12: Multiple Regression and Issues in Regression Ana 2010, interpret, represent, equation

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Session 3: Quantitative Methods: Quantitative
Methods for Valuation
Reading 12: Multiple Regression and Issues in Regression Analysis

LOS f: Formulate a multiple regression equation by using dummy variables to represent qualitative factors and interpret the coefficients and regression results.

 

 

 

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) 11.

B) 13.

C) 12.

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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) 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.

C) The desired impact cannot be measured.

土豆妮

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) 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.

C) The desired impact cannot be measured.

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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.

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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) one dummy variables.

B) four dummy variables.

C) three dummy variables.

土豆妮

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) one dummy variables.

B) four dummy variables.

C) three dummy variables.

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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.

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

EPS_t = α + β₁Q_1t + β₂Q_2t + β₃Q_3t

where:
EPS_t is a quarterly observation of earnings per share
Q_1t takes on a value of 1 if period t is the second quarter, 0 otherwise
Q_2t takes on a value of 1 if period t is the third quarter, 0 otherwise
Q_3t 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) 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).

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

土豆妮

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

EPS_t = α + β₁Q_1t + β₂Q_2t + β₃Q_3t

where:
EPS_t is a quarterly observation of earnings per share
Q_1t takes on a value of 1 if period t is the second quarter, 0 otherwise
Q_2t takes on a value of 1 if period t is the third quarter, 0 otherwise
Q_3t 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) 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).

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

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

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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) Dummy variable regression.

B) Paired-comparisons.

C) Difference of means.

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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) Dummy variable regression.

B) Paired-comparisons.

C) Difference of means.

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

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An analyst is trying to determine whether fund return performance is persistent. The analyst divides funds into three groups based on whether their return performance was in the top third (group 1), middle third (group 2), or bottom third (group 3) during the previous year. The manager then creates the following equation: R = a + b₁D₁ + b₂D₂ + b₃D₃ + ε, where R is return premium on the fund (the return minus the return on the S& 500 benchmark) and D_i is equal to 1 if the fund is in group i. Assuming no other information, this equation will suffer from:

A) collinearity.

B) heteroskedasticity.

C) serial correlation.