Exam 4: Sample Exam for Chapters 8-10

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$$\begin{array} { l c c c c } \text { (a) Coefficient } & \beta _ { \mathrm { p } } & \beta _ { \mathrm { Y } } & \beta _ { \mathrm { A } } & \beta _ { \mathrm { R } } \\\text { Expected sign } & - & + & + & - \\\text { Calculated } t \text {-score } & - 4.0 & 5.0 & 3.0 & - 3.0 \\\text { Decision } & \text { reject } & \text { reject } & \text { reject } & \text { reject }\end{array}$$ (given a 1% critical t-score of 2.528)
In addition, the DW =1.86 is higher than the d_U of 1.77, so there is no evidence of positive serial correlation.
(b) There may be theoretically sound variables that have been omitted, for instance some measure of competition from foreign-made cars, but the results themselves give no indication of any problems.
(c) These results are clear indications of multicollinearity but not of heteroskedasticity.
(d) Unless a theoretically sound variable can be added measuring competition, the regression need not be changed at all.

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(a) See Section 9.1.
(b) See Section 8.1.
(c) See Section 8.3.
(d) See Section 9.4.
(e) The answer depends on whether you encourage your students to use one-sided or two-sided tests. For a one-sided test, the correct answer is that we can reject the null hypothesis of positive serial correlation. For a two-sided test, the correct answer is that the test is inconclusive.

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(a) Pure heteroskedasticity refers to a situation where the variance of the error term in a regression model is not constant across all levels of the independent variables. In other words, the variability of the errors is not the same for all observations.

(b) The consequences of pure heteroskedasticity include biased and inefficient estimates of the regression coefficients, leading to incorrect inferences about the significance of the independent variables. It can also result in inflated standard errors and unreliable hypothesis tests.

(c) Pure heteroskedasticity can be diagnosed through visual inspection of residual plots, such as a plot of the residuals against the predicted values or the independent variables. Statistical tests, such as the Breusch-Pagan test or the White test, can also be used to formally test for heteroskedasticity.

(d) To address pure heteroskedasticity, one can use heteroskedasticity-robust standard errors or weighted least squares estimation. Alternatively, transforming the dependent or independent variables, or using a different functional form for the model, may also help to mitigate the effects of heteroskedasticity. If the heteroskedasticity is severe, more advanced techniques such as generalized least squares or heteroskedasticity-consistent standard errors may be necessary.