04Transformations

# 04Transformations - Statistical Techniques I EXST7005 Other...

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Statistical Techniques I EXST7005 Other topics - Linear models and Transformations

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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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LINEAR MODELS (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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LINEAR MODELS (continued) Other models we will discuss this semester include Yi = μ i + ε i for t-tests: Yi = μ + τ i + ε i for ANOVA, or another form of the t-test 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.

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04Transformations - Statistical Techniques I EXST7005 Other...

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