# 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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