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321_09_slides3

# 321_09_slides3 - Week 2 Review Econ 321 Introduction to...

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Week 2 Review Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1

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Outline Review of steps in statistical analysis: CLT Hypothesis testing Confidence Intervals Covariance/Correlation Simple regression Econ 321-Stéphanie Lluis 2
Central Limit Theorem Let Y 1 . .. Y n be a random sample with mean μ and variance σ 2 then : has an asymptotic standard normal distribution Econ 321-Stéphanie Lluis 3

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Central Limit Theorem Central Limit Theorem tells us that the means of samples of 30 or more observations are normally distributed around the population mean E(Y n ) = μ and V(Y n )= σ 2 /n, sd(Y n )= σ / Ѵ n Econ 321-Stéphanie Lluis 4
Central Limit Theorem We don’t know the mean and variance of a population, nor do we know the distribution. with the CLT, we can say something about the average from a random sample for any population We know its asymptotic distribution around the “true value” for large samples Econ 321-Stéphanie Lluis 5

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Example Let’s suppose we have an examination in which the mean score is 550 and the variance is 81. What is the probability that we draw a single exam with a score over 560? For a single observation sample: Econ 321-Stéphanie Lluis 6
Example Now suppose we take a sample of 25 exams Econ 321-Stéphanie Lluis 7 => The sample is much less likely to be “far” from the mean (to be over 560) than a single observation

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Estimation Use samples to estimate population characteristics Ex 1: The sample mean is an estimator of the population mean Ex: is an estimator of μ Ex 2: The OLS estimator of the effect b of variable x on variable y in a linear relationship (y=a + b*x + ε ) Econ 321-Stéphanie Lluis 8
Properties of Estimators Unbiased the estimator does not systematically over or undershoot the population parameter of interest systematically Consistent as the number of observations increases, the variability of our estimator decreases. Example: the variance of the sample mean falls at rate n

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321_09_slides3 - Week 2 Review Econ 321 Introduction to...

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