M21- Scatterplot

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Lesson Objectives

• Learn to visually assess the relationship
  between two quantitative variables.
• Understand scatterplots.
• Understand linear relationships.

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Analyzing the relationshipbetween two variables
Is one variable influenced by or related to a
second variable?
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Y X

• Test Score Hrs. Studied
• MPG Weight of car
• Time of trip

______________
Key Question As X changes, does the mean
of Y also change?
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Case

• One individual person, animal, or object for
  which values of two or more variables are
  recorded.
• If population is Honda vehicles,
  variables could be
• Model, Age, Owners MPG, Weight, Color,
  Current value, Original cost,
• Variables can be quantitative or categorical.

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Response variable (Y), a.k.a., Dependent var.
Population Honda vehicles.

• The main variable of interest Owners
  Actual Miles per gallon
• Explanatory variable (X)
• a.k.a., independent var. A helper variable
  used to improve the estimate of the mean of the
  response variable

Age, Weight, horsepower, etc.
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Scatterplot
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What criteria were usedto make the statements
given in the previous three examples?

• Does a _______________________________________ten
  d to run through the pattern of data points?
• Are the points __________________________________
  ________________________________________ ?

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Scatterplot

• Best graphical tool for examining the
  relationship between two quantitative variables.
• Helps to identify
• _______________________________________________
  ____
• _______________________________________________
  ____

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Recall Boxplots

• Best graphical tool for examining the
  relationship between a quantitative variable and
  a categorical variable,(i.e., comparing
  distributions).

Example Weight vs. Country of Origin
Boxplot can be used to answer
Do the distributions of weights vary for
different countries of origin?
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Example 4
5th Grade Class Data
Height Weight Boy/Girl Height Weight Boy/Girl
60 85 Girl 57 92 Boy 56 88 Boy 57 65 Girl 54 71
Girl 59 98 Boy 63 90 Girl 57 95 Boy
54 65 Girl 57 76 Boy 54 64 Girl 56 65 Girl
60 79 Girl 57 95 Boy 57 90 Boy 62 100 Boy
60 79 Girl 60 89 Girl
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Example 4
Scatterplot of Weight vs. Height




Ht Wt 60 85 56 88 54 71 63 90 ... ...














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Example 4
Scatterplot of Weight vs. Height


Girls line





q
Boys line,w/o point.
q
q

q
q

q
Boy
q
q
q
q
Girl
q
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Example 5
Weight vs. Height for ST 260 Students
300
Wt(lb)


260










220





















































180



































































































140














































































100



50
60
70
80
Height (inches)
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Example 6
Y
________________Linear Relationship
X
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Example 7
Y
________________ Linear Relationship
X
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Example 8
Y
________________ Relationship!
Does thisline fit the datawell?
X
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Example 9
Y
_______ linear Relationship
X