Economics 301 Test 3 Sample Problems

 

1. Identify and explain each of the terms in the following multiple regression model:

Yi = b 0 + b 1 X1i + b 2 X2i + b 1 X3i + e i

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Yi = b 0 + b 1 X1i + b 2 X2i + b 1 X3i

2. a) Identify and explain the 6 main assumptions of the multiple regression model.

b) Violation of which assumption may result in heteroskedasticity?

c) Violation of which assumption may result in serial correlation (auto correlation)?

d) Violation of which assumption may result in multicollinerity?
  1. Given the following consumption function for the time period 1920 to 1950

Ct = b 0 + b 1 Ydt + e t

Where:

Ct = Aggregate personal consumption expenditures in period t

Ydt = Aggregate disposable personal income in period t

How would you capture the effects of World War II on autonomous consumption? Hint: construct a qualitative (dummy) variable and explain how it would be utilized.

4. Given the following consumption function for a cross-section of individuals.

Ci = b 0 + b 1 Ydi + e i

Where:

Ci = Personal consumption expenditures for individual i.

Ydi = Disposable income for individual i.

How would you capture the effects of gender on the marginal propensity to consume? Hint construct a qualitative (dummy) variable and explain how it would be utilized. (assume you have the data needed from a survey)

5. Let’s say we are trying to estimate monthly electric usage of three different building types. Construct a multiple regression model that uses as explanatory variables the price of electricity, the average temperature and your approach for dealing with the three different building types. Be specific as to how you handle the different building types and explain how your model would work.

  1. Construct a hypothesis test for the significance of all of the slope coefficients taken together for the following regression model (test the validity of the model).

Yi = b 0 + b 1 X1i + b 2 X2i + b 3 X3i + e i

Assume n=30, Fcomputed = 4.23, and the significance level is 5%. Be sure to state the null and alternative hypotheses and explain your conclusions.

7. Given the following, how would you estimate the own price elasticity?

Qdxi = b 0 + b 1 Pxi + b 2 Ydi + e i

Where:

Qdxi = The quantity of good x demanded by individual i.

Pxi = The price of good x faced by individual i

Ydi = Disposable income for individual i.

8. In question 7, above, what would you change in the above regression model to account for diminishing returns from increases in income? Be specific.

  1. Explain the problem of excluding a relevant varaible(s). Use an example to aid your answer.
  2. a) Explain the problem of multicollinearity - both the perfect and imperfect cases.: (Use an example to aid your answer). see Chapter 19.

    3. b) What are the causes?

    c) What are the consequences?

    d) How would one test for multicollinearity (detection)?

    e) If present, how would it be corrected? Provide an example.

  3. a) Explain the problem of heteroskedasticity: (Use an example and a graphical illustration to aid your answer – see Chapter 18).

    4. b) What are the causes?

    c) What are the consequences?

    d) How would one test for heteroskedasticity (detection)?

    e) If present, how would it be corrected? Provide an example.

  4. a) Explain the problem of serial correlation (auto correlation): (Use an example and a graphical illustration to aid your answer). see Chapter 19
    1. What are the causes?
    2. What are the consequences?
    3. How would one test (detection) for serial correlation?

13. Given the following regression model:

Yt = b 0 + b 1 X1t + b 2 X2t + b 3 X3t + e t

DW = 1.32, n = 30

Conduct a Durbin-Watson (DW) test for first order serial correlation given the information above. Be sure to state the null and alternative hypotheses and explain your conclusions.

 

 

 

 

 

14.

The regression results above are for the following model:

lnChickent = b 0 + b 1 lnPCt + b 2 lnPBt + b 3 lnYdt + e t

Where:

lnChickent = Log of chicken sales in period t.

lnPCt = Log of price of chicken in period t.

lnPBt = Log of price of beef in period t.

lnYdt = Log of disposable personal income in period t.

 

  1. Show the sample regression line (equation).
  2. Test the entire group of regression slope coefficients Test the significance of the individual slope coefficients.
  3. Provide an interpretation of the coefficient of determination (R-square) both adjust and non-adjusted.
  4. Provide an interpretation of the individual slope coefficients.