# US Statistics Manufacturer Worksheet

Questions requiring numerical/written answers1. A manufacturer has accumulated the following information from its

two factories

Sample mean

Sample standard deviation

Sample size

Daily defects in Sydney

4000

100

100

Daily defects in Melbourne

4300

70

100

The manager of the Melbourne factory claims there is no significant difference in the

number of defects in the two factories. Test the manager’s claim at 1% level of

significance (assume that the population are normally distributed and have equal

variances).

2. Referring to the above table, what is the estimated standard error of the difference

between the two sample means? (Assume that the two population variances are equal)

3.Given the following information on two independent samples calculate a 95% confidence

interval. Assume the populations have equal variances

Introductory Econometrics

Problem Set 1

Assignment instructions

•

•

•

•

•

•

•

You must submit your work via the Turnitin link on moodle by 18:00 on Friday

March 11.

This assignment will be marked for the course assessment and will be worth 7.5% of

your final mark. You must attach your Stata do-file to your answers (by typing

Stata codes or pasting screenshots of the do-file window or the result window in

your answer) and failure to do so will result in a zero mark for the computing

questions.

Name, student number, course title, tutorial group number and tutor’s name should be

clearly included in the submission. Your answers including Stata do-file should not

exceed 6 pages. The Assignment is based on the material covered in both lectures and

tutorials up to the end of Week 3.

The assignment is INDIVIDUAL work. You may discuss the assignment with your

peers, but you must submit YOUR OWN answers.

If the answer requires some mathematical calculation, show the steps, don’t just report

the final results.

This assignment has a total of 100 points awarded.

All submissions may be checked for plagiarism. The University regards plagiarism as

a form of academic misconduct and has very strict rules regarding plagiarism. For

UNSW policies, penalties, and information to help you avoid plagiarism see:

https://student.unsw.edu.au/plagiarism as well as the guidelines in the online ELISE

tutorials for all new UNSW students: http://subjectguides.library.unsw.edu.au/elise .

To see if you understand plagiarism, do this short quiz:

https://student.unsw.edu.au/plagiarism-quiz

The fish.dta dataset contains information on the price and quantity of fish sold at various fish

markets in different locations.

We are interested in the determinants of fish price and we consider the following population

regression models:

𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝛼2 𝑤𝑎𝑣𝑒 + 𝑈,

log(𝑝𝑟𝑖𝑐𝑒) = 𝛽0 + 𝛽1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝑉,

(1)

(2)

log(𝑝𝑟𝑖𝑐𝑒) = 𝛾0 + 𝛾1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝛾2 𝑤𝑎𝑣𝑒 + 𝐸,

(3)

𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝑤𝑎𝑣𝑒 𝛼2 + 𝑍,

(4)

log(𝑝𝑟𝑖𝑐𝑒) = 𝛿0 + 𝛿1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝛿2 𝑤𝑎𝑣𝑒 + 𝛿3 𝑤𝑎𝑣𝑒 2 + 𝑊,

1/𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝛼2 𝑤𝑎𝑣𝑒 + 𝛼3 𝑡𝑜𝑡𝑞𝑡𝑦 ∗ 𝑤𝑎𝑣𝑒 + 𝑄,

(5)

(6)

log(𝑝𝑟𝑖𝑐𝑒 + 𝛽0 ) = 𝛽1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝑅, (7)

where 𝑝𝑟𝑖𝑐𝑒 is fish price per kg ($100 per kg), totqty is the total quantity sold (kg), wave is the

max height of waves in the last 2 days (meter).

1. [10pts] Which of the above models are linear regression models?

2. [10pts] Using the data in fish.dta, estimate model (1) by OLS and report the results in

equation or tabular form, including the sample size and 𝑅 2 . Assume that the GaussMarkov assumptions hold and interpret the estimated coefficient for 𝛼1 . (Please pay

attention to the unit of measurement when interpreting the coefficient).

