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  2. Derive the critical values of β0^ and β1^ that minimize the residual sum of squares for the following sample regression model Yi=β0^+β1^Xi+ei^

Derive the critical values of β0^ and β1^ that minimize the residual sum of squares for the following sample regression model Yi=β0^+β1^Xi+ei^

Assignment 2

Instructions

For questions 1-2, you can submit a PDF or scanned copy of your work.Consult with me if you don’t know how to accomplish this.

For questions 3-4, you must use STATA, and must turn in a copy of your Do-file. The Do-file must perform every task below neatly and correctly.

The work you hand in must be your own. You must NOT copy any answers from anyone or anywhere else. Please review FIU’s policy on academic misconduct for more information.

 

Questions

  1. Derive the critical values of β0^ and β1^ that minimize the residual sum of squares for the following sample regression model Yi=β0^+β1^Xi+ei^
  2. Derive the critical values of α0^ and α1^ that minimize the residual sum of squares for the following sample regression model Yi=α0^+α1^(Xi−X¯)+ei^
  3. Download this dataset and load it into STATA for this question. Alternatively you can load the dataset directly from http://estebanch.com/ECO4421/HW02/question4.dta
  4. a) Use the answers from question 1 to get the values for β0^ and β1^.
  5. b) Generate the predicted values of Y
  6. c) Calculate the mean of the true value of Y , and compare it to the mean of the predicted value of Y. Are they the equal?
  7. d) Generate the sample error term
  8. e) Derive the value of R2
  9. f) How much of the variation in Y is explained by X?

Hint: Use preserve, collapse, and restore to make everything a bit easier

 

  1. Download this dataset and load it into STATA for this question. Alternatively, you can load the dataset directly from http://estebanch.com/ECO4421/HW02/question5.dta

The dataset has information on CEOs of US Corporations. There are 177 observations, and two variables: ceoten has the years the individual has been a CEO of that company, and salary is the compensation in thousands of dollars.

  1. a) Find the average salary and the average tenure in the sample
  2. b) Identify how many CEOs are in their first year as CEO
  3. c) Estimate the values of the parameters β0^ and β1^ for the following simple regression model:

salaryi=β0^+β1^ceoteni+ei^

  1. d) On average, what is the predicted increase in salary given one additional year as CEO?
  2. e) How much of the variation in salary is explained by years as CEO?
  3. f) Is years as CEO a good predictor of the variation in CEO salary? Explain.

 


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