GRA 6020 Multivariate Statistics Regression examples - PowerPoint PPT Presentation

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GRA 6020 Multivariate Statistics Regression examples

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Title: Making Sense/ Making Numbers/ Making Significance Author: BI User Last modified by: default Created Date: 6/3/2003 6:09:32 PM Document presentation format – PowerPoint PPT presentation

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Title: GRA 6020 Multivariate Statistics Regression examples


1
GRA 6020Multivariate StatisticsRegression
examples
  • Ulf H. Olsson
  • Professor of Statistics

2
Regression Analysis
3
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

4
GAUSS-MARKOV
  • OLS is BLUE given the Classical Assumptions
  • B Best
  • LLinear
  • UUnbiased
  • EEstimator

5
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

6
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

7
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)

8
Kleins equations
9
Factor Analysis
  • Data Reduction
  • Common Factor
  • Latent variable
  • Factor Loading
  • How many factors
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