and the person’s birthmonth
5.Number of hours spent in safety trainingand the number of accidents that occur
--
++
nono
--
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2. Form: Linear, Curved, or None?
If there is a straight line(linear) relationship, itwill appear as a cloudor swarm of pointsstretched out in agenerally consistent,straight form.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
2. Form: Linear, Curved, or None?
Form:
If the relationship isn’t straight, but curvesgently, while still increasing or decreasingsteadily,
we can often find ways to make it more nearlystraight.
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2. Form: Linear, Curved, or None?
Form:
If the relationship curves sharply,
the methods of this book cannot really help us.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
3. Strength: Weak, Moderate, or Strong?
Strength: Strong
At one extreme, the points appear to follow asingle stream
(whether straight, curved, or bending all overthe place).
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
3. Strength: Weak, Moderate, or Strong?
Strength: Weak
At the other extreme, the points appear as avague cloud with no discernable trend orpattern:
Note: we will quantify the amount of scattersoon.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Looking at Scatterplots (cont.)
Unusual features:
Look for the unexpected.
One example of such a surprise is an outlierstanding away from the overall pattern of thescatterplot.
Clusters or subgroups should also raisequestions.
Describe the Scatterplots: *D.U.F.S.*
Set A
Set B
Set C
Set A shows a strong, positivelinear relationship.
Set B shows little or norelationship.
Set C shows a weaker (moderate),negative linear relationship.
Set D
Set D shows astrong,positive curvedrelationship.
The Dating Habits of Celebrities
http://curvewire.com/posts/blog/math-nerds-track-dating-habits-stars
Activity: Create a Scatterplot
•Plot on the scatterplot (# hours studying, GPA)
Homework
Due after Lesson 5.1b
•Pg.232: #5.1-5.13
(skip 5.7, 5.8, 5.11)