MATH 302 APU Cost of Living Multiple Linear Regression Model Executive Summary

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nebq78216

Mathematics

MATH 302

American Public University

MATH

Description

A marketing company based out of New York City is doing well and is looking to expand internationally. The CEO and VP of Operations decide to enlist the help of a consulting firm that you work for, to help collect data and analyze market trends.

You work for Mercer Human Resources. The Mercer Human Resource Consulting websitelists prices of certain items in selected cities around the world. They also report an overall cost-of-living index for each city compared to the costs of hundreds of items in New York City (NYC). For example, London at 88.33 is 11.67% less expensive than NYC.

More specifically, if you choose to explore the website further you will find a lot of fun and interesting data. You can explore the website more on your own after the course concludes.

https://mobilityexchange.mercer.com/Insights/ cost-of-living-rankings#rankings

ASSIGNMENT GUIDANCE:

In the Excel document, you will find the 2018 data for 17 cities in the data set Cost of Living. Included are the 2018 cost of living index, cost of a 3-bedroom apartment (per month), price of monthly transportation pass, price of a mid-range bottle of wine, price of a loaf of bread (1 lb.), the price of a gallon of milk and price for a 12 oz. cup of black coffee. All prices are in U.S. dollars.

You use this information to run a Multiple Linear Regression to predict Cost of living, along with calculating various descriptive statistics. This is given in the Excel output (that is, the MLR has already been calculated. Your task is to interpret the data).

Based on this information, in which city should you open a second office in? You must justify your answer. If you want to recommend 2 or 3 different cities and rank them based on the data and your findings, this is fine as well.

DELIVERABLE REQUIREMENTS:

This should be ¾ to 1 page, no more than 1 single-spaced page in length, using 12-point Times New Roman font. You do not need to do any calculations, but you do need to pick a city to open a second location at and justify your answer based upon the provided results of the Multiple Linear Regression.

The format of this assignment will be an Executive Summary. Think of this assignment as the first page of a much longer report, known as an Executive Summary, that essentially summarizes your findings briefly and at a high level. This needs to be written up neatly and professionally. This would be something you would present at a board meeting in a corporate environment. If you are unsure of an Executive Summary, this resource can help with an overview. What is an Executive Summary?

THINGS TO CONSIDER:

To help you make this decision here are some things to consider:

  • Based on the MLR output, what variable(s) is/are significant?
  • From the significant predictors, review the mean, median, min, max, Q1 and Q3 values?
    • It might be a good idea to compare these values to what the New York value is for that variable. Remember New York is the baseline as that is where headquarters are located.
  • Based on the descriptive statistics, for the significant predictors, what city has the best potential?
    • What city or cities fall are below the median?
    • What city or cities are in the upper 3rd quartile?

