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Statistical Techniques I
EXST7005
Other topics  Linear models and
Transformations
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View Full Document Course Progression
■
Objective  Hypothesis testing Background
➨
Transformation 
–
Many applications in statistics require modifyin
an existing distribution to a recognized statistic
distribution
–
Particularly, tests of hypotheses require taking
an observed distribution and transforming to a
recognized statistical distribution.
LINEAR MODELS
■
The simplest form of the linear additive model
➨
Yi =
μ
+
ε
i
for i=1, 2, 3,.
..,N
➨
This is a population version of the model, so
the term
μ
is a constant, the population mean
➨
The sample version would use
f8e5
Yi, which is a
variable.
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(continued)
■
Yi =
μ
+
ε
i
for i=1, 2, 3,.
..,N
➨
ε
i represents the deviations of the
observations from the mean. It has a mean o
zero since deviations sum to zero.
➨
ei would be used to represent sample
deviations,
➨
and or course N would be changed to n for a
sample.
■
Yi =
f8e5
Y + ei
for i=1, 2, 3,.
..,n
LINEAR MODELS
(continued)
■
This is a mathematical representation of a
population or sample.
All of the analyses
discussed in the Statistical Methods courses
have a linear model.
The models get more
complex as the analysis gets more advanced.
■
Multiplicative models and multiplicative errors
exist, but are not covered in basic statistical
methods.
NOTE THAT THE ERROR TERM IN
THIS MODEL IS ADDITIVE.
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(continued)
■
Other models we will discuss this semester
include
■
Yi =
μ
i +
ε
i
for ttests:
■
Yi =
μ
+
τ
i +
ε
i
for ANOVA, or another
form of the ttest
■
Yi =
β0
+
β1
Xi +
ε
i
Simple Linear
Regression
CODING and TRANSFORMATIONS
■
THEOREMS
➨
If a constant "a" is added to each observation
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.
 Fall '08
 Wang,J

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