3. [8pts] Explain the meaning of the zero-conditional-mean assumption for the model in

equation (1). Interpret 𝛼̂1 if the “zero conditional mean assumption” did not hold.

4. [10pts] Using the data in fish.dta, estimate model (2) by OLS and report the results in

equation or tabular form, including the sample size and 𝑅 2 . Interpret the estimated

coefficients for 𝛽1. (For your convenience I already generated log(price) (lprice) and

log(totqty) (ltotqty). Log here refers to the natural logarithm).

5. [20pts] Consider an extended model of (2) given by (3). For this problem, assume that

the Gauss-Markov assumptions hold for (3).

a. Estimate equation (3) and present the results in equation or tabular form,

including the sample size and 𝑅 2 .

b. Interpret 𝛾̂1 and 𝛾̂2 .

c. Compare 𝛾̂1 and 𝛽̂1 obtained in question 4 (from model (2)). What do you

conclude about the sign of the bias on 𝛽̂1 in model (2)?

d. Given the estimates of equation (3) and the sign of the bias on 𝛽̂1, are log(totqty)

and Wave positively or negatively correlated?

e. Looking at the estimated 𝛾̂2 , can the result be explained by the mechanism that

stormy seas decrease the supply of fish caught and therefore increase the price

of fish?

6. [10pts] Using model (3) and assuming that the Gauss-Markov assumptions hold, is

log(𝑡𝑜𝑡𝑞𝑡𝑦)statistically significant at the 1% significance level? Conduct the test

manually and present your conclusion.

7. [8pts] Using the estimates of equation (3) answer the following question. Find the

predicted selling price of a market where 200 kg of fish were sold and the max height

of waves in the last 2 days was 5 meters. You can assume that the Gauss-Markov

assumptions hold.

8. [10pts] Estimate model (5) and use the estimates of equation (5) to answer the following

question. On Saturday, 200 kg of fish were sold in the Sydney fish market and the max

height of waves in the last 2 days was 5 meters. Predict the change or percent change

in fish price in the Sydney fish market if the same amount of fish (200 kg) were sold

but the max height of waves in the last 2 days increased by 1 meter. You can assume

that the Gauss-Markov assumptions hold. (For your convenience I already generated

𝑊𝑎𝑣𝑒 2 (wavesq)).

9. [6pts] Interpret the 𝑅 2 of the OLS estimates of equations (2) and (3). Explain why the

𝑅 2 is higher for equation (3) than for equation (2).

10. [8pts] We were able to obtain the quantity of fish sold to men and women separately.

Your friend thought that the selling price might depends on the quantity sold to each

group differently, and proposed the following regression to examine the determinants

of fish price.

log(𝑝𝑟𝑖𝑐𝑒) = 𝛾0 + 𝛾1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + γ2 log(𝑡𝑜𝑡𝑞𝑡𝑦𝑀 ) + 𝛾3 log(𝑡𝑜𝑡𝑞𝑡𝑦𝐹 ) + 𝛾4 𝑤𝑎𝑣𝑒 + 𝐸

(8)

where 𝑡𝑜𝑡𝑞𝑡𝑦𝑀 and 𝑡𝑜𝑡𝑞𝑡𝑦𝐹 are the total quantities sold to male and female customers,

respectively.

Data were collected in developed countries. Which Gauss-Markov assumptions are

potentially violated in equation (8)? Include all that apply.

Introductory Econometrics

Problem Set 1

Assignment instructions

•

•

•

•

•

•

•

You must submit your work via the Turnitin link on moodle by 18:00 on Friday

March 11.

This assignment will be marked for the course assessment and will be worth 7.5% of

your final mark. You must attach your Stata do-file to your answers (by typing

Stata codes or pasting screenshots of the do-file window or the result window in

your answer) and failure to do so will result in a zero mark for the computing

questions.

