GRA 6020 Multivariate Statistics Regression examples

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GRA 6020Multivariate StatisticsRegression
examples

• Ulf H. Olsson
• Professor of Statistics

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Regression Analysis
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Classical Assumptions

• Y is stochastic, x1, x2,.,xk are not
• Linearity in the parameters
• The error term has const.variance
• The error term is norm. Distributed with
  expectation equal to zero

• The error terms are independent
• The x-variables are linearly independent

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GAUSS-MARKOV

• OLS is BLUE given the Classical Assumptions
• B Best
• LLinear
• UUnbiased
• EEstimator

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Regression Analysis

• The error term has constant variance
• The error term follows a normal distribution with
  expectation equal to zero

• The x-variables are independent of the error term
• The x-variables are linearly independent

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TSLS

• If the error term is correlated with one or more
  of the independent variables The OLS estimate is
  not consitent, i.e., it is biased even in large
  samples.
• If there are instrument variables, that are not
  correlated with the error term The TSLS
  estimator can be used to estimate the Betas
  consistently.
• The TSLS is a two-step OLS procedure
• For every x-variable which is correlated with the
  error term there must be at least one instrument
  variable outside the set of x-variables

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TSLS and Heteroscedasticity

• Heteroscedastic Errors
• There are many forms of heteroscedasticity
• The most common is on the form
• TSLS might be a better alternative if the error
  term is heteroscedastic (asymptotically)

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Kleins equations
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Factor Analysis

• Data Reduction
• Common Factor
• Latent variable
• Factor Loading
• How many factors