Equivalently it is called a 1001 \u03b1 confidence interval Usually \u03b1 001 or \u03b1 005

# Equivalently it is called a 1001 α confidence

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Equivalently it is called a 100(1- α )% confidence interval. Usually α = 0.01 or α = 0.05, so that we obtain a 99% confidence interval or a 95% confidence interval. 3.1 Interval Estimation 3.1.2 Obtaining Interval Estimates Principles of Econometrics, 4t h Edition Page 49 Chapter 1: An Introduction to Econometrics The interpretation of confidence intervals requires a great deal of care The properties of the interval estimation procedure are based on the notion of repeated sampling Any one interval estimate, based on one sample of data, may or may not contain the true parameter β k , and because β k is unknown, we will never know whether it does or does not When ‘‘confidence intervals’’ are discussed, remember that our confidence is in the procedure used to construct the interval estimate; it is not in any one interval estimate calculated from a sample of data 3.1 Interval Estimation 3.1.2 Obtaining Interval Estimates Principles of Econometrics, 4t h Edition Page 50 Chapter 1: An Introduction to Econometrics For the food expenditure data The critical value t c = 2.024, which is appropriate for = .05 and 38 degrees of freedom To construct an interval estimate for 2 we use the least squares estimate b 2 = 10.21 and its standard error 3.1.3 An Illustration 95 . 0 024 . 2 024 . 2 2 2 2 2 2 b se b b se b P Eq. 3.6 09 . 2 38 . 4 r a ˆ v 2 2 b b se 3.1 Interval Estimation 