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GRA 6020 Multivariate Statistics Regression examples Ulf H. Olsson Professor of Statistics
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Ulf H. Olsson Regression Analysis
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Ulf H. Olsson 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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Ulf H. Olsson GAUSS-MARKOV OLS is BLUE given the Classical Assumptions B = Best L=Linear U=Unbiased E=Estimator
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Ulf H. Olsson 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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Ulf H. Olsson 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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Ulf H. Olsson 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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Ulf H. Olsson Klein’s equations
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Ulf H. Olsson Factor Analysis Data Reduction Common Factor Latent variable Factor Loading How many factors
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