bapswarrior

Which of the following statements regarding the R2 is least accurate?

A) The adjusted-R2 is greater than the R2 in multiple regression.

B) The adjusted-R2 not appropriate to use in simple regression.

C) It is possible for the adjusted-R2 to decline as more variables are added to the multiple regression.

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The adjusted-R2 will always be less than R2in multiple regression.

bapswarrior

Which of the following statements regarding the R2 is least accurate?

A) The R2 of a regression will be greater than or equal to the adjusted-R2 for the same regression.

B) The F-statistic for the test of the fit of the model is the ratio of the mean squared regression to the mean squared error.

C) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable.

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The R2 is the ratio of the explained variation to the total variation.

bapswarrior

An analyst is estimating a regression equation with three independent variables, and calculates the R2, the adjusted R2, and the F-statistic. The analyst then decides to add a fourth variable to the equation. Which of the following is most accurate?

A) The R2 will be higher, but the adjusted R2 and F-statistic could be higher or lower.

B) The R2 and F-statistic will be higher, but the adjusted R2 could be higher or lower.

C) The adjusted R2 will be higher, but the R2 and F-statistic could be higher or lower.

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The R2 will always increase as the number of variables increase. The adjusted R2 specifically adjusts for the number of variables, and might not increase as the number of variables rise. As the number of variables increases, the regression sum of squares will rise and the residual T sum of squares will fall—this will tend to make the F-statistic larger. However, the number degrees of freedom will also rise, and the denominator degrees of freedom will fall, which will tend to make the F-statistic smaller. Consequently, like the adjusted R2, the F-statistic could be higher or lower.

bapswarrior

An analyst regresses the return of a S&P 500 index fund against the S&P 500, and also regresses the return of an active manager against the S&P 500. The analyst uses the last five years of data in both regressions. Without making any other assumptions, which of the following is most accurate? The index fund:

A) regression should have higher sum of squares regression as a ratio to the total sum of squares.

B) should have a higher coefficient on the independent variable.

C) should have a lower coefficient of determination.

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The index fund regression should provide a higher R2 than the active manager regression. R2 is the sum of squares regression divided by the total sum of squares.

bapswarrior

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

The values of R2 and the F-statistic for the fit of the model are:

A) R2 = 0.25 and F = 0.909.

B) R2 = 0.20 and F = 10.

C) R2 = 0.25 and F = 10.

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R2 = RSS / SST = 20 / 100 = 0.20
The F-statistic is equal to the ratio of the mean squared regression to the mean squared error.F = 20 / 2 = 10

bapswarrior

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

The values of R2 and the F-statistic for the fit of the model are:

A) R2 = 0.25 and F = 13.333.

B) R2 = 0.20 and F = 13.333.

C) R2 = 0.25 and F = 0.930.

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R2 = RSS / SST = 100 / 400 = 0.25
The F-statistic is equal to the ratio of the mean squared regression to the mean squared error.
F = 100 / 7.5 = 13.333

bapswarrior

Which of the following statements regarding the analysis of variance (ANOVA) table is least accurate? The:

A) F-statistic is the ratio of the mean square regression to the mean square error.

B) standard error of the estimate is the square root of the mean square error.

C) F-statistic cannot be computed with the data offered in the ANOVA table.

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The F-statistic can be calculated using an ANOVA table. The F-statistic is MSR/MSE.

bapswarrior

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 CORRECT?

A) If the F-statistic is less than its critical value, we can reject the null hypothesis that all coefficients are equal to zero.

B) R2 = SSRegression / SSTotal.

C) R2 = SSError / SSTotal.

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The coefficient of determination is the proportion of the total variation of the dependent variable that is explained by the independent variables.

bapswarrior

An analyst is trying to determine whether stock market returns are related to size and the market-to-book ratio, through the use of multiple regression. However, the analyst uses returns of portfolios of stocks instead of individual stocks in the regression. Which of the following is a valid reason why the analyst uses portfolios? The use of portfolios:

A) will increase the power of the test by giving the test statistic more degrees of freedom.

B) reduces the standard deviation of the residual, which will increase the power of the test.

C) will remove the existence of multicollinearity from the data, reducing the likelihood of type II error.

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The use of portfolios reduces the standard deviation of the returns, which reduces the standard deviation of the residuals.

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bapswarrior

Lynn Carter, CFA, is an analyst in the research department for Smith Brothers in New York. She follows several industries, as well as the top companies in each industry. She provides research materials for both the equity traders for Smith Brothers as well as their retail customers. She routinely performs regression analysis on those companies that she follows to identify any emerging trends that could affect investment decisions.
Due to recent layoffs at the company, there has been some consolidation in the research department. Two research analysts have been laid off, and their workload will now be distributed among the remaining four analysts. In addition to her current workload, Carter will now be responsible for providing research on the airline industry. Pinnacle Airlines, a leader in the industry, represents a large holding in Smith Brothers’ portfolio. Looking back over past research on Pinnacle, Carter recognizes that the company historically has been a strong performer in what is considered to be a very competitive industry. The stock price over the last 52-week period has outperformed that of other industry leaders, although Pinnacle’s net income has remained flat. Carter wonders if the stock price of Pinnacle has become overvalued relative to its peer group in the market, and wants to determine if the timing is right for Smith Brothers to decrease its position in Pinnacle.  
Carter decides to run a regression analysis, using the monthly returns of Pinnacle stock and airlines industry.

Analysis of Variance Table (ANOVA)
Source	df (Degrees of Freedom)	SS (Sum of Squares)	Mean Square (SS/df)
Regression	1	3,257 (RSS)	3,257 (MSR)
Error	8	298 (SSE)	37.25 (MSE)
Total	9	3,555 (SS Total)

Which of the following are least likely to be major assumptions regarding linear regression?

A) The independent variable is correlated with the residuals.

B) A linear relationship exists between the dependent and independent variables.

C) The variance of the residual term is constant.

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Although the linear regression model is fairly insensitive to minor deviations from any of these assumptions, the independent variable is typically uncorrelated with the residuals. (Study Session 3, LOS 11.d)

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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:

A) are perfectly correlated.

B) have no linear relationship.

C) have a positive linear relationship.

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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)

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Based upon the information presented in the ANOVA table, what is the standard error of the estimate?

A) 6.10.

B) 57.07.

C) 37.25.

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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)

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Based upon the information presented in the ANOVA table, what is the coefficient of determination?

A) 0.916, indicating the variability of company returns explains about 91.6% of the variability of industry returns.

B) 0.084, indicating that the variability of industry returns explains about 8.4% of the variability of company returns.

C) 0.916, indicating that the variability of industry returns explains about 91.6% of the variability of company returns.

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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)

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Based upon her analysis, Carter has derived the following regression equation: Ŷ = 1.75 + 3.25X1. The predicted value of the Y variable equals 50.50, if the:

A) predicted value of the independent variable equals 15.

B) predicted value of the dependent variable equals 15.

C) coefficient of the determination equals 15.

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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)

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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?

A) Points 2, 3, and 4.

B) Points 1, 2, and 3.

C) Points 1, 3, and 4.

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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)