Examining Relationships
Main Goals:
1 graphically and numerically describe relation between 2 quantitative
variables
Stat 226 – Introduction to Business Statistics I
Spring 2009
Professor: Dr. Petrutza Caragea
Section A
Tuesdays and Thursdays 9:30-10:50 a.m.
2
Identify if one variable can help predict/explain another variable
variable associations
Two variables (measured on the same individual) are associated if certain
values of one variable tend to occur often with certain values of a second
variable.
Example:
Chapter 2
# of items sold on a given day and daily gross sales
Examining Relationships
height and weight of a person
assessed value and sale price of a home
In general, associations will not be exact — as there is always variation!
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Introduction to Business Statistics I
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Introduction to Business Statistics I
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Examining Relationships
We distinguish two types of variables:
response variable:
result or outcome of interest
often also called dependent variable
denoted using the letter y
Chapter 2.1 – Scatterplots
explanatory variable:
explains changes in the response variable
often also called independent variable
denoted using the letter x
Examples: explanatory variable (x)
Stat 226 (Spring 2009, Section A)
response variable y
Introduction to Business Statistics I
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Introduction to Business Statistics I
Chapter 2.1 – Scatterplots
Chapter 2.1 – Scatterplots
exploring relationships graphically
We can display the explanatory and the response variable in a so-called
scatterplot showing their relationship.
1100
explanatory variable ⇒ x-axis
25
1050
20
sat
Carbon Monoxide
1000
response variable ⇒ y -axis
950
900
850
180000
1200
800
160000
1000
750
Salary in
Thousands
salary
140000
120000
100000
80000
15
10
5
.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0
0
5
ltakers
800
10
15
20
25
30
TAR (in miiligrams)
600
400
200
60000
0
40000
0
5
10
15
20
25
30
35
Stat 226 (Spring 2009, Section A)
40
45
50
55
60
65
70
75
Age
years experience
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Chapter 2.1 – Scatterplots
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Introduction to Business Statistics I
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Chapter 2.1 – Scatterplots
Example: # number of radio ads aired/week and amount of sales (in
$1,000)
No. of ads x
2 5 8 8 10 12
Sales
y 2 4 7 6 9 10
FOUR features to look for in a scatterplot
1
Direction: positive or negative
positive association:
No. ads helps explain/predict sales
scatterplot:
y
negative association:
x
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Introduction to Business Statistics I
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Introduction to Business Statistics I
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Chapter 2.1 – Scatterplots
2
Chapter 2.1 – Scatterplots
Form:
linear (straight line)
3
Strength: strong vs. weak and moderate
4
Outliers:
curved
scattered
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Introduction to Business Statistics I
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Introduction to Business Statistics I
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