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r代写-G 6541/6551
时间：2021-11-05
Econometrics/G 6541/6551 2021 S2
Final Project
Instructions:
1. This project is due Saturday 6 Nov 2021, 9pm and must be submitted to Canvas.
2. This project is based on content from the entire semester and is worth 50% of your final grade.
3. This project is to be completed individually.
4. This project can be completed in Word with Excel or R. Please submit both your Word file and
Excel or R code file.
5. There are different requirements for undergraduate and graduate students. Please read the project
details carefully to make sure you address the criteria relevant to you.
Overall task description:
In this project, you are to respond to the four questions given below. The datasets required for each
question can be found on the Canvas site (more information on the dataset in each question is provided
later in this document).
Note the different requirements relevant to your cohort below:
Undergraduate students (unit 6541): Attempt all questions, except for the last three parts of question 3
and the last part of question 4.
Graduate students (unit 6551): Attempt all questions.
Bibliography:
Please list any sources you used in the bibliography. In-text referencing is not required.
Marking guide:
This project is graded out of 100 marks. The table below describes the general marking criteria.
Knowledge/Technical
• Calculations are performed correctly.
• The appropriate model is identified and fit successfully.
• Appropriate statistics are correctly identified and interpreted.
• Appropriate hypothesis tests are conducted correctly and the
correct conclusions are drawn.
• Appropriate model diagnostics are conducted and interpreted.
• Accurate predictions using models are made.
• Evaluates and compares performance of individual models.
• Includes relevant plots where appropriate.
Communication/
presentation
• Language is coherent, concise, clear and appropriate for the
audience.
• Communication of ideas and analysis is logical and flows well.
• Plots are presented clearly with appropriate labelling.
• Files are formatted nicely and minimal errors with grammar,
layout, etc.
QUESTION 1 [25 MARKS]
For a random sample of 19 students, their working-hours spent on the assignment and their assignment
marks were collected. This is shown in the table below.
The complete data are in the “Q1data” sheet of the Excel file available on Canvas.
The variables in the data are as follows:
ID: observation number
X: working-hours spent on the assignment
Y: mark (out of 100)
___________________
ID Y X
___________________
1 61 4.5
2 63 5.5
3 67 3.5
…
18 95 7
19 97 8
___________________
We wish to determine the relationship between working-hours on the assignment and marks.
a) Find the average working-hour on the assignment and the average mark for the 19 students.
b) Assume the following regression model
Y = 1 + 2 X +e.
Write down your fitted model and interpret the estimates of 1 and 2.
c) What is the coefficient of correlation? Interpret it.
d) Test if the fitted model is significant using =0.01.
e) Present a residual plot for the fitted model for Y on X, with brief comments.
QUESTION 2 [30 MARKS]
The managing director of a real estate company wanted to study why certain branches of the company
outperformed others.
[1] First she felt that the key variables in determining total annual sales (in $ millions) were the
advertising budget (in $000s) and the number of sales agents. She took a sample of 14 branches (and
you will be asked in question a) to analyse the data to get this first summary output for her).
[2] Later on she added a third variable, the average number of years of experience in the real estate
business for each branch, and analysed the data to get this second summary output.
The data are in the “Q2data” sheet of the Excel file available on Canvas.
The following variables are included (in two steps):
Y: annual sales ($millions)
X1: advertising budget ($000s)
X2: number of sales agents
X3: average years of experience for each branch
________________________________
office Y X1 X2 X3
________________________________
1 33 249 15 12
2 47 292 18 15
3 18 183 14 8
4 25 201 16 12
5 49 310 21 16
…
11 43 248 21 17
12 28 210 18 9
13 24 256 20 11
14 37 275 16 10
________________________________
a) Analyse the data to get the first summary output and write down the fitted model using the first
summary output.
b) Test if the fitted model as a whole is significant using the first summary output. Use =0.05.
c) Present the residual plot using the first summary output, with brief comments on whether:
i) the errors are independent,
ii) the errors have the same variance,
iii) the error variable is normal and
iv) the errors have any outliers.
d) Fit a new model by adding the third variable to get the second summary output. Comment on
the key differences you observe between the two summary outputs.
e) Which model should the managing director use to predict how well a newly-opened branch
will do? Using this selected model, what is the predicted total annual sales for a newly-opened
branch with 15 sales agents with 5 years of experience on average and an advertising budget of
$200,000? Comment on the reliability of your prediction.
