ETC1010:Assignment 2 Semester 2:2015
Instructions
Assignment 2 is due on Wednesday, 21 October, 2015 at 5pm. You are required to submit a hard copy of the assignment in the assignment drop box on Level 7 (outside the Admin Office E757) in the Menzies Building. Your hard copy should be a typed document, containing the relevant tables from Excel, as well as the rest of the solutions. In addition, you are required to email your Excel spreadsheets to your tutor by the same date.
Question 1 [20pt]:
ROFiL Pizza Delivery is planning to open new stores in different other regions so that the excess demand for the pizza home delivery services is met. The locations under consideration and the potential areas (coded in numbers 1-9) that can be reached quickly from the considered locations for home delivery are given in the following table:
Store
Location Potential Areas Covered
L1 3, 4, 6, 8
L2 1, 5, 9
L3 1, 4, 7
L4 2, 6, 7
L5 3, 4, 9
L6 2, 7, 9
L7 4, 8, 9
L8 1, 2, 5, 6
L9 3, 6, 8
Develop and solve an integer programming model that could be used to find the minimum number of stores to open in order to cover customers of all areas for the home delivery service.
Question 2 [20pt]:
Jim is trying to solve a problem where point A should be within the radius of 15cms from the points B, C, D, E and F. The decision variables are defined as below.
X = horizontal coordinate of point A
Y = vertical coordinate of point A
The data on the distances is given below:
Formulate a model to find the optimal location of the point A and solve it in excel.
Question 3 [20pt]:
George & Kate are interested in an investment property. They found a house on a main street next to several shops. Rumours say that it will be possible to rezone this property from residential into commercial. If the council approves the rezoning request, George & Kate will be able to renovate the house and lease it as a clinic building. However, if rezoning is not approved, the couple will lose money on renting this house as a regular residential house. The potential profits in thousands of dollars are shown in the following payoff table:
State of Nature
Decision Alternative Rezoning approved, s1 Rezoning not approved, s2
Purchase, d1 600 (-200)
Do not purchase, d2 0 0
a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? What is the expected profit?
b. The couple can purchase an option to buy the house. (Under the option the couple maintains the rights to buy the house in three months time). This will give George & Kate opportunity to learn more about the possibility of rezoning. The probabilities for rezoning are the following,
Let H = high resistance to rezoning & L=low resistance to rezoning
P(H) = 0.55 & P(L) = 0.45
P(s1|H) = 0.18 & P(s2|H) = 0.82
P(s1|L) = 0.89 & P(s2|L) = 0.11
Draw the decision tree for the problem
c. What is the optimal decision strategy if the couple uses the option period to learn more about the resistance to rezoning before making the purchase decision?
d. If the option will cost the couple additional $10,000, should they purchase the option? Why?
e. What is the maximum amount the couple should pay for this option?
Question 4 [40pts]:
The data set GDPData.xls contains data on GDP growth (GDP), population growth (PoP), investment (I) and secondary school enrolment rates (SS) for 86 countries. We believe that the GDP growth of country “i” is related to population growth (PoP), investment (I) and secondary school enrolment rates (SS) according to the linear regression model:
𝐺𝐷𝑃𝑖 = 𝛽0 + 𝛽1𝑃𝑜𝑃𝑖 + 𝛽2𝐼𝑖 + 𝛽3𝑆𝑆𝑖 + 𝜖𝑖.
We will use the above regression model to test various hypothesis about the coefficients of the above linear regression model.
1. Run the above regression using excel and the data in GDPData.xls
2. Using the regression results, we will now test various hypotheses about 𝛽1, 𝛽2 𝑎𝑛𝑑 𝛽3 in the above regression model.
a. We suspect that population growth is positively related to GDP growth. Test the null hypothesis of no relationship between GDP and PoP against the alternative that the relationship is positive.
i. State the null and alternative hypothesis. Is this a one or two-sided test?
ii. Find the test statistic in the excel results.
iii. What critical value should we use in the hypothesis test?
iv. What is our decision?
b. There is a long standing belief among economists that the relationship between investment and GDP growth is positive. Test this hypothesis using the regression output obtained in question 1.
i. State the null and alternative hypothesis. Is this a one or two-sided test?
ii. Find the test statistic in the excel results. iii. What critical value should we use in the hypothesis test?
iv. What is our result
c. We believe the relationship between school enrolment and GDP growth is positive. Using the regression results in question 1.
i. State the null and alternative hypothesis. Is this a one or two-sided test?
ii. Find the test statistic in the excel results. iii. What critical value should we use in the hypothesis test? iv. What is our result?
v. Use an approach based on confidence intervals to test for the significance of school enrolment. State all testing steps.
d. Comment on the overall fit of the model using R-squared.
e. Test for the overall significance of the regression model using the F-test
3. Plot the residuals from this regression and use the result to answer the following question
a. Do the residuals appear uniformly distributed?
b. Graphically do there appear to be any outliers? If so, please state which countries (1-86) appear to be outliers.