Q53. Rains asks his students to test the null hypothesis that states for every new well drilled, profits will be increased by the given multiple of the coefficient, all other factors remaining constant. The appropriate hypotheses for this two-tailed test can best be stated as:

A)   H₀: b₁ ≤ 0.98 versus H_a: b₁ > 0.98.

B)   H₀: b₁ = 0.98 versus H_a: b₁ ≠ 0.98.

C)   H₀: b₁ = 0.35 versus H_a: b₁ ≠ 0.35.

Q54. Continuing with the analysis of Big Rig, Rains asks his students to calculate the mean squared error(MSE). Assume that the sum of squared errors (SSE) for the regression model is 359.

A)   21.118.

B)   17.956.

C)   18.896.

Q55. Rains now wants to test the students’ knowledge of the use of the F-test and the interpretation of the F-statistic. Which of the following statements regarding the F-test and the F-statistic is the most correct?

A)   The F-statistic is used to test whether at least one independent variable in a set of independent variables explains a significant portion of the variation of the dependent variable.

B)   The F-test is usually formulated as a two-tailed test.

C)   The F-statistic is almost always formulated to test each independent variable separately, in order to identify which variable is the most statistically significant.

Q56. One of the main assumptions of a multiple regression model is that the variance of the residuals is constant across all observations in the sample. A violation of the assumption is known as:

A)   robust standard errors.

B)   heteroskedasticity.

C)   positive serial correlation.

Q57. Rains reminds his students that a common condition that can distort the results of a regression analysis is referred to as serial correlation. The presence of serial correlation can be detected through the use of:

A)   the Breusch-Pagen test.

B)   the Durbin-Watson statistic.

C)   the Hansen method.

[此贴子已经被作者于2009-1-8 13:38:07编辑过]

答案和详解如下：

Q53. Rains asks his students to test the null hypothesis that states for every new well drilled, profits will be increased by the given multiple of the coefficient, all other factors remaining constant. The appropriate hypotheses for this two-tailed test can best be stated as:

A)   H₀: b₁ ≤ 0.98 versus H_a: b₁ > 0.98.

B)   H₀: b₁ = 0.98 versus H_a: b₁ ≠ 0.98.

C)   H₀: b₁ = 0.35 versus H_a: b₁ ≠ 0.35.

Correct answer is B)

The coefficient given in the above table for the number of new wells drilled (WLS) is 0.98. The hypothesis should test to see whether the coefficient is indeed equal to 0.98 or is equal to some other value. Note that hypotheses with the “greater than” or “less than” symbol are used with one-tailed tests.

Q54. Continuing with the analysis of Big Rig, Rains asks his students to calculate the mean squared error(MSE). Assume that the sum of squared errors (SSE) for the regression model is 359.

A)   21.118.

B)   17.956.

C)   18.896.

Correct answer is A)

The MSE is calculated as SSE / (n – k – 1). Recall that there are twenty observations and two independent variables. Therefore, the SEE in this instance = 359 / (20 – 2 − 1) = 21.118.

Q55. Rains now wants to test the students’ knowledge of the use of the F-test and the interpretation of the F-statistic. Which of the following statements regarding the F-test and the F-statistic is the most correct?

A)   The F-statistic is used to test whether at least one independent variable in a set of independent variables explains a significant portion of the variation of the dependent variable.

B)   The F-test is usually formulated as a two-tailed test.

C)   The F-statistic is almost always formulated to test each independent variable separately, in order to identify which variable is the most statistically significant.

Correct answer is A)

An F-test assesses how well a set of impendent variables, as a group, explains the variation in the dependent variable. It tests all independent variables as a group, and is always a one-tailed test. The decision rule is to reject the null hypothesis if the calculated F-value is greater than the critical F-value.

Q56. One of the main assumptions of a multiple regression model is that the variance of the residuals is constant across all observations in the sample. A violation of the assumption is known as:

A)   robust standard errors.

B)   heteroskedasticity.

C)   positive serial correlation.

Correct answer is B)

Heteroskedasticity is present when the variance of the residuals is not the same across all observations in the sample, and there are sub-samples that are more spread out than the rest of the sample.

Q57. Rains reminds his students that a common condition that can distort the results of a regression analysis is referred to as serial correlation. The presence of serial correlation can be detected through the use of:

A)   the Breusch-Pagen test.

B)   the Durbin-Watson statistic.

C)   the Hansen method.

Correct answer is B)

The Durbin-Watson test (DW ≈ 2(1 − r)) can detect serial correlation. Another commonly used method is to visually inspect a scatter plot of residuals over time. The Hansen method does not detect serial correlation, but can be used to remedy the situation. Note that the Breusch-Pagen test is used to detect heteroskedasticity.

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