Econ 399 Chapter6b

# Econ 399 Chapter6b - 6.4Prediction However,...

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6.4 Prediction -We have already seen how to make predictions about our dependent variable using our OLS estimates and values for our independent variables -However, these estimates are subject to sampling variation -a confidence interval is therefore often preferable to a point estimate

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6.4 Prediction -Assume we want to obtain the value of y (denoted by θ) given certain independent values x j =c j : ) ,..., , | ( (6.27) ... 2 2 1 1 2 2 1 1 0 k k k k c x c x c x y E c c c -since we don’t have actual values for B J , our estimator of θ becomes: (6.29) ˆ ... ˆ ˆ ˆ ˆ 2 2 1 1 0 k k c c c
6.4 Prediction -However, due to uncertainty, we may prefer a confidence interval estimate for θ: ) ˆ ( * ˆ se t CI -Since we don’t know the above standard error, similar to F tests we construct a new regression using the calculation: k k c c c ... 2 2 1 1 0

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6.4 Prediction -substituting this calculation into the population regression function gives us: (6.30) u ) ( ... ) ( ) ( 2 2 2 1 1 1 k k k c x c x c x y -In this regression, the intercept gives us the needed predicted value and intercept to construct our confidence interval -note that all our slope coefficients and their standard errors must be the same as the original regression
6.4 Prediction Notes 1) Note that the variance of this prediction will be smallest at the mean values of x j -This is due to the fact that we have

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