QUESTION 3 [20 MARKS]
In the sheet “Q3data” of the Excel file available on Canvas, there are data on public expenditure on
education (EE), gross domestic product (GDP), and population (P) for 34 countries in the year 2015. It
is hypothesised that per capita expenditure on education is linearly related to per capita GDP. That is
Yi = β0 + β1 Xi + ui,
where Yi = EEi/Pi and Xi = GDPi/Pi
It is suspected that ui may be heteroskedastic with a variance related to Xi.
a) Write a short description (one page maximum) for your junior colleague introducing the issue
of heteroskedasticity in models. Why is heteroskedasticity an issue and how might it be
addressed? Why might the suspicion about heteroskedasticity be reasonable in this context?
b) Estimate the model using least squares and plot the least squares line and the residuals. Is there
any evidence of heteroskedasticity?
c) Test for the existence of heteroskedasticity using a Breusch-Pagan test with α=0.05.
d) Re-estimate the model under the assumption that var(ui) = σ2 Xi. Report your results.
e) [G students (6551) students only to complete this question] Test for the existence of
heteroskedasticity using a F test with α=0.05.
f) [G students (6551) students only to complete this question] Test for the existence of
heteroskedasticity using the special form of White test with α=0.05.
g) [G students (6551) students only to complete this question] Compare the results of the three
tests for the existence of heteroskedasticity. Provide some brief comments.
QUESTION 4 [25 MARKS]
The general public and government agencies have discussed if climate change is ‘real’. Let us look at
the mean maximum and mean minimum temperatures in Canberra for September 2008 to August 2021
and analyse the data in order to get some evidence-based understanding.
The data are in the “Q4data” sheet in the Excel file available on Canvas.
a) Write a short description (500 words maximum) for the general public introducing time-series data
and models.
b) Present a time series plot for the mean maximum and mean minimum temperatures, respectively.
c) Are both the time series data stationary or non-stationary? Explain why or why not, referencing the
time series plot, and then conducting a Dickey-Fuller test (no time trend).
d) Fit an AR(1) model for the mean maximum temperature time series if the time series is stationary
OR fit an AR(1) model for the differenced mean maximum temperature time series. Make brief
comments on the fitted model.
e) Evaluate the fit of your model from d). Then use your fitted model from d) to predict the mean
maximum and mean minimum temperatures in Canberra for the month of September 2021.
f) [G students (6551) students only to complete this question] Test if there is an ARCH effect in
the data, with α=0.05.
学霸联盟
Final Project
Instructions:
1. This project is due Saturday 6 Nov 2021, 9pm and must be submitted to Canvas.
2. This project is based on content from the entire semester and is worth 50% of your final grade.
3. This project is to be completed individually.
4. This project can be completed in Word with Excel or R. Please submit both your Word file and
Excel or R code file.
5. There are different requirements for undergraduate and graduate students. Please read the project
details carefully to make sure you address the criteria relevant to you.
Overall task description:
In this project, you are to respond to the four questions given below. The datasets required for each
question can be found on the Canvas site (more information on the dataset in each question is provided
later in this document).
Note the different requirements relevant to your cohort below:
Undergraduate students (unit 6541): Attempt all questions, except for the last three parts of question 3
and the last part of question 4.
Graduate students (unit 6551): Attempt all questions.
Bibliography:
Please list any sources you used in the bibliography. In-text referencing is not required.
Marking guide:
This project is graded out of 100 marks. The table below describes the general marking criteria.
Knowledge/Technical
• Calculations are performed correctly.
• The appropriate model is identified and fit successfully.
• Appropriate statistics are correctly identified and interpreted.
• Appropriate hypothesis tests are conducted correctly and the
correct conclusions are drawn.
• Appropriate model diagnostics are conducted and interpreted.
• Accurate predictions using models are made.
• Evaluates and compares performance of individual models.
• Includes relevant plots where appropriate.
Communication/
presentation
• Language is coherent, concise, clear and appropriate for the
audience.
• Communication of ideas and analysis is logical and flows well.
• Plots are presented clearly with appropriate labelling.
• Files are formatted nicely and minimal errors with grammar,
layout, etc.
QUESTION 1 [25 MARKS]
For a random sample of 19 students, their working-hours spent on the assignment and their assignment
marks were collected. This is shown in the table below.
The complete data are in the “Q1data” sheet of the Excel file available on Canvas.
The variables in the data are as follows:
ID: observation number
X: working-hours spent on the assignment
Y: mark (out of 100)
___________________
ID Y X
___________________
1 61 4.5
2 63 5.5
3 67 3.5
…
18 95 7
19 97 8
___________________
We wish to determine the relationship between working-hours on the assignment and marks.
a) Find the average working-hour on the assignment and the average mark for the 19 students.
b) Assume the following regression model
Y = 1 + 2 X +e.
