Chapter 2.2 – Correlation
Stat 226 – Introduction to Business Statistics I
Consider the the following two scenarios:
Spring 2009
Professor: Dr. Petrutza Caragea
Section A
Tuesdays and Thursdays 9:30-10:50 a.m.
Chapter 2, Section 2.2
both are
Question of interest: How strong exactly is the linear relationship
between x and y ?
Measuring the Strength of Linear
Relationships— Correlation
Introduction to Business Statistics I
Section 2.2
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Chapter 2.2 – Correlation
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
We can describe the strength of a linear relationship numerically by the
so-called correlation coefficient r :
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.5
1.0
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4.5
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ltakers
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Age
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Stat 226 (Spring 2009, Section A)
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Salary in
Thousands
salary
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TAR (in miiligrams)
income
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Defn: correlation r
is a numerical measure of the direction and strength of a linear
relationship between two quantitative variables.
120000
Section 2.2
Chapter 2.2 – Correlation
Carbon Monoxide
Stat 226 (Spring 2009, Section A)
and form is
, but strength is certainly different for both.
Introduction to Business Statistics I
Section 2.2
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Stat 226 (Spring 2009, Section A)
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expend
Introduction to Business Statistics I
Section 2.2
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Chapter 2.2 – Correlation
Chapter 2.2 – Correlation
How to compute r ?
We have n observations on two variables
x
y
2
2
5
4
8
7
8
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10
9
Fill
x
2
5
8
8
10
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sum
2
12
10
y
scatterplot:
x
1
Find the mean of x:
Stat 226 (Spring 2009, Section A)
in the following table
y
(x − x̄) (y − ȳ )
2
4
7
6
9
10
(x − x̄)2
(y − ȳ )2
(x − x̄)(y − ȳ )
and the mean of y:
Introduction to Business Statistics I
Section 2.2
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Chapter 2.2 – Correlation
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Section 2.2
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Chapter 2.2 – Correlation
What does the value of r mean? How do we interpret r ?
3
calculate standard deviations for x and y
4
the correlation coefficient is given by
1 !
(xi − x̄)(yi − ȳ )
r = n−1
sx ∗ sy
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Section 2.2
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Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Section 2.2
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Chapter 2.2 – Correlation
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Chapter 2.2 – Correlation
Section 2.2
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Chapter 2.2 – Correlation
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Section 2.2
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Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Section 2.2
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