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5/10/10
Lecture 28
Section 201 M/W/F
10:0011:00
COMM 291
Applications of Statistics in
1
1
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The Population and the Sample
2
2
§
Chapter 8: We can model relationships by fitting a
straight line to a
sample
of ordered pairs.
§
But,
observation
s
differ
from sample to sample:
0
1
ˆ
y
b
b x
=
+
1
0,1
1,1
2
0,2
2
1,2
1
ˆ
sample 1
ˆ
sam
ˆ
ˆ
Lines
and
are not necessarily the same
ple
.
2
y
b
b x
y
y
b
b x
y
=
+
=
+
5/10/10
The Population and the Sample
3
3
§
We can imagine a
true line
that summarizes the
relationship between
x
and
y
for the
entire population
,
where l
y
is the
population mean
of
y
at a given
value of
x
.
NOTE: We are assuming an idealized case in which the
points (
x
,
y
) are in fact
exactly linear
.
0
1
y
x
μ
β
=
+
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The Population and the Sample
4
4
§
For a given value
x
:
§
The value
ŷ
(
x
)
obtained from a particular
sample may not lie on the line
µy
.
§
The sampled
ŷ
’
s will be
distributed about
µy
.
§
We can account for the error between
ŷ
and
µy
by adding the error l :
0
1
y
x
β
ε
=
+
+
5/10/10
The Population and the Sample
5
5
§
Regression Inference
§
Collect a sample and
estimate the population
o ’s
by finding a regression line (Chapter 8):
§
The residuals
e = y – ŷ
are the sample
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This note was uploaded on 04/29/2010 for the course COMM 291 taught by Professor E.fowler during the Spring '10 term at The University of British Columbia.
 Spring '10
 E.Fowler

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