Expert answer:Statistics Assignment Completion – Focusing on Dat
Expert answer:Hi there – i have a quick stats assignment to complete which I’d like some help with. It’s basic undergrad statistics, mostly descriptive. Please note that only excel can be used (not R, etc.)
assignment_december.docx
question_2___hedge_fund.xlsx
question_3___fcm.xlsx
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1. Descriptive Statistics and Normal Distribution: Vasiliki is a T-Shirt designer who sells her products
exclusively online. To cut costs, she outsources the production in Asia. As it takes more than 60 days for
Vasiliki to receive her order from her Asian suppliers, she has to place her order before the summer
selling season starts, and she has no opportunity to replenish inventory during the selling season. This
April, Vasiliki needs to decide how much to order from her suppliers for this summer. Based on historical
data, Vasiliki estimates that the demand of her T-shirt this year approximately follows a Normal
distribution with mean 4650 and standard deviation 550.
a) (7 points) Last year, Vasiliki ordered 5000 T-shirts. If she orders the same quantity this year, what is
the probability that she will sell all T-shirts?
b) (8 points) Based on her calculation of the margins and inventory related costs, Vasiliki wants to make
sure that she can reach a 98% service level, i.e., she can satisfy all demand 98% of the time. To achieve
this target, how many T-shirts should Vasiliki order?
c) (5 points) Remembering vaguely from his college statistics class, Gabriel, Vasiliki’s assistant, warns
Vasiliki that the Normal distribution assumption is problematic here: for the demand to follow a Normal
distribution, there must be times that demand is negative. So one cannot use this assumption to determine
inventory level. Do you agree with Gabriel? Why?
2. Confidence Interval and Hypothesis Testing: Denial Kahn decides to invest one million dollars in a
hedge fund. He is considering two candidates: YS Asset Management’s flagship fund YS Growth, and
HAZ Asset Management’s HAZ Alpha. The annual returns (net fees) of the two funds from 2007 – 2016
are summarized in Q2_Hedge Fund.xlsx.
a) (10 points) Based on the information you have, what is your best estimate (including confidence
interval) of the average annual return of these two funds?
b) (10 points) Nick Smith, the fund manager of YS Growth is proud of the high return of the fund. In
fact, he claims that the average return of his fund will be at least 2% higher than that of HAZ Alpha.
Based on the data, can you accept Nick’ claim? Please explain clearly how you set up the statistical test
and draw your conclusion.
c) (5 points) Are you concerned that the conclusion is drawn based on only 10 years of data? Why?
d) (5 points) If you are the sale manager of HAZ, what do you think is the selling point of your fund?
3. Regression: Multiple Regression: Frank’s Convenience Marts are located throughout metropolitan
Chicago in the States. Suzanne, the business development manager, plans to open a new store in the
Jackson Park neighbourhood in south Chicago. She has found a potential location. To help with the
financial analysis, she wants to forecast the daily sales based on data she draws from current stores.
Specifically, she selected a random sample of 15 existing stores, and her assistant Nick helped her collect
average daily sales, the floor space (area, square feet) and the median income of families in that ZIP code
region for each store. The data is under the worksheet SaleAreaIncome in the file Q3_FCM.xlsx.
a) (5 points) Develop a correlation matrix. What is the correlation between Daily Sales and the other two
variables? Interpret their managerial implications.
b) (5 points) Conduct a simple regression using Daily Sales as the dependent variable and Store Area as
independent variable. Provide the regression output and write out the regression equation based on this
model.
c) (10 points) Conduct a multiple regression using Daily Sales as the dependent variable and Store Area
and Area Income as the independent variables. Provide the regression output and write out the regression
equation based on this model. Explain the meaning of each of the coefficients. Should all independent
variables be included in the model, and why? What is the overall quality of this regression model?
d) (5 points) In the regression in c), is the coefficient associated with Store Area the same as the one
obtained in b)? Does this worry you? Why?
e) (5 points) The location Suzanne has in mind is in a neighbourhood with a median area income of
$45000, and the store area is 550 square feet. Can you help Suzanne predict the daily sales for the store?
How confident are you about the estimate?
f) (5 points) Nick reminded Suzanne that the landlord of the potential location highlighted that the
location has 5 designated parking spaces. Nick then collected parking space information for the 15
sampled stores and the data is provided under the worksheet Parking in Q3_FCM.xlsx. How will this new
information change your forecast for the new location?
g) (8 points) Based on her experience, Suzanne believes that if a store is close to (within a 200metre radius) to a gas station, the store’s sales will be affected. However, the effect depends on
whether the neighbouring gas station has a convenient store of its own or not. If the gas station
does not have its own convenient store, then a gas station in the proximity should increase sales
for the FCM. If it does, then it hurts the sales of the FCM. Now Nick has also collected
information about the gas stations (the data is available under the worksheet Gas Station in
Q3_FCM.xlsx). Nick then suggests that they should create a new “dummy variable” to capture
the impact of the gas station. Specifically, he proposes to assign a value of “`0” to the dummy
variable if the store is NOT close to a gas station, a value of “1” to the dummy variable, if the
store is close to a gas station without a convenient store, and a value of “-1” to the dummy
variable if the store is close to a gas station with a convenient store. Do you agree with Nick’s
approach? If yes, please conduct the analysis as Nick suggests and interpret the results
for Suzanne. If you do not agree with Nick, please explain why, and help Suzanne estimate the impact of
a gas station in proximity to test her hypotheses.
h) (7 points) Suzanne also hypothesizes that the Daily Sales per square meter is lower for larger stores
than for smaller stores. Can you help Suzanne design and conduct a regression analysis to test this
hypothesis? Does your find support Suzanne’s hypothesis?
Year
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
YS Growth (%) HAZ Alpha (%)
14.16
4.52
-33.8
-16.51
35.45
22.44
47.86
13.37
14.45
4.43
25.86
7.49
49.08
24.99
23.73
11.17
-2.17
0.55
-15.3
7.85
Sampled Mart Daily Sales Store Area
1
1840
532
2
1746
478
3
1812
530
4
1806
508
5
1792
514
6
1825
556
7
1811
541
8
1803
513
9
1830
532
10
1827
537
11
1764
499
12
1825
510
13
1763
490
14
1846
516
15
1815
482
Area Income ($
thousand)
44
51
45
46
44
46
49
52
46
46
48
47
48
45
43
Sampled Mart
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Parking Spaces
6
4
7
7
5
6
4
6
5
5
3
8
4
8
7
Sampled Mart
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Next to gas station?
Yes, the gas station has its own convenient store.
No
Yes, the gas station has its own convenient store.
Yes, the gas station has its own convenient store.
Yes, the gas station does not have its own convenient store.
No
Yes, the gas station does not have its own convenient store.
No
Yes, the gas station does not have its own convenient store.
No
No
Yes, the gas station has its own convenient store.
No
No
No
…
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