Applications Of Statistical Methods Assignment.
ADM 2304 – ASSIGNMENT 4 (50 marks)
Due date: Friday, April 9 2021 at 11:30 pm (Brightspace).
Instructions:
• For each numerical question, you must first show your manual computations and then
use Minitab, MS Excel, or any other statistical software to confirm your results. You
must paste your output onto your assignment to show your use of software; however,
this output does not replace any of the steps outlined below. This means that answers that
are exclusively software output will receive only partial marks.
• If you are performing a hypothesis test, make sure you state the hypotheses, the level of
significance, the rejection region, the test statistic (and/or p-value, if requested), your
decision (whether to reject or not to reject the null hypothesis), and a conclusion in
managerial terms that answers the question posed. These steps must be completed in
addition to any software output.
• The data for this homework assignment can be found in the files Assign4Data.mpx and
Assign4Data.xlsx.
• Your assignment must be typed and uploaded to Brightspace in one single pdf file.
You may upload several files, but only the most recent submission before the deadline will
be graded. You must start each question on a different page and answer the questions
in order. Students who fail to follow these instructions will be penalized with 10% of the
marks (for example, if the assignment is marked out of 50, the penalty will be five marks).
• Late submissions will be accepted according to the late submission policy discussed in class
and posted on Brightspace.
• Remember to include your integrity statement. Assignments submitted without a signed
integrity statement will not be graded.
Question 1 – Investment Portfolio (12 marks)
Consider the daily percent change in the stock price of two companies, A and B, in an
investment portfolio. The dataset is called Investment Portfolio.
Answer the following questions manually. Use statistical software or MS Excel for help with
the computation of any summary statistics needed for manual computations.
a) Draw a scatterplot of the company A daily percent changes against the company B daily
percent changes. Describe the relationship between daily percent changes that you see
in this scatterplot.
b) Determine the regression equation to predict the daily percent change in the stock price
of company A from the daily percent change in the stock price of company B. Interpret
the value of the slope coefficient.
c) Find the correlation between the percent changes. Does the correlation value support
your description of the scatterplot in part a)?
d) Compute the corresponding coefficient of determination and interpret its value. In
financial terms, it represents the proportion of non-diversifiable risk in company A.
e) Compute the 95% confidence interval for the slope coefficient.
f) Test at the 5% significance level whether the slope coefficient is significantly different
from 1, representing the beta of a highly diversified portfolio. Don’t forget to show your
computations.
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Questions 2 – Location Analysis (38 marks)
Location analysis is an important decision in operations management of production and
service industries. A critical decision for many organizations is where to locate a processing
plant, warehouse, retail outlet, etc. A large number of business variables are typically
considered in this decision problem.
The management of a large motel/inn chain is aware of the challenges in choosing new motel
locations. The chain’s management uses the “operating margin,” which is the ratio of the sum
of profit, depreciation, and interest expenses divided by total revenue, to make this type of
decision. In general, the higher the “operating margin,” the greater the success of the
motel/inn.
The chain’s management has collected data on 100 randomly selected of its current inns. By
measuring the “operating margin,” the objective is to predict which sites would likely
generate more profit. Below is a description of the different variables considered in this
analysis.Applications Of Statistical Methods Assignment.
Variable Description
Location ID Number Location identifier
Operating Margin Operating margin, in percent
Number Number of motels, inns, and hotel rooms within 5 miles
Nearest Number of miles to the closest competitors
Enrollment Number of college and university enrollment (in thousands) in nearby college and
universities
Income Average household income (in thousands) of the neighborhood
Distance Distance from downtown
Quality The quality of the service level of the location (1 = bad, 2 = average, 3 = good, 4 =
excellent)
High Speed Internet High speed internet availability (1 = no, 2 = yes)
Gym Gym availability (1 = no, 2 = yes)
The dataset is called Location Analysis.
Part 1 (10 marks)
Using Minitab or any other statistical software, run a simple linear regression model to
predict Operating Margin based on Distance and answer the following questions:
a) Using an appropriate graph, plot Operating Margin versus Distance and comment on the
relationship between these two variables.
b) Write down your estimation of the regression equation for predicting Operating Margin
from Distance. Draw the regression line on the plot in part a).
c) Assuming α = 0.01, test whether Distance has statistically significant predictive power in
estimating Operating Margin. State the hypotheses, provide a test statistic and p-value,
and state your conclusion. Show your calculations.
d) Interpret the values of the regression coefficients (slope and intercept).
Part 2 (6 marks)
Using Minitab or any other statistical software, now perform a multiple linear regression
analysis of Operating Margin (response variable) against all the remaining variables as
predictors, excluding Location ID Number.
a) Write down the regression equation and provide at least two summary measures of the
fit of the model. Based on the summary measures, does the model provide a good fit for
the data? Explain.
b) Plot the residuals against the fitted values and comment on whether the usual model
conditions are met.
c) The variable Operating Margin New in the dataset corresponds to the Operating Margin
variable from which some values have been recorded as missing values. Identify those
missing values and explain what they are and why they were recorded as missing.
Part 3 (12 marks)
Using statistical software, run the same multiple linear regression model as in Part 2 above
but this time using Operating Margin New as the response variable. Then, answer the
following questions:
a) Briefly compare the resulting regression equation and fit with those obtained in Part 2.
b) Plot the residuals against the fitted values and comment on whether the model complies
with the usual conditions for multiple linear regression.
c) Provide an interpretation for the model intercept and for the regression coefficients
associated with variables Income and Distance. Is an interpretation of the model intercept
appropriate in this case? Compare the value of the regression coefficient for Distance with
the one obtained in Part 1 above and clearly explain any difference.
d) Do you see any justification for dropping any variable(s) from the model? Explain (hint:
multicollinearity; the significance of predictors).Applications Of Statistical Methods Assignment.
e) Run a final model using Operating Margin New as the response variable and including
only the significant predictors (hint: those with a p-value ≤ 5%).
f) Test the overall significance of the final model in part e). Use a 1% significance level and
follow all the steps for hypothesis testing indicated in the Instructions section.
Part 4 (10 marks)
Based on your final model in Part 3 above, answer the following questions:
a) Test the marginal contribution of Quality, assuming that the other variables in the model
remain constant. Use a 1% significance level, and make sure you follow all the steps for
hypothesis testing indicated in the Instructions section. Show the computation of the tstatistics (i.e., the ratio used to compute it).
b) Calculate the 99% prediction interval for the actual operating margin of a new location
with the same characteristics as those for Location ID Number 3098 in the data file. Check
if the prediction interval includes the actual operating margin associated with Location
ID Number 3098 and explain why it does or does not.
c) Calculate the 99% confidence interval for the mean operating margin of a new location
with the same characteristics as those for Location ID Number 3098 in the data file.
Explain any difference between the size of this interval and the one in part b) above
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