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Lecture3 - Lecture 3 Review of Statistics Ordinary Least...

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Lecture 3 : Review of Statistics & Ordinary Least Square(OLS) Econ 444, Winter 2010 Jan 13, 2010
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6. Statistical Inference Problem : The true probability distribution of the population understudy is characterized by unknown parameters like mean ( E ( X )) , variance(Var(X)) etc. Solution : We use a sample and compute the sample estimates X , s 2 X etc. Since we use only one sample to get estimates for the true population parameters like mean, variance and correlation how do we ensure reliability of our estimates? We exploit the fact that our sample estimates or statistics are simply a function of the sample we used.
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6. Statistical Inference Sampling Distribution : The sample estimates or statistics like X are a function of the sample used to compute them. For example : Suppose we use data on test scores of Econ 444 students at OSU and compute the sample mean X = 72 . Now we use sample of say Cornell university we may find that the sample mean for E444 is 65. Similarly the sample mean will be different for Michigan State E444 students and so on. If we repeat this process many times we will end up with a distribution of sample mean scores , X in E444. This distribution is called sampling distribution of X . This distribution will have a mean, E ( X ) and a variance, Var ( X ) .
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6. Statistical Inference Using the above properties of the sampling distribution we can establish the validity of our sample estimates and also compare between various estimators to choose the ‘best’ estimator. (For the sake of exposition let us work with sample mean X .
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