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Welcome to Econ 420 Applied Regression Analysis

This study guide covers topics such as sampling distribution, biased/unbiased estimator, best estimator, and the Gauss-Markov Theorem in applied regression analysis. It also includes Assignment 3 details.

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Welcome to Econ 420 Applied Regression Analysis

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  1. Welcome to Econ 420 Applied Regression Analysis Study Guide Week Three (continued) Ending Sunday, September 16 (Assignment 3 which is included in this study guide is due before Sunday at 10:00 PM)

  2. The Graded Assignment 2 will be send to you in a couple of days • Note • This is an applied class. That means that you will get a lot of assignments. • Be ready & don’t complain.

  3. Recap • Suppose the population of students at Marietta College = 1200 • The model is • Y = β0 + β1 X1 + β2 X2 + e • Y = GPA • X1 = hours of study • X2 = IQ score • We don’t see the true βs • We choose a sample of 50 students and estimate β^s • Are our β^s the same as true βs? • No • What if we chose another sample of 50 observations? • We will get different β^s • Most likely

  4. The sampling distribution of the estimated coefficients • Displays the values of all possible β^s that we can get if we draw an infinite number of samples from the population to estimate our equation using a given procedure. • If the error term is normally distributed  the estimated coefficients are normally distributed too

  5. So the distribution of β^s will be just like the Z distribution below.

  6. Biased/ Unbiased Estimator • Is a method of estimation which results in β^s that belong to a distributions whose means are equal to the true βs

  7. Best (most efficient) Estimator • Is a method of estimation whose β^s belong to distributions with the lowest possible variances.

  8. Consistent Estimator Is a method of estimation that results in β^s that get closer and closer to the true βs as the sample size is increased.

  9. The Gauss- Markov Theorem • Given assumptions 1 through 6, the OLS estimator is BLUE (Best Linear Unbiased Estimator)

  10. Important note on the meaning of the estimated slope coefficients • Suppose the estimated model is • Y^ = β^0 + β^1 X1 + β^2 X2 • β^1 measures the effect of 1 more unit of X1 on Y^, holding X2 constant and ignoring the effects of other relevant but omitted independent variables. • Key: you can only hold an independent variable constant if it is included in your model. If X3 is another relevant variable and it is excluded from your model, you can’t hold it constant.

  11. Assignment 3 • Has 40 points • It is due before Sunday, September 16, at 10:00 PM. • Send your answers to me as one (not multiple documents, please) email attachment. • Don’t forget to include your name on the assignment and on the subject of the email. • Answer Questions 5, 6, 8 and 13 on Pages 37 and 40.

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