Name, student number, course title, tutorial group number and tutor’s name should be

clearly included in the submission. Your answers including Stata do-file should not

exceed 6 pages. The Assignment is based on the material covered in both lectures and

tutorials up to the end of Week 3.

The assignment is INDIVIDUAL work. You may discuss the assignment with your

peers, but you must submit YOUR OWN answers.

If the answer requires some mathematical calculation, show the steps, don’t just report

the final results.

This assignment has a total of 100 points awarded.

All submissions may be checked for plagiarism. The University regards plagiarism as

a form of academic misconduct and has very strict rules regarding plagiarism. For

UNSW policies, penalties, and information to help you avoid plagiarism see:

https://student.unsw.edu.au/plagiarism as well as the guidelines in the online ELISE

tutorials for all new UNSW students: http://subjectguides.library.unsw.edu.au/elise .

To see if you understand plagiarism, do this short quiz:

https://student.unsw.edu.au/plagiarism-quiz

The fish.dta dataset contains information on the price and quantity of fish sold at various fish

markets in different locations.

We are interested in the determinants of fish price and we consider the following population

regression models:

𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝛼2 𝑤𝑎𝑣𝑒 + 𝑈,

log(𝑝𝑟𝑖𝑐𝑒) = 𝛽0 + 𝛽1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝑉,

(1)

(2)

log(𝑝𝑟𝑖𝑐𝑒) = 𝛾0 + 𝛾1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝛾2 𝑤𝑎𝑣𝑒 + 𝐸,

(3)

𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝑤𝑎𝑣𝑒 𝛼2 + 𝑍,

(4)

log(𝑝𝑟𝑖𝑐𝑒) = 𝛿0 + 𝛿1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + 𝛿2 𝑤𝑎𝑣𝑒 + 𝛿3 𝑤𝑎𝑣𝑒 2 + 𝑊,

1/𝑝𝑟𝑖𝑐𝑒 = 𝛼0 + 𝛼1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝛼2 𝑤𝑎𝑣𝑒 + 𝛼3 𝑡𝑜𝑡𝑞𝑡𝑦 ∗ 𝑤𝑎𝑣𝑒 + 𝑄,

(5)

(6)

log(𝑝𝑟𝑖𝑐𝑒 + 𝛽0 ) = 𝛽1 𝑡𝑜𝑡𝑞𝑡𝑦 + 𝑅, (7)

where 𝑝𝑟𝑖𝑐𝑒 is fish price per kg ($100 per kg), totqty is the total quantity sold (kg), wave is the

max height of waves in the last 2 days (meter).

1. [10pts] Which of the above models are linear regression models?

2. [10pts] Using the data in fish.dta, estimate model (1) by OLS and report the results in

equation or tabular form, including the sample size and 𝑅 2 . Assume that the GaussMarkov assumptions hold and interpret the estimated coefficient for 𝛼1 . (Please pay

attention to the unit of measurement when interpreting the coefficient).

3. [8pts] Explain the meaning of the zero-conditional-mean assumption for the model in

equation (1). Interpret 𝛼̂1 if the “zero conditional mean assumption” did not hold.

4. [10pts] Using the data in fish.dta, estimate model (2) by OLS and report the results in

equation or tabular form, including the sample size and 𝑅 2 . Interpret the estimated

coefficients for 𝛽1. (For your convenience I already generated log(price) (lprice) and

log(totqty) (ltotqty). Log here refers to the natural logarithm).

5. [20pts] Consider an extended model of (2) given by (3). For this problem, assume that

the Gauss-Markov assumptions hold for (3).

a. Estimate equation (3) and present the results in equation or tabular form,

including the sample size and 𝑅 2 .

b. Interpret 𝛾̂1 and 𝛾̂2 .

c. Compare 𝛾̂1 and 𝛽̂1 obtained in question 4 (from model (2)). What do you

conclude about the sign of the bias on 𝛽̂1 in model (2)?

d. Given the estimates of equation (3) and the sign of the bias on 𝛽̂1, are log(totqty)

and Wave positively or negatively correlated?

e. Looking at the estimated 𝛾̂2 , can the result be explained by the mechanism that

stormy seas decrease the supply of fish caught and therefore increase the price

of fish?

