# 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
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
• 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,
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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##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Math Week 8

Pay attention to the full question (all parts of the question).

1.  For the following system of equation, find a solution or show that no solution exists:

2y +3x – 3z  = 16

2x + 3y + 4z = -8

3z + 2x – 5y = 26

Show details:

The solution is:  x = 6;   y = -4;  z = -2

2. A goldsmith combined an alloy that costs \$4.30 per ounce with an alloy that costs \$1.80 per ounce. How many ounces of each were used to make a mixture of 200 ounces costing \$2.50 per ounce?

Show details:

3. An airplane travels 1,200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?

Show all work.

4) Write the augmented matrix for the system of equations shown.

5z + 4x + 4y = 22

3x + 7y = -2z -17

4x + 3y + 3z =6

5) Write the system of equations for the augmented matrix shown.

-2   3  4  |  18

-3   4  2  |  5

-2   3  3  |  12

6) For the following system of equation, find a solution or show that no solutionexists:

5y +3z – 4x  = -3z + 3

4z + 6y + 5x = -19

5y + 3x + 4z = -12

7) For the following system of equation, find a solution or show that no solutionexists:

x + y + z  = 1

2x – 3y + 7z = 0

3x – 2y + 8z = 4

8) If 105 people attended a concert and tickets for adults costs \$2.50 while tickets for children cost \$1.75 and total receipts for the concert were \$228, how many children and how many adults went to the concert?

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Competencies

In this project, you will demonstrate your mastery of the following competencies:

• Apply statistical techniques to address research problems
• Perform regression analysis to address an authentic problem

## Overview

The purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.

## Scenario

You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict median housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the median housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.

## Directions

Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate County Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.

Note: Present your data in a clearly labeled table and using clearly labeled graphs.

Specifically, include the following in your report:

Introduction

1. Describe the report: Give a brief description of the purpose of your report.
2. Explain when using linear regression is most appropriate.
1. When using linear regression, what would you expect the scatterplot to look like?
3. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Data Collection

1. Sampling the data: Select a random sample of 50 counties.
1. Identify your response and predictor variables.
2. Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.

Data Analysis

1. Histogram: For your two variables, create histograms.
2. Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
3. Interpret the graphs and statistics:
1. Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
2. Compare and contrast the shape, center, spread, and any unusual characteristic for your sample of house sales with the national population. Is your sample representative of national housing market sales?

1. Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
1. Explain if a regression model is appropriate to develop based on your scatterplot.
2. Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
1. Identify any possible outliers or influential points and discuss their effect on the correlation.
2. Discuss keeping or removing outlier data points and what impact your decision would have on your model.
3. Find r: Find the correlation coefficient (r).
1. Explain how the r value you calculated supports what you noticed in your scatterplot.

Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.

1. Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
2. Interpret regression equation: Interpret the slope and intercept in context.
3. Strength of the equation: Provide and interpret R-squared.
1. Determine the strength of the linear regression equation you developed.
4. Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.

Conclusions

1. Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
1. Did you see the results you expected, or was anything different from your expectations or experiences?
1. What changes could support different results, or help to solve a different problem?
2. Provide at least one question that would be interesting for follow-up research.

## What to Submit

To complete this project, you must submit the following:

Project One Template: Use this template to structure your report, and submit the finished version as a Word document.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Essay

*There are several assumptions for the use of an independent samples t test. State each of these and the implications should these assumptions be violated. Is it possible for a p value to equal 0? Why or why not? *There are several indices on effect sizes for independent samples t tests. Describe three of these and when one might be used over the others. Next, given a situation in which a research reports a large eta squared effect size (eta squared = .64), why might their reported t value be small and not statistically significant? What may be inference from such a situation? Indicate and provide examples of three of the factors that influence the size of t.

*  For each essay assignment, answer both essay questions using a minimum of 300 words for each essay. A title page (no abstract) and reference page are required. Current APA 7th Edition must be used to cite sources. There must also be 3 References.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Statistic

1.  What does Anova Stand for and what is it used for?

2. In a one way Anova, what is the difference between the among group variation and the within-group variances?

3. What are the 3 assumptions needed to complete the ANOVA analysis and explain

4.  Use the Classwork week 6 excel spreadsheet below and solve the problem provided.  You will need the following table to find the Qcritical value.

##### http://davidmlane.com/hyperstat/sr_table.html

Watch the following video on how to find the tukey-kramer comparison for part b of the problem

the excel file “one-way ANOVA”  workbook provides examples and formulas. Worksheet TK and TK_Formulas provides formulas for the Tukey Kramer part of the problem

5. Go over the Ch. 12 lecture slides and answer the following questions:

a. what are contingency tables used for? Provide 3 reasons

b. Draw a sample Contingency table and put the appropriate labels

c. What is the Chi-Squared Test Statistic? Write out the formula ( do it by hand if you can’t use a math editor program)

d. what is fo ?

e. What is fe  ?

f. Is there a Chi critical value and if so, how do you find it?

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Project: Final Project SPSS With VOICE PRESENTATION

For the final project, you must employ one of the statistical models that you learned in the class, and are listed below:

**Factorial ANOVA

Final Project DETAILS:

A Psychology Professor is interested in understanding factors that impact final exam grades for his 100-level freshman Psychology Statistics class.

For each of the (N=) one-hundred student in the class, the professor collects data for Math Placements results obtained during pre-semester orientation/registration – 38 students had low-level (Developmental) Math skills; 38 were proficient in basic 9th grade Arithmetic and Algebra only;  and 24 students had advanced Math skills at the Calculus level.  Math levels were recorded as 1 = Low Math Skills; 2 = Moderate Skills, and 3 = High math skills.  The professor also obtains data on the number of hours (1, 2, or 3) that each student studied for the exam.

Select and conduct an appropriate analysis to assess impact of math Placement (X1), Study Hours (X2) and possible interaction, on the DV Exam Grades (Y).  Be sure to test the assumptions for that analysis using EDA.

Develop a research hypothesis to test based on the literature. Summarize the results using correct APA style. Be sure to include the appropriate Tables and Graphs. You can use my sample summaries for as a guide for your summary.

ATTACHED is the 2 x 3 Factorial ANOVA SPSS

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Statistical Techniques

For this final paper, you will develop a research proposal to solve a business problem choosing one of the statistical techniques we covered in this course. Your paper must:

• Justify statistical technique choice for your problem.
• Analyze three peer-reviewed research articles applying your chosen statistical technique to similar business problems.
• Synthesize the anticipated type of data you will use for the statistical analysis.
• Propose expected results.
• Evaluate how the analysis results would help solve your business problem.

### Submission Details:

• Submit a 5 – 6 page Microsoft Word document, using APA style.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Skill Exercise

Develop a five-question multiple-choice quiz covering at least three of the topics listed below. Include an answer key with a brief explanation of your choice. Your answer key should include appropriate citations and references to support the accuracy of your answers.

• Scatter diagram
• Correlation coefficient
• Range for correlation coefficient
• Independent and dependent variables
• Simple linear regression
• Multiple linear regression
• Prediction

### Submission Details:

• Submit your quiz as a Microsoft Word document.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!" ## Skill Exercise

Develop a five-question multiple-choice quiz covering at least three of the topics listed below. Include an answer key with a brief explanation of your choice. Your answer key should include appropriate citations and references to support the accuracy of your answers.

• Scatter diagram
• Correlation coefficient
• Range for correlation coefficient
• Independent and dependent variables
• Simple linear regression
• Multiple linear regression
• Prediction

### Submission Details:

• Submit your quiz as a Microsoft Word document. 