Write down your fitted model and interpret the estimates of 1 and 2.
c) What is the coefficient of correlation? Interpret it.
d) Test if the fitted model is significant using =0.01.
e) Present a residual plot for the fitted model for Y on X, with brief comments.
QUESTION 2 [30 MARKS]
The managing director of a real estate company wanted to study why certain branches of the company
outperformed others.
[1] First she felt that the key variables in determining total annual sales (in $ millions) were the
advertising budget (in $000s) and the number of sales agents. She took a sample of 14 branches (and
you will be asked in question a) to analyse the data to get this first summary output for her).
[2] Later on she added a third variable, the average number of years of experience in the real estate
business for each branch, and analysed the data to get this second summary output.
The data are in the “Q2data” sheet of the Excel file available on Canvas.
The following variables are included (in two steps):
Y: annual sales ($millions)
X1: advertising budget ($000s)
X2: number of sales agents
X3: average years of experience for each branch
________________________________
office Y X1 X2 X3
________________________________
1 33 249 15 12
2 47 292 18 15
3 18 183 14 8
4 25 201 16 12
5 49 310 21 16
…
11 43 248 21 17
12 28 210 18 9
13 24 256 20 11
14 37 275 16 10
________________________________
a) Analyse the data to get the first summary output and write down the fitted model using the first
summary output.
b) Test if the fitted model as a whole is significant using the first summary output. Use =0.05.
c) Present the residual plot using the first summary output, with brief comments on whether:
i) the errors are independent,
ii) the errors have the same variance,
iii) the error variable is normal and
iv) the errors have any outliers.
d) Fit a new model by adding the third variable to get the second summary output. Comment on
the key differences you observe between the two summary outputs.
e) Which model should the managing director use to predict how well a newly-opened branch
will do? Using this selected model, what is the predicted total annual sales for a newly-opened
branch with 15 sales agents with 5 years of experience on average and an advertising budget of
$200,000? Comment on the reliability of your prediction.
QUESTION 3 [20 MARKS]
In the sheet “Q3data” of the Excel file available on Canvas, there are data on public expenditure on
education (EE), gross domestic product (GDP), and population (P) for 34 countries in the year 2015. It
is hypothesised that per capita expenditure on education is linearly related to per capita GDP. That is
Yi = β0 + β1 Xi + ui,
where Yi = EEi/Pi and Xi = GDPi/Pi
It is suspected that ui may be heteroskedastic with a variance related to Xi.
a) Write a short description (one page maximum) for your junior colleague introducing the issue
of heteroskedasticity in models. Why is heteroskedasticity an issue and how might it be
addressed? Why might the suspicion about heteroskedasticity be reasonable in this context?
b) Estimate the model using least squares and plot the least squares line and the residuals. Is there
any evidence of heteroskedasticity?
c) Test for the existence of heteroskedasticity using a Breusch-Pagan test with α=0.05.
d) Re-estimate the model under the assumption that var(ui) = σ2 Xi. Report your results.
e) [G students (6551) students only to complete this question] Test for the existence of
heteroskedasticity using a F test with α=0.05.
f) [G students (6551) students only to complete this question] Test for the existence of
heteroskedasticity using the special form of White test with α=0.05.
g) [G students (6551) students only to complete this question] Compare the results of the three
tests for the existence of heteroskedasticity. Provide some brief comments.
QUESTION 4 [25 MARKS]
The general public and government agencies have discussed if climate change is ‘real’. Let us look at
the mean maximum and mean minimum temperatures in Canberra for September 2008 to August 2021
and analyse the data in order to get some evidence-based understanding.
The data are in the “Q4data” sheet in the Excel file available on Canvas.
a) Write a short description (500 words maximum) for the general public introducing time-series data
and models.
b) Present a time series plot for the mean maximum and mean minimum temperatures, respectively.
c) Are both the time series data stationary or non-stationary? Explain why or why not, referencing the
time series plot, and then conducting a Dickey-Fuller test (no time trend).
d) Fit an AR(1) model for the mean maximum temperature time series if the time series is stationary
OR fit an AR(1) model for the differenced mean maximum temperature time series. Make brief
comments on the fitted model.
e) Evaluate the fit of your model from d). Then use your fitted model from d) to predict the mean
maximum and mean minimum temperatures in Canberra for the month of September 2021.
f) [G students (6551) students only to complete this question] Test if there is an ARCH effect in
the data, with α=0.05.
学霸联盟