6. [10pts] Using model (3) and assuming that the Gauss-Markov assumptions hold, is

log(𝑡𝑜𝑡𝑞𝑡𝑦)statistically significant at the 1% significance level? Conduct the test

manually and present your conclusion.

7. [8pts] Using the estimates of equation (3) answer the following question. Find the

predicted selling price of a market where 200 kg of fish were sold and the max height

of waves in the last 2 days was 5 meters. You can assume that the Gauss-Markov

assumptions hold.

8. [10pts] Estimate model (5) and use the estimates of equation (5) to answer the following

question. On Saturday, 200 kg of fish were sold in the Sydney fish market and the max

height of waves in the last 2 days was 5 meters. Predict the change or percent change

in fish price in the Sydney fish market if the same amount of fish (200 kg) were sold

but the max height of waves in the last 2 days increased by 1 meter. You can assume

that the Gauss-Markov assumptions hold. (For your convenience I already generated

𝑊𝑎𝑣𝑒 2 (wavesq)).

9. [6pts] Interpret the 𝑅 2 of the OLS estimates of equations (2) and (3). Explain why the

𝑅 2 is higher for equation (3) than for equation (2).

10. [8pts] We were able to obtain the quantity of fish sold to men and women separately.

Your friend thought that the selling price might depends on the quantity sold to each

group differently, and proposed the following regression to examine the determinants

of fish price.

log(𝑝𝑟𝑖𝑐𝑒) = 𝛾0 + 𝛾1 log(𝑡𝑜𝑡𝑞𝑡𝑦) + γ2 log(𝑡𝑜𝑡𝑞𝑡𝑦𝑀 ) + 𝛾3 log(𝑡𝑜𝑡𝑞𝑡𝑦𝐹 ) + 𝛾4 𝑤𝑎𝑣𝑒 + 𝐸

(8)

where 𝑡𝑜𝑡𝑞𝑡𝑦𝑀 and 𝑡𝑜𝑡𝑞𝑡𝑦𝐹 are the total quantities sold to male and female customers,

respectively.

Data were collected in developed countries. Which Gauss-Markov assumptions are

potentially violated in equation (8)? Include all that apply.

2 / 3

125%

=

log(price + B.) = Bitotqty + R,

(7)

where price is fish price per kg ($100 per kg), totqty is the total quantity sold (kg), wave is the

max height of waves in the last 2 days (meter).

1. [10pts] Which of the above models are linear regression models?

2. [10pts] Using the data in fish.dta, estimate model (1) by OLS and report the results in

equation or tabular form, including the sample size and R2. Assume that the Gauss-

Markov assumptions hold and interpret the estimated coefficient for Q1. (Please pay

attention to the unit of measurement when interpreting the coefficient).

3. [8pts] Explain the meaning of the zero-conditional-

mean assumption for the model in

equation (1). Interpret âı if the “zero conditional mean assumption” did not hold.

4. [10pts] Using the data in fish.dta, estimate model (2) by OLS and report the results in

equation or tabular form, including the sample size and R2. Interpret the estimated

coefficients for $1. (For your convenience I already generated log(price) (Iprice) and

log(totqty) (ltotqty). Log here refers to the natural logarithm).

5. [20pts] Consider an extended model of (2) given by (3). For this problem, assume that

the Gauss-Markov assumptions hold for (3).

a. Estimate equation (3) and present the results in equation or tabular form,

including the sample size and R2.

b. Interpret Û1 and Û2 .

c. Compare ûn and ß1 obtained in question 4 (from model (2)). What do you

conclude about the sign of the bias on ß, in model (2)?