Test1_Sol - Solutions to Test 1 Econ 3200 - Introduction to...

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Econ 3200 - Introduction to Econometrics Spring 2010 Cornell University Prof. Molinari Part I 20 points (4 points each) 1. R 2 : In a regression model, the proportion of the total sample variation in the dependent variable that is explained by the independent variable(s). In other words, the ratio of SSE to SST: R 2 close to 1 indicates a regression with a strong &t; R 2 close to zero indicates a In a simple linear regression model, R 2 is the squared sample correlation between Y and X: 2. Explained Sum of Squares: SSE = P n i =1 ^ Y Y ± 2 : This is a measure of the sample 1 n 1 SSE is the sample variance of ^ Y : 3. Mean Squared Error: The expected value of the square of the di/erence between an estimator, and the parameter it estimates. If ^ is an estimator of the parameter then MSE ^ ± = E ² ^ ± 2 ³ = V ar ^ ± + h Bias ^ ±i 2 : The MSE measures the e¢ ciency of an estimator, taking into account also its bias. 4. Interpreting the slope coe¢ cient of a linear regression: The slope parameter tells us the expected change in Y associated with a 1 unit increase in X: 5. Convergence in mean squared: A sequence of random variables X n converges in mean squared to X (which can be a random variable or a constant) if lim n !1 E h ( X n X ) 2 i = 0 : This means that as n ! 1 ; the realizations of X n become arbitrarily close to those of X . Con- vergence in mean squared implies convergence in probability, but the reverse is not true. 1
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This note was uploaded on 04/14/2010 for the course ECON 3200 taught by Professor Neilsen during the Spring '08 term at Cornell University (Engineering School).

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Test1_Sol - Solutions to Test 1 Econ 3200 - Introduction to...

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