Reading 12- LOS g(Part 1): Q1-5 interest, will, following, equation

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1.An analyst is estimating whether a fund’s excess return for a quarter is related to interest rates and last quarter’s excess return. The regression equation is found to have unconditional heteroskedasticity and serial correlation. Which of the following will be TRUE? Parameter estimates will be:
A)    accurate but statistical inference about the parameters will not be valid.
B)    accurate and statistical inference about the parameters will be valid.
C)    inaccurate and statistical inference about the parameters will not be valid.
D)    inaccurate but statistical inference about the parameters will be valid.

2.Which of the following is NOT a method of detecting autocorrelations?
A)    A Goldfeld-Quandt test.
B)    A scatter plot of the residuals over time.
C)    The first-order correlation of the residuals over time.
D)    The Durbin-Watson test.

3.George Smith, an analyst with Great Lakes Investments, has created a comprehensive report on the pharmaceutical industry at the request of his boss. The Great Lakes portfolio currently has a significant exposure to the pharmaceuticals industry through its large equity position in the top two pharmaceutical manufacturers. His boss requested that Smith determine a way to accurately forecast pharmaceutical sales in order for Great Lakes to identify further investment opportunities in the industry as well as to minimize their exposure to downturns in the market. Smith realized that there are many factors that could possibly have an impact on sales, and he must identify a method that can quantify their effect. Smith used a multiple regression analysis with five independent variables to predict industry sales. His goal is to not only identify relationships that are statistically significant, but economically significant as well. The assumptions of his model are fairly standard: a linear relationship exists between the dependent and independent variables, the independent variables are not random, and the expected value of the error term is zero. 
Smith is confident with the results presented in his report. He has already done some hypothesis testing for statistical significance, including calculating a t-statistic and conducting a two-tailed test where the null hypothesis is that the regression coefficient is equal to zero versus the alternative that it is not. He feels that he has done a thorough job on the report and is ready to answer any questions posed by his boss.
However, Smith’s boss, John Sutter, is concerned that in his analysis, Smith has ignored several potential problems with the regression model that may affect his conclusions. He knows that when any of the basic assumptions of a regression model are violated, any results drawn for the model are questionable. He asks Smith to go back and carefully examine the effects of heteroskedasticity, multicollinearity, and serial correlation on his model. In specific, he wants Smith to make suggestions regarding how to detect these errors and to correct problems that he encounters. 
Suppose that there is evidence that the residual terms in the regression are positively correlated. The most likely effect on the statistical inferences drawn from the regressions results is for Smith to commit a:
A)    Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero.
B)    Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
C)    Type II error by incorrectly rejecting the null hypothesis that the regression parameters are equal to zero.
D)    Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

4.Sutter has detected the presence of conditional heteroskedasticity in Smith’s report. This is evidence that:
A)    two or more of the independent variables are highly correlated with each other.
B)    the error terms are correlated with each other.
C)    the variance of the error term is correlated with the values of the independent variables.
D)    the error term is normally distributed.

5.Suppose there is evidence that the variance of the error term is correlated with the values of the independent variables. The most likely effect on the statistical inferences Smith can make from the regressions results is to commit a:
A)    Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
B)    Type II error by incorrectly rejecting the null hypothesis that the regression parameters are equal to zero.
C)    Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero.
D)    Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

[此贴子已经被作者于2008-4-12 16:35:29编辑过]

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1.An analyst is estimating whether a fund’s excess return for a quarter is related to interest rates and last quarter’s excess return. The regression equation is found to have unconditional heteroskedasticity and serial correlation. Which of the following will be TRUE? Parameter estimates will be:
A)    accurate but statistical inference about the parameters will not be valid.
B)    accurate and statistical inference about the parameters will be valid.
C)    inaccurate and statistical inference about the parameters will not be valid.
D)    inaccurate but statistical inference about the parameters will be valid.
The correct answer was C)
One of the independent variables is a lagged value of the dependent variable. This means that serial correlation will cause an inaccurate parameter estimate. Serial correlation always impacts the statistical inference about the parameters. Unconditional heteroskedasticity never impacts statistical inference or parameter accuracy.

