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Unformatted text preview: Confidence Intervals for Multiple Regressions Testing Hypothesis about Individual Partial Regression Coefficients Testing Joint Hypo Chapter 5 Chapter 5: Confidence Interval Estimation and Hypothesis Testing Lecture 3 Masao Ogaki Department of Economics, Ohio State University October 24, 2007 Masao Ogaki Department of Economics, Ohio State University Chapter 5 Chapter 5: Confidence Interval Estimation and Hypothesis Testing Lecture 3 Confidence Intervals for Multiple Regressions Testing Hypothesis about Individual Partial Regression Coefficients Testing Joint Hypo Confidence Intervals for Multiple Regressions In multiple regressions ( K > 1), the standard errors for the OLS estimators are calculated by computer programs from appropriate formulas. We denote them by SE ( ˆ β 1 ) , SE ( ˆ β 2 ) , etc. For the Kvariable regression model, we use t = ˆ β k β k SE ( ˆ β k ) (1) which is distributed as the tdistribution with ( N K ) degrees of freedom for k=1,2,...,K. Masao Ogaki Department of Economics, Ohio State University Chapter 5 Chapter 5: Confidence Interval Estimation and Hypothesis Testing Lecture 3 Confidence Intervals for Multiple Regressions Testing Hypothesis about Individual Partial Regression Coefficients Testing Joint Hypo To form a confidence interval, we first choose the confidence level, say 0.95, and find the t C value such that P [ ˆ β k t C SE ( ˆ β k ) ≤ β k ≤ ˆ β k + t C SE ( ˆ β k )] = 1 . 95 . (2) To see how this works, let us consider an example. Imagine that demand for coffee is regressed on the price of coffee and the price of tea. The regression results are Masao Ogaki Department of Economics, Ohio State University...
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 Fall '07
 OGAKI
 Statistics, Econometrics, Statistical hypothesis testing, Department of Economics, Ohio State University, Masao Ogaki

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