Which equation would be a better choice for making a forecast?
A) Equation TWO because serial correlation is not a problem.
B) Equation ONE because serial correlation is not a problem.
C) Equation TWO because it has a higher adjusted R-squared.
D) Equation ONE because it has a higher R-squared.
The correct answer was C)
Equation TWO has a higher adjusted R-squared and thus would produce the more reliable estimates. As is always the case when a variable is removed, R-squared for Equation TWO is lower. The increase in adjusted R-squared indicates that the removed variable, Q3, has very little explanatory power, and removing it should improve the accuracy of the estimates. With respect to the references to autocorrelation, we can compare the Durbin-Watson statistics to the critical values on a Durbin-Watson table. Since the critical DW statistics for Equation ONE and TWO respectively are 1.01 (>0.7856) and 1.10 (>0.7860), serial correlation is a problem for both equations.
9.Using Equation ONE, what is the sales forecast for the second quarter of the next year?
A) $56.02 million.
B) $51.09 million.
C) $49.72 million.
D) $46.31 million.
The correct answer was B)
The estimate for the second quarter of the following year would be (in millions):
31.4083 + (-2.4631) + (24+2)*0.851786 = 51.091666.
10.Which of the coefficients that appear in both equations are not significant at the five percent level in a two-tailed test?
A) The coefficients on Q1 and Q2 only.
B) The TREND coefficient only.
C) The intercept only.
D) The coefficient on Q2 only.
The correct answer was D)
The absolute value of the critical T-statistics for Equation ONE and TWO are 2.093 and 2.086, respectively. Since, the t-statistics for Q2 in Equations ONE and TWO are -1.6685 and -1.9188, respectively, these fall below the critical values for both equations.
11.Conditional heteroskedasticity is a problem for:
A) Equation ONE but not Equation TWO.
B) Equation TWO but not Equation ONE.
C) neither equation.
D) both Equations ONE and TWO.
The correct answer was C)
Mercado would use the Breusch-Pagan test for heteroskedasticity. Mercado regressed the squared residuals from each equation on the respective independent variables. The R-squared values were 0.008801 and 0.006313 respectively. The test-statistic for the Breusch-Pagan test is n*(R-squared) which is distributed as a Chi-squared statistic with degrees of freedom equal to the number of independent variables. Assuming a five percent level of significance, the respective critical values are 7.815 and 9.488. The respective test statistic values are 24*0.008801 = 0.2112 and 24*0.006313 = 0.1515. Both computed test statistics are much less than their respective critical values; thus, Mercado would conclude that conditional heteroskedasticity is not a problem.
12.Mercado probably did not include a fourth dummy variable Q4, which would have had 0, 0, 0, 1 as its first four observations because:
A) it would not have been significant.
B) the intercept is essentially the dummy for the fourth quarter.
C) it would have lowered the explanatory power of the equation.
D) the average of the other dummy variables in the equation serves as the dummy for the fourth quarter.
The correct answer was B)
The fourth quarter serves as the base quarter, and for the fourth quarter, Q1=Q2=Q3=0. Had the equation included a Q4 as specified, we could not have had an intercept. In that case, for Equation ONE for example, the estimate of Q4 would have been 31.40833. The dummies for the other quarters would be the 31.40833 plus the estimated dummies from Equation ONE. In an equation that included Q1, Q2, Q3, and Q4 but no intercept, for example:
Q1 = 31.40833 + (-3.77798) = 27.63035
Such an equation would produce the same estimated values for the dependent variable.
13.If Mercado determines that Equation TWO is the appropriate specification, then he is essentially saying that for each year, value of sales from quarter three to four is expected to:
A) grow by more than $1,000,000.
B) remain approximately the same.
C) grow, but by less than $1,000,000.
D) to decline by more than $1,000,000.
The correct answer was C)
The specification of Equation TWO essentially assumes there is no difference attributed to the change of the season from the third to fourth quarter. However, the time trend is significant. The trend effect for moving from one season to the next is the coefficient on TREND times $1,000,000 which is $852,182 for Equation TWO.
14.The F-statistic is the ratio of the mean square regression to the mean square error. The mean squares are provided directly in the analysis of variance (ANOVA) table. Which of the following statements regarding the ANOVA table for a regression is TRUE?
A) R2 = SSError / SSTotal.
B) If the F-statistic is less than its critical value, we can reject the null hypothesis that all coefficients are equal to zero.
C) R2 = SSRegression / SSTotal.
D) R2 tells us whether or not the regression model is correctly specified.
The correct answer was C)
The coefficient of determination is the proportion of the total variation of the dependent variable that is explained by the independent variables.
15.Which of the following statements regarding the analysis of variance (ANOVA) table is FALSE? The:
A) F-statistic is the ratio of the mean square regression to the mean square error.
B) coefficient of determination is the ratio of the sum of squares regression to the total sum of squares.
C) F-statistic cannot be computed with the data offered in the ANOVA table.
D) standard error of the estimate is the square root of the mean square error.
The correct answer was C)
The F-statistic can be calculated using an ANOVA table. The F-statistic is MSR/MSE.
16.Wilson estimated a regression that produced the following analysis of variance (ANOVA) table: Source | Sum of squares | Degrees of freedom | Mean square | Regression | 100 | 1 | 100.0 | Error | 300 | 40 | 7.5 | Total | 400 | 41 |
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The values of R2 and the F-statistic for the fit of the model are:
A) R2 = 0.25 and F = 0.930.
B) R2 = 0.20 and F = 13.333.
C) R2 = 0.25 and F = 0.930.
D) R2 = 0.25 and F = 13.333.
The correct answer was D)
R2 = 100/400 = 0.25
F = 100 / 7.5 = 13.333
17.May Jones estimated a regression that produced the following analysis of variance (ANOVA) table: Source | Sum of squares | Degrees of freedom | Mean square | Regression | 20 | 1 | 20 | Error | 80 | 40 | 2 | Total | 100 | 41 |
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The values of R2 and the F-statistic for the fit of the model are:
A) R2 = 0.20 and F = 10.
B) R2 = 0.25 nd F = 0.909.
C) R2 = 0.20 and F = 0.909.
D) R2 = 0.25 and F = 10.
The correct answer was A)
R2 = 20/100 = 0.20
F = 20 / 2 = 10
[此贴子已经被作者于2008-4-12 16:23:21编辑过] | 
发表于 2008-4-12 16:18
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1,0,0,0), Q2