2.Which of the following is NOT a method of detecting autocorrelations?
A)    A Goldfeld-Quandt test.
B)    A scatter plot of the residuals over time.
C)    The first-order correlation of the residuals over time.
D)    The Durbin-Watson test.
The correct answer was A)
The Goldfeld –Quandt test is a test of the variances, not of autocorrelation.

3.George Smith, an analyst with Great Lakes Investments, has created a comprehensive report on the pharmaceutical industry at the request of his boss. The Great Lakes portfolio currently has a significant exposure to the pharmaceuticals industry through its large equity position in the top two pharmaceutical manufacturers. His boss requested that Smith determine a way to accurately forecast pharmaceutical sales in order for Great Lakes to identify further investment opportunities in the industry as well as to minimize their exposure to downturns in the market. Smith realized that there are many factors that could possibly have an impact on sales, and he must identify a method that can quantify their effect. Smith used a multiple regression analysis with five independent variables to predict industry sales. His goal is to not only identify relationships that are statistically significant, but economically significant as well. The assumptions of his model are fairly standard: a linear relationship exists between the dependent and independent variables, the independent variables are not random, and the expected value of the error term is zero. 
Smith is confident with the results presented in his report. He has already done some hypothesis testing for statistical significance, including calculating a t-statistic and conducting a two-tailed test where the null hypothesis is that the regression coefficient is equal to zero versus the alternative that it is not. He feels that he has done a thorough job on the report and is ready to answer any questions posed by his boss.
However, Smith’s boss, John Sutter, is concerned that in his analysis, Smith has ignored several potential problems with the regression model that may affect his conclusions. He knows that when any of the basic assumptions of a regression model are violated, any results drawn for the model are questionable. He asks Smith to go back and carefully examine the effects of heteroskedasticity, multicollinearity, and serial correlation on his model. In specific, he wants Smith to make suggestions regarding how to detect these errors and to correct problems that he encounters. 
Suppose that there is evidence that the residual terms in the regression are positively correlated. The most likely effect on the statistical inferences drawn from the regressions results is for Smith to commit a:
A)    Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero.
B)    Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
C)    Type II error by incorrectly rejecting the null hypothesis that the regression parameters are equal to zero.
D)    Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
The correct answer was A)
One problem with positive autocorrelation (also known as positive serial correlation) is that the standard errors of the parameter estimates will be too small and the t-statistics too large. This may lead Smith to incorrectly reject the null hypothesis that the parameters are equal to zero. In other words, Smith will incorrectly conclude that the parameters are statistically significant when in fact they are not. This is an example of a Type I error: incorrectly rejecting the null hypothesis when it should not be rejected.

4.Sutter has detected the presence of conditional heteroskedasticity in Smith’s report. This is evidence that:
A)    two or more of the independent variables are highly correlated with each other.
B)    the error terms are correlated with each other.
C)    the variance of the error term is correlated with the values of the independent variables.
D)    the error term is normally distributed.
The correct answer was C)
Conditional heteroskedasticity exists when the variance of the error term is correlated with the values of the independent variables.
Multicollinearity, on the other hand, occurs when two or more of the independent variables are highly correlated with each other. Serial correlation exists when the error terms are correlated with each other. One assumption of multiple regression is that the error term is normally distributed.

5.Suppose there is evidence that the variance of the error term is correlated with the values of the independent variables. The most likely effect on the statistical inferences Smith can make from the regressions results is to commit a:
A)    Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
B)    Type II error by incorrectly rejecting the null hypothesis that the regression parameters are equal to zero.
C)    Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero.
D)    Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.
The correct answer was C)
One problem with heteroskedasticity is that the standard errors of the parameter estimates will be too small and the t-statistics too large. This will lead Smith to incorrectly reject the null hypothesis that the parameters are equal to zero. In other words, Smith will incorrectly conclude that the parameters are statistically significant when in fact they are not. This is an example of a Type I error: incorrectly rejecting the null hypothesis when it should not be rejected.