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.

---

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.

---

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.

---

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.

---

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

---

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.

---

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)

---

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.

---

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?

A) 6.10.

B) 57.07.

C) 37.25.

---

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?

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.

---

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: 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.

---

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?

A) Points 2, 3, and 4.

B) Points 1, 2, and 3.

C) Points 1, 3, and 4.

---

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)

bapswarrior

The management of a large restaurant chain believes that revenue growth is dependent upon the month of the year. Using a standard 12 month calendar, how many dummy variables must be used in a regression model that will test whether revenue growth differs by month?

A) 13.

B) 11.

C) 12.

---

The appropriate number of dummy variables is one less than the number of categories because the intercept captures the effect of the other effect. With 12 categories (months) the appropriate number of dummy variables is 11 = 12 – 1. If the number of dummy variables equals the number of categories, it is possible to state any one of the independent dummy variables in terms of the others. This is a violation of the assumption of the multiple linear regression model that none of the independent variables are linearly related

bapswarrior

A fund has changed managers twice during the past 10 years. An analyst wishes to measure whether either of the changes in managers has had an impact on performance. The analyst wishes to simultaneously measure the impact of risk on the fund’s return. R is the return on the fund, and M is the return on a market index. Which of the following regression equations can appropriately measure the desired impacts?

A) R = a + bM + c1D1 + c2D2 + c3D3 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the second manager, and D3 = 1 is the return is from the third manager.

B) The desired impact cannot be measured.

C) R = a + bM + c1D1 + c2D2 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager.

---

The effect needs to be measured by two distinct dummy variables. The use of three variables will cause collinearity, and the use of one dummy variable will not appropriately specify the manager impact.

bapswarrior

Jill Wentraub is an analyst with the retail industry. She is modeling a company’s sales over time and has noticed a quarterly seasonal pattern. If she includes dummy variables to represent the seasonality component of the sales she must use:

A) three dummy variables.

B) one dummy variables.

C) four dummy variables.

---

Three. Always use one less dummy variable than the number of possibilities. For a seasonality that varies by quarters in the year, three dummy variables are needed.

bapswarrior

Consider the following model of earnings (EPS) regressed against dummy variables for the quarters:

EPSt = α + β1Q1t + β2Q2t + β3Q3t
where:
EPSt is a quarterly observation of earnings per share
Q1t takes on a value of 1 if period t is the second quarter, 0 otherwise
Q2t takes on a value of 1 if period t is the third quarter, 0 otherwise
Q3t takes on a value of 1 if period t is the fourth quarter, 0 otherwise

Which of the following statements regarding this model is most accurate? The:

A) EPS for the first quarter is represented by the residual.

B) significance of the coefficients cannot be interpreted in the case of dummy variables.

C) coefficient on each dummy tells us about the difference in earnings per share between the respective quarter and the one left out (first quarter in this case).

---

The coefficients on the dummy variables indicate the difference in EPS for a given quarter, relative to the first quarter.

bapswarrior

An analyst wishes to test whether the stock returns of two portfolio managers provide different average returns. The analyst believes that the portfolio managers’ returns are related to other factors as well. Which of the following can provide a suitable test?

A) Paired-comparisons.

B) Difference of means.

C) Dummy variable regression.

---

The difference of means and paired-comparisons tests will not account for the other factors