# L3 - Econ 102B Introduction to Econometrics Winter 2011...

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Econ 102B Introduction to Econometrics Winter 2011 Simple Linear Regression Model II Testing, Predicting and Modeling Matt Harding Stanford University mch@stanford.edu 1

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Agenda for today (01/11/11) Hypothesis Testing Making Predictions Goodness of Fit Other Modeling Issues 2
Last time … 3

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Food consumption 4
Figure 2.8 The fitted regression line 5

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How precise are our estimates?
2.4.3 Repeated Sampling: estimators are random variables!

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2.4.1 The estimator b 2 (2.10) (2.11) (2.12)
2.4.2 The Expected Values of b 1 and b 2 We will show that if our model assumptions hold, then , which means that the estimator is unbiased . We can find the expected value of b 2 using the fact that the expected value of a sum is the sum of expected values (2.13)

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2.4.4 The Variances and Covariances of b 1 and b 2 If the regression model assumptions SR1-SR5 are correct (assumption SR6 is not required), then the variances and covariance of b 1 and b 2 are: (2.14) (2.15) (2.16)
2.4.4 The Variances and Covariances of b 1 and b 2 The larger the variance term , the greater the uncertainty there is in the statistical model, and the larger the variances and covariance of the least squares estimators. The larger the sum of squares, , the smaller the variances of the least squares estimators and the more precisely we can estimate the unknown parameters. The larger the sample size N , the smaller the variances and covariance of the least squares estimators. The larger this term is, the larger the variance of the least squares estimator b 1 . The absolute magnitude of the covariance increases the larger in magnitude is the sample mean , and the covariance has a sign opposite to that of .

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Gauss-Markov Theorem