Carter wants to test the strength of the relationship between the two variables. She calculates a correlation coefficient of 0.72. This means that the two variables:
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A) |
have a positive linear relationship. | |
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B) |
are perfectly correlated. | |
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C) |
have no linear relationship. | |
If the correlation coefficient (r) is greater that 0 and less than 1, then the two variables are said to be positively correlated. (Study Session 3, LOS 11.a)
Based upon the information presented in the ANOVA table, what is the standard error of the estimate?
The standard error of the estimate (SEE) measures the “fit” of the regression line, and the smaller the standard error, the better the fit. The SSE can be calculated as √(MSE) = √(SSE / (n ? 2) = √(298 / 8) = 6.10. (Study Session 3, LOS 12.g)
Based upon the information presented in the ANOVA table, what is the coefficient of determination?
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A) |
0.916, indicating the variability of company returns explains about 91.6% of the variability of industry returns. | |
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B) |
0.916, indicating that the variability of industry returns explains about 91.6% of the variability of company returns. | |
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C) |
0.084, indicating that the variability of industry returns explains about 8.4% of the variability of company returns. | |
The coefficient of determination (R2) is the percentage of the total variation in the dependent variable explained by the independent variable.
The R2 = (RSS / SS) Total = (3,257 / 3,555) = 0.916. This means that the variation of independent variable (the airline industry) explains 91.6% of the variations in the dependent variable (Pinnacle stock). (Study Session 3, LOS 12.g)
Based upon her analysis, Carter has derived the following regression equation: ? = 1.75 + 3.25X1. The predicted value of the Y variable equals 50.50, if the:
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A) |
predicted value of the independent variable equals 15. | |
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B) |
predicted value of the dependent variable equals 15. | |
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C) |
coefficient of the determination equals 15. | |
Note that the easiest way to answer this question is to plug numbers into the equation.
The predicted value for Y = 1.75 + 3.25(15) = 50.50.
The variable X1 represents the independent variable. (Study Session 3, LOS 13.a)
Carter realizes that although regression analysis is a useful tool when analyzing investments, there are limitations. Carter made a list of points describing limitations that Smith Brothers equity traders should be aware of when applying her research to their investment decisions.
- Point 1: Data derived from regression analysis may be homoskedastic.
- Point 2: Data from regression relationships tends to exhibit parameter instability.
- Point 3: Results of regression analysis may exhibit autocorrelation.
- Point 4: The variance of the error term changes over time.
When reviewing Carter’s list, one of the Smith Brothers’ equity traders points out that not all of the points describe regression analysis limitations. Which of Carter’s points most accurately describes the limitations to regression analysis?
One of the basis assumptions of regression analysis is that the variance of the error terms is constant, or homoskedastic. Any violation of this assumption is called heteroskedasticity. Therefore, Point 1 is incorrect, but Point 4 is correct. Points 2 and 3 also describe limitations of regression analysis. (Study Session 3, LOS 11.j) | 
发表于 2011-3-3 11:25
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