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LIR832 Final Exam Answer Key Fall 2003

# LIR832 Final Exam Answer Key Fall 2003 - 1 Which of these...

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1. Which of these equations is it possible to estimate using regression techniques? a.) Y i = β 0 + β 1 X 1i + β 2 X 2i + ε This equation is already in a form interpreted to be capable of estimating through standard regression techniques. See equation (1.12) in the Studenmund book – this is the definition of a multivariate regression model with two explanatory variables. b.) Y i = e β 0+ β 1X1i+ ε i This equation is capable of being transformed into a something a little more familiar: First, take the log of both sides: ln Y i = ln e β 0+ β 1X1i+ ε I Using the properties of logs given in Chapter 7 of Studenmund: ln Y i = ( β 0 + β 1 X 1i + ε i )*ln e Since the ln e = 1, we then have: ln Y i = β 0 + β 1 X 1i + ε I, which is just the standard semilog equation from Chapter 7. c.) Y i = β 0 X 1i β1 X 2i β2 e ε I Again, this equation can be transformed into something more useful by taking the log of both sides: ln Y i = ln ( β 0 X 1i β1 X 2i β2 e ε I ) Using the properties of logs given on the bottom of page 205, we can rewrite the right-side as: ln Y i = ln β 0 + ln X 1i β1 + ln X 2i β2 + ln e ε I Using the exponent rule of logs also listed on page 205, we can rewrite it as: ln Y i = ln β 0 + β 1 ln X 1i + β 2 ln X 2i + ε i ln e And since ln e = 1, we have:

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ln Y i = ln β 0 + β 1 ln X 1i + β 2 ln X 2i + ε I , which is just the double-log form listed in Chapter 7 (ln β 0 is still just a constant). d.) Y i = β 0 + X 1i β1 + X 2i β2 + e ε I This model is not able to be estimated by any regression techniques, as the coefficients in the exponent of addition terms prohibit it from being estimated. Even if one tries to take the log of both sides of the model, it would get them no where in advancing this model as something capable of being estimated. e.) Y i = β 0 + β 1 (1/X 1i ) + β 2 X 2i + ε i If you look at equation (7.13) from Studenmund, this model is the standard Inverse Form equation given. It is quite capable of being estimated, with the values of the coefficients described in pages 211-212. 2) We are interested in the effect of the presence of various benefit programs on employee views of their boss…. A) Interpret the impact of each factor on job satisfaction and test the null. Critical t-values: Two tailed one tailed 10% - 1.645 1.282 5% - 1.960 1.645 1% - 2.576 2.32 Note that all the hypothesis tests except the test for the coefficient on female have a positive alternative hypothesis and a null of less than or equal to zero. The test for female is two tailed.
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