Estimated variance and covariance of the least

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Estimated variance and covariance of the Least Squared Estimators are: 2.7.1 Estimating the Variance and Covariance of the Least Squares Estimators 2.7 Estimating the Variance of the Error Term ² ³ ² ³ ² ³ ² ³ ² ³ ² ³ » » ¼ º « « ¬ ª ´ ´ ´ » » ¼ º « « ¬ ª ´ ¦ ¦ ¦ ¦ 2 2 ^ 2 2 2 2 ^ 2 2 2 2 ^ 1 ˆ , cov ˆ var ˆ var x x x b b x x b x x N x b i i i i V V V Principles of Econometrics, 4t h Edition Page 37 Chapter 2: The Simple Linear Regression Model The square roots of the estimated variances are the “standard errors” of b 1 and b 2 : 2.7 Estimating the Variance of the Error Term 2.7.1 Estimating the Variance and Covariance of the Least Squares Estimators Standard Errors of the Least Squares Estimators ² ³ ² ³ ² ³ ² ³ ^ 2 2 ^ 1 1 var se var se b b b b
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Principles of Econometrics, 4t h Edition Page 38 Chapter 2: The Simple Linear Regression Model The estimated variances and covariances for a regression are arrayed in a rectangular array, or matrix , with variances on the diagonal and covariances in the “off-diagonal” positions. ± ± ± ± 1 1 2 1 2 2 var( ) cov( , ) cov( , ) var( ) b b b b b b ª º « » « » ¬ ¼ 2.7 Estimating the Variance of the Error Term 2.7.2 Calculations for the Food Expenditure Data Principles of Econometrics, 4t h Edition Page 39 Chapter 2: The Simple Linear Regression Model For the food expenditure data the estimated covariance matrix is: 2.7.2 Calculations for the Food Expenditure Data C Income C 1884.442 -85.90316 Income -85.90316 4.381752 2.7 Estimating the Variance of the Error Term
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