Consider a simple econometric model (mean or intercept model) for one variable as yi ui , where E(yi), is an unknown parameter, yi is ith sample observation on an economic

   

 

 

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(1.1) Consider the simple linear regression model y, =B₁ + B₂x₁+₁, i=1,2,..., N where E(e) = 0, E(e)=o² and E(e₁,e;)=0 for ij. Provide short answers to the following questions. (a) (b) (1.2) When using N=50 observations to estimate the model y₁ =B₁ + B₂x; +B3z, +e; you obtain SSE=2132.65. After augmenting this model with the model becomes and V₁ =B₁ + B₂x₁ +B3²₁ +Y₁+₂+e, and you obtain SSE=1072.88. Use RESET to test for misspecification at a 1% level of significance. (5 marks) Give two reasons for why the random error e, exists. (2 marks) Explain briefly how the factors o' and N affect the precision with which we estimate the unknown parameter ₂. (2 marks) (1.3) Consider a regression model that explains the starting salaries (SAL) for students with an undergraduate degree in Business and Economics. You wish to examine whether taking econometrics affects starting salary. The model is: SAL, =B₁ + B₂GPA; +³₂METRICS; +e; = salary in dollars = grade point average = 1 if a student took econometrics, = 0 otherwise. where (a) (b) SAL GPA METRICS (1.1) How would you modify the equation to investigate whether women had lower starting salaries than men? (2 marks) How would you modify the equation in (a) to investigate whether the effect of taking econometrics on starting salary was the same for men and women? (2 marks) (1.1) Consider the simple linear regression model y, =B₁ + B₂x₁+₁, i=1,2,..., N where E(e) = 0, E(e)=o² and E(e₁,e;)=0 for ij. Provide short answers to the following questions. (a) (b) (1.2) When using N=50 observations to estimate the model y₁ =B₁ + B₂x; +B3z, +e; you obtain SSE=2132.65. After augmenting this model with the model becomes and V₁ =B₁ + B₂x₁ +B3²₁ +Y₁+₂+e, and you obtain SSE=1072.88. Use RESET to test for misspecification at a 1% level of significance. (5 marks) Give two reasons for why the random error e, exists. (2 marks) Explain briefly how the factors o' and N affect the precision with which we estimate the unknown parameter ₂. (2 marks) (1.3) Consider a regression model that explains the starting salaries (SAL) for students with an undergraduate degree in Business and Economics. You wish to examine whether taking econometrics affects starting salary. The model is: SAL, =B₁ + B₂GPA; +³₂METRICS; +e; = salary in dollars = grade point average = 1 if a student took econometrics, = 0 otherwise. where (a) (b) SAL GPA METRICS (1.1) How would you modify the equation to investigate whether women had lower starting salaries than men? (2 marks) How would you modify the equation in (a) to investigate whether the effect of taking econometrics on starting salary was the same for men and women? (2 marks)

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a Two reasons for why the random error e exists in the simple linear regression model are 1 Inherent variability The relationship between the dependent variable y and the independent variable x is not ... View the full answer