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5/10/10
Lecture 34/35
Section 201 M/W/F
10:0011:00
COMM 291
Applications of Statistics in
1
1
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Summary of Multiple Regression
2
2
Parameter
Significance
Sum of Squared Residuals
Larger
SSE
= “noisier” data and less precise
prediction
Regression Sum of Squares
Larger
SSR
= stronger model correlation
Total Sum of Squares
Larger
SST
= larger variability in
y
, due to
“noisier” data (
SSE
) and/or stronger model
correlation (
SSR
)
2
SSE
e
=
( 29
2
SST
y
y
or
SST
SSR SSE
=

=
+
( 29
2
ˆ
SSR
y
y
=

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Relationship between
F
and
R
2
3
3
R
2 in Multiple Regression:
R
2 =
fraction of the total variation in
y
accounted for by the model (all the
predictor variables included)
2
1
SSR
SSE
R
SST
SST
=
= 
F
and
R
2:
By using the expressions for
SSE
,
SSR
,
SST
, and
R
2, it
can be shown that:
So,
testing whether
F
= 0 is equivalent to testing
whether
R
2 = 0
.
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R
2 and Adjusted
R
2
4
4
§
Adding new predictor variables to a model
never decreases
R
2 and may increase it.
§
But each added variable increases the model
complexity
, which may not be desirable.
§
Adjusted
R
2
imposes a “penalty” on the
correlation strength of larger models,
depreciating their
R
2 values to account for an
undesired increase in complexity:
( 29
2
2
1
1
1
1
adj
n
R
R
n k

= 

 
Adjusted
R
2 permits a more equitable comparison
between models of different sizes.
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Chapter 23
5
5
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Observational Studies
A statistical study is
observational
when it is
conducted using preexisting data 
collected without any particular design.
Example
: Many companies collect a variety
of data via registration or warranty cards.
This data might be utilized later in some
observational study that seeks to discover
correlations between the collected data.
An observational study is
retrospective
if it
studies an outcome in the present by
examining historical records.
6
6
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An observational study is
prospective
if it
seeks to identify subjects in advance and
collects data as events unfold.
Example
: Follow a sample of smokers and
runners to discover the occurrence of
emphysema.
An
experiment
is a study in which the
experimenter
manipulates
attributes of the
study participants and observes the
consequences.
The attributes, called
factors
, are
7
7
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The Four Principles of
1)
Control. We control sources of variation
other than the factors we are testing by
making conditions as similar as possible for
all treatment groups.
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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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