Department of Economics
ECON 222/2 SECTIONS A and B
STATISTICAL METHODS II
FALL 2015 – ASSIGNMENT 3
Due: Monday, November 23, before 3:00 pm
1. (14 marks) Consider the multiple regression model y i = β 1 x 1i + β 2 x 2i + β 3 x 3i +e i with the
following nine observations.
y i x 1i x 2i x 3i
1 1 0 1
2 1 1 -2
3 1 2 1
-1 1 -2 0
0 1 1 -1
-1 1 -2 -1
2 1 0 1
1 1 -1 1
2 1 1 0
Use a hand calculator to answer the following questions.
a. (2 marks) Calculate the observations in terms of deviations from their means. That is,
find y i
= y i − y , x 2i
= x 2i − x 2 and x 3i
= x 3i − x 3 .
b. (2 marks) Calculate y i
, x 2i
, y i
, x 3i
and x 2i
c. (2 marks) Find least square estimates b 1 , b 2 and b 3 . (Hint: See Appendix 5A.)
d. (2 marks) Find the lease squares residuals
1 , ê 2 ,…, ê 9 .
e. (2 marks) Find the variance estimate ˆ σ
f. (2 marks) Find the sample correlation between x 2 and x 3 .
g. (2 marks) Find the standard error for b 2 .
h. (2 marks) Find SSE, SST, SSR and R 2 .
2. (10 marks) Use a computer to verify your answers to problem 1, parts (c) and (e) – (h).
Attach your results.
3. (14 marks) Lion Forest has been a very successful golf professional. However, at age 45 his
game is not quite what it used to be. He started the pro tour when he was only 20 and he has
been looking back examining how his scores have changed, as he got older. In the file golf.dat,
the first column contains his final score (relative to par) for 150 tournaments. The second
column contains his age (in units of 10 years). There are scores for 6 major tournaments in
each year for the last 25 years. Denoting his score by SCORE and his age by AGE, estimate
the following model and obtain the within-sample predictions:
SCORE = β 1 + β 2 AGE+ β 3 AGE 2 + β 4 AGE 3 +e
a. (2 marks) Test the null hypothesis that a quadratic function is adequate against the cubic
function as an alternative. What are the characteristics of the cubic equation that might
make it appropriate?
b. (10 marks) Use the within-sample predictions to answer the following questions:
(i) (2 marks) At what age was Lion at the peak of his career?
(ii) (2 marks) When was Lion’s game improving at an increasing rate?
(iii) (2 marks) When was Lion’s game improving at a decreasing rate?
(iv) (2 marks) At what age did Lion start to play worse than he had played when he was
20 years old?
(v) (2 marks) When could he no longer score less than par (on average)?
c. (2 marks) When he is aged 70, will he be able to break 100? (Assume par is 72.)
4. (6 marks) Output for the two models y = β 1 + β 2 x+ β 3 w+e and y = β 1 + β 2 x+e , based on 35
observations, are given below.
Variable Coefficient Std Error t-value Coefficient Std Error t-value
RESET applied to the second model yields F-values of 17.98 (for
) and 8.72 (for
3 ). The correlation between x and w is r
xw = 0.975 . Discuss the following questions.
a. (2 marks) Should w be included in the model?
b. (2 marks) What can you say about omitted-variable bias?
c. (2 marks) What can you say about the existence of collinearity and its possible effect?
5. (16 marks) Using data in the file beer.dat, apply RESET to the following two alternative models.
a. (2 marks) lnQ = β 1 + β 2 lnPB+ β 3 lnPL+ β 4 lnPR+ β 5 lnI +e .
b. (2 marks) Q = β 1 + β 2 PB+ β 3 PL+ β 4 PR+ β 5 I +e .
c. (2 marks) Which model seems to better reflect the demand for beer?
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
Australia Assessments has gained an international reputation of being the leading website in custom assignment writing services. Once you give us the instructions of your paper through the order form, we will complete the rest.
As we work towards providing the best custom assignment services, our company provides assignment services for any type of academic essay. We will help you develop professionally written essays that are rich in content and free from plagiarism.
Admission and Business Papers
Our skilled team of professional writers will ensure that we help you craft a remarkable admission essay for your desired Master's program in your institution of choice. We won't stop there. Once you enter the job market, we will be available to secure you a position at your desired worksite by creating an outstanding portfolio or resume.
Editing and Proofreading
Our editorial team is always available for all editing and proofreading services. They check completed papers by our writers and also provide professional opinions to papers completed by our clients.
We harbor professional academic writers with different qualifications in diverse academic fields. As such, we are capable of handling both simple and technical papers. Ensure that you provide us with correct and complete instructions in the order form.