Consider the multiple regression model with the seven observations on (y_{i}, x_{i 1}, x_{i 2}), and (x_{i

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Consider the multiple regression model

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with the seven observations on \(y_{i}, x_{i 1}, x_{i 2}\), and \(x_{i 3}\) given in Table 5.5.

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Use a hand calculator or spreadsheet to answer the following questions:

a. Calculate the observations in terms of deviations from their means. That is, find \(x_{i 2}^{*}=x_{i 2}-\bar{x}_{2}\), \(x_{i 3}^{*}=x_{i 3}-\bar{x}_{3}\), and \(y_{i}^{*}=y_{i}-\bar{y}\).

b. Calculate \(\sum y_{i}^{*} x_{i 2}^{*}, \sum x_{i 2}^{* 2}, \sum y_{i}^{*} x_{i 3}^{*}, \sum x_{i 2}^{*} x_{i 3}^{*}\), and \(\sum x_{i 3}^{* 2}\).

c. Use the expressions in Appendix \(5 \mathrm{~A}\) to find least squares estimates \(b_{1}, b_{2}\), and \(b_{3}\).

d. Find the least squares residuals \(\hat{e}_{1}, \hat{e}_{2}, \ldots, \hat{e}_{7}\).

e. Find the variance estimate \(\hat{\sigma}^{2}\).

f. Find the sample correlation between \(x_{2}\) and \(x_{3}\).

g. Find the standard error for \(b_{2}\).

h. Find \(S S E, S S T, S S R\), and \(R^{2}\).

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Principles Of Econometrics

ISBN: 9781118452271

5th Edition

Authors: R Carter Hill, William E Griffiths, Guay C Lim

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