# Syll0910 - EC220 Syllabus 2009/2010 This syllabus is...

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EC220 Syllabus 2009/2010 This syllabus is intended to provide an explicit list of all the mathematical formulae and proofs that you are expected to know for the examination. You are warned that a knowledge of the formulae and proofs is taken for granted in the examination and that relatively little credit is given for it in the marking scheme. The examination is intended to be an opportunity for you to display your understanding of the material, rather than to reproduce standard items. Review: Random variables and sampling theory Probability distribution of a random variable. Expected value of a random variable. Expected value of a function of a random variable. Population variance of a discrete random variable and alternative expression for it. Expected value rules. Independence of two random variables. Population covariance, covariance and variance rules, and correlation. Sampling and estimators. Unbiasedness. Efficiency. Loss functions and mean square error. Estimators of variance, covariance and correlation. Probability limits and their rules. Consistency. The central limit theorem. Formulae and proofs : This chapter is concerned with statistics, not econometrics, and is not examinable. However you are expected to know the results in this chapter and to be able to use them. Chapter 1 Simple regression analysis Simple regression model. Derivation of linear regression coefficients. Interpretation of a regression equation. Goodness of fit. Formulae and proofs : You are expected to know, and be able to derive, the expressions for the regression coefficients in a simple regression model, including variations where either the intercept or the slope coefficient may be assumed to be zero. You are expected to know the definition of R 2 and how it is related to the residual sum of squares. You are expected to know the relationship between R 2 and the correlation between the actual and fitted values of the dependent variable, but not to be able to prove it. Chapter 2 Properties of the regression coefficients Types of data and regression model. Assumptions for Model A. Regression coefficients as random variables. Unbiasedness of the regression coefficients. Precision of the regression coefficients. Gauss– Markov theorem. t test of a hypothesis relating to a regression coefficient. Type I error and Type II error. Confidence intervals. One-sided tests. F test of goodness of fit. Formulae and proofs : You are expected to know the regression model assumptions for Model A. You are expected to know, though not be able to prove, that, in the case of a simple regression model, an F test on the goodness of fit is equivalent to a two-sided t test on the slope coefficient. You are expected to know how to make a theoretical decomposition of an estimator and hence how to investigate whether or not it is biased. In particular, you are expected to be able to show that the OLS estimator of the slope coefficient in a simple regression model can be decomposed into the true value plus a weighted linear combination of the values of the disturbance term in the sample.

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