Reading 12- LOS f: Q1- 5 education, political, class, allocated

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1.The amount of the State of Florida’s total revenue that is allocated to the education budget is believed to be dependent upon the total revenue for the year and the political party that controls the state legislature. Which of the following regression models is most appropriate for capturing the effect of the political party on the education budget? Assume Y_t is the amount of the education budget for Florida in year t, X is Florida’s total revenue in year t, and D_t = {1 if the legislature has a Democratic majority in year t, 0 otherwise}.
A)    Y_t = b₀ + b₁D_t + b₂X_t + _t.
B)    Y_t = b₀ + b₁D_t + _t.
C)    Y_t = b₁D_t + b₂X_t + _t.
D)    Y_t = b₀ + b₂X_t + _t.

2.Suppose the analyst wants to add a dummy variable for whether a person has an undergraduate college degree and a graduate degree.  What is the correct representation if a person has both degrees?
              Undergraduate Degree  Graduate Degree
                  Dummy Variable      Dummy Variable
A)                        0                                 0
B)                        0                                 1
C)                        1                                 0
D)                        1                                 1

3.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)    heteroskedasticity.
B)    collinearity.
C)    serial correlation.
D)    non-normality

4.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)    Difference of means.
B)    Paired-comparisons.
C)    Discriminant analysis.
D)    Dummy variable regression.

5.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 TRUE? The:
A)    change in EPS for the fourth quarter is estimated to be β₁ + β₂ + β₃.
B)    EPS for the first quarter is represented by the residual.
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).
D)    significance of the coefficients cannot be interpreted in the case of dummy variables.

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1.The amount of the State of Florida’s total revenue that is allocated to the education budget is believed to be dependent upon the total revenue for the year and the political party that controls the state legislature. Which of the following regression models is most appropriate for capturing the effect of the political party on the education budget? Assume Y_t is the amount of the education budget for Florida in year t, X is Florida’s total revenue in year t, and D_t = {1 if the legislature has a Democratic majority in year t, 0 otherwise}.
A)    Y_t = b₀ + b₁D_t + b₂X_t + e_t.
B)    Y_t = b₀ + b₁D_t + e_t.
C)    Y_t = b₁D_t + b₂X_t + e_t.
D)    Y_t = b₀ + b₂X_t + e_t.
The correct answer was A)
In this application, b₀, b₁, and b₂ are estimated by regressing Y_t against a constant, D_t, and X_t.  The estimated relationships for the two parties are:

Non-Democrats:	Ŷ = b0 + b2Xt
Democrats:	Ŷ = (b0 + b1) + b2Xt

2.Suppose the analyst wants to add a dummy variable for whether a person has an undergraduate college degree and a graduate degree.  What is the correct representation if a person has both degrees?
       Undergraduate Degree Graduate Degree
           Dummy Variable  Dummy Variable
A)                        0                                 0
B)                        0                                 1
C)                        1                                 0
D)                        1                                 1
The correct answer was D)     
Assigning a zero to both categories is appropriate for someone with neither degree. Assigning one to the undergraduate category and zero to the graduate category is appropriate for someone with only an undergraduate degree. Assigning zero to the undergraduate category and one to the graduate category is appropriate for someone with only a graduate degree. Assigning a one to both categories is correct since it reflects the possession of both degrees.
3.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)    heteroskedasticity.
B)    collinearity.
C)    serial correlation.
D)    non-normality
The correct answer was B)
There are too many dummy variables specified, so the equation will suffer from collinearity.
4.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)    Difference of means.
B)    Paired-comparisons.
C)    Discriminant analysis.
D)    Dummy variable regression.
The correct answer was D)
Discriminant analysis cannot test the significance of the difference. The difference of means and paired-comparisons tests will not account for the other factors.
5.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 TRUE? The:
A)    change in EPS for the fourth quarter is estimated to be β₁ + β₂ + β₃.
B)    EPS for the first quarter is represented by the residual.
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).
D)    significance of the coefficients cannot be interpreted in the case of dummy variables.
The correct answer was C)
The coefficients on the dummy variables indicate the difference in EPS for a given quarter, relative to the first quarter.