Reading 12: Multiple Regression and Issues in Regression A return, class, whether, groups, determine

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Q6. 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)   serial correlation.

C)   collinearity.

Q7. 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)                        1                     1

B)                        0                     0

C)                        0                     1

Q8. 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 = b₁D_t + b₂X_t + e_t.

B)    Y_t = b₀ + b₁D_t + e_t.

C)    Y_t = b₀ + b₁D_t + b₂X_t + e_t.

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答案和详解如下：

Q6. 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)   serial correlation.

C)   collinearity.

Correct answer is C)

There are too many dummy variables specified, so the equation will suffer from collinearity.

Q7. 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)                        1                     1

B)                        0                     0

C)                        0                     1

Correct answer is A)

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.

Q8. 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 = b₁D_t + b₂X_t + e_t.

B)    Y_t = b₀ + b₁D_t + e_t.

C)    Y_t = b₀ + b₁D_t + b₂X_t + e_t.

Correct answer is C)         

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

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