Unformatted Attachment Preview

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.935824078 0.875766706 80.12% 8.30945321 17 ANOVA df Regression Residual Total SS 4867.380768 690.4701265 5557.850894 MS 811.2301279 69.04701265 Coefficients Standard Error 35.63950178 15.41876933 -0.003212852 0.003974813 0.299650003 0.076964051 16.59481787 6.713301249 2.912081706 1.98941146 -0.889805486 0.740190296 -2.527438053 6.484555358 t Stat 2.311436213 -0.808302603 3.89337619 2.47193106 1.463790555 -1.202130709 -0.389762738 6 10 16 Intercept Rent (in City Centre) Monthly Pubic Trans Pass Loaf of Bread Milk Bottle of Wine (mid-range) Coffee RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Predicted Cost of Living Index 34.32607137 53.21656053 49.41436121 58.63611785 73.08449538 86.50256003 75.89216916 67.7257781 90.51996071 81.07358731 83.80564633 80.02510391 82.41624318 97.75654811 87.73993924 86.81668291 94.36817468 Residuals -2.586071368 -2.266560525 -3.964361215 4.42388215 5.105504624 -3.052560026 6.307830843 -0.975778105 -16.45996071 8.866412685 9.134353675 -8.37510391 3.483756815 2.243451893 3.040060757 1.11331709 -6.038174677 Standard Residuals -0.39366613 -0.345028417 -0.603477056 0.673427882 0.777188237 -0.464677621 0.960213003 -0.148538356 -2.50562653 1.349694525 1.390481989 -1.274904778 0.530316788 0.341510693 0.462774913 0.169475303 -0.919164446 F Significance F 11.74895331 0.00049963 P-value 0.043401141 0.437722785 0.002993072 0.032995588 0.173964311 0.257006081 0.704884259 City Mumbai Prague Warsaw Athens Rome Seoul Brussels Madrid Vancouver Paris Tokyo Berlin Amsterdam New York Sydney Dublin London Lower 95% 1.284342794 -0.012069287 0.128163411 1.636650533 -1.520603261 -2.539052244 -16.97592778 Upper 95% 69.99466077 0.005643584 0.471136595 31.55298521 7.344766672 0.759441271 11.92105168 Lower 95.0% Upper 95.0% 1.284342794 69.99466077 -0.012069287 0.005643584 0.128163411 0.471136595 1.636650533 31.55298521 -1.520603261 7.344766672 -2.539052244 0.759441271 -16.97592778 11.92105168 City Mumbai Prague Warsaw Athens Rome Seoul Brussels Madrid Vancouver Paris Tokyo Berlin Amsterdam New York Sydney Dublin London mean median min max Q1 Q3 New York Cost of Living Index 31.74 50.95 45.45 63.06 78.19 83.45 82.2 66.75 74.06 89.94 92.94 71.65 85.9 100 90.78 87.93 88.33 75.49 82.2 31.74 100 66.75 88.33 100 Rent (in City Centre) $1,642.68 $1,240.48 $1,060.06 $569.12 $2,354.10 $2,370.81 $1,734.75 $1,795.10 $2,937.27 $2,701.61 $2,197.03 $1,695.77 $2,823.28 $5,877.45 $3,777.72 $3,025.83 $4,069.99 $2,463.12 $2,354.10 $569.12 $5,877.45 $1,695.77 $2,937.27 $5,877.45 Monthly Pubic Trans Pass $7.66 $25.01 $30.09 $35.31 $41.20 $50.53 $57.68 $64.27 $74.28 $85.92 $88.77 $95.34 $105.93 $121.00 $124.55 $144.78 $173.81 $78.01 $74.28 $7.66 $173.81 $41.20 $105.93 $121.00 Loaf of Bread $0.41 $0.92 $0.69 $0.80 $1.38 $2.44 $1.66 $1.04 $2.28 $1.56 $1.77 $1.24 $1.33 $2.93 $1.94 $1.37 $1.23 $1.47 $1.37 $0.41 $2.93 $1.04 $1.77 $2.93 Milk $2.93 $3.14 $2.68 $5.35 $6.82 $7.90 $4.17 $3.63 $7.12 $4.68 $6.46 $3.52 $4.34 $3.98 $4.43 $4.31 $4.63 $4.71 $4.34 $2.68 $7.90 $3.63 $5.35 $3.98 Bottle of Wine (mid-range) $10.73 $5.46 $6.84 $8.24 $7.06 $17.57 $8.24 $5.89 $14.38 $8.24 $17.75 $5.89 $7.06 $15.00 $14.01 $14.12 $10.53 $10.41 $8.24 $5.46 $17.75 $7.06 $14.12 $15.00 Coffee $1.63 $2.17 $1.98 $2.88 $1.51 $1.79 $1.51 $1.58 $1.47 $1.51 $1.49 $1.71 $1.71 $0.84 $2.26 $2.06 $1.90 $1.76 $1.71 $0.84 $2.88 $1.51 $1.98 $0.84 MATH302 Final Project Description Evaluation/Grading of your Final Project Math 302 Final Project will open up Friday morning of Week 6 in the course. You have 3 full weekends to review and work on the Final Project. Content addressed in the Final Project In the final project, you are given a data set and a regression output. The concept of a data set should be something that you are familiar with because you collected one during Week 1. There are descriptive statistics that go along with said data set, which should also be familiar because you calculated descriptive statistics during Week 2. The Regression output won’t look familiar to you until Week 7. Once you go through the Lessons and the Discussion Forum, (particularly your second response post) you should be familiar on how to run a Regression and what a Regression output looks like from the ToolPak. By the end of Week 7, you will have all the information needed to write up the Final Project. There is nothing new that you learn in Week 8 needed for the write up of the final project. Final Project Overview The final project is worth 100 points and no calculations are needed. You will write up an Executive Summary on what city you chose to open a second location in and justify the results. Again, no calculations are needed because you will be writing up your own Executive Summary that will then be submitted through Turnitin. From Turnitin, an originality report will be generated. No Turnitin report should exceed 20% of originality because you are writing this up in your own words. If any originality report is over 20%, then further action will need to be required from your instructor. This can include an automatic failure and 0 for plagiarism. If you have questions on what Academic Plagiarism is, please contact your instructor. Grading Breakdown: 1) Executive Summary – up to 10% a. Please review what an Executive Summary looks like: ▪ What is an Executive Summary? b. Must have cover page. 2) Grammar – up to 10% a. Spell and grammar check your work. b. Make sure you have correct punctuation and complete sentences. 3) State significant predictors – up to 25% a. Must state which predictors are significant at predicting Cost of Living and how do you know. b. Show the comparison to alpha to state your results and conclusion. c. Do these significant predictors make sense, if you want to relocate? 4) Discuss descriptive statistics for the significant predictors – up to 25% a. From the significant predictors, review the mean, median, min, max, Q1 and Q3 values. b. What city or cities fall above or below the median and/or the mean? c. What city or cities are in the upper 3rd quartile? Or the bottom quartile? d. How do these predictors compare to the baseline of NYC? What cost more or less money than NYC? 5) Recommend at least 2 cities to open a second location in – up to 30% a. You must justify your answer for full credit. b. You need to use the Significant Predictors AND Descriptive Statistics in your justification. c. Justification without the use of Significant Predictors WILL NOT get full credit. d. Justification without the use of Descriptive Statistics WILL NOT get full credit. You need to use both. e. For example, let’s look back at London. London at 88.33, is 11.67% less expensive than NYC. But that doesn’t mean London is a good place to open a second location once you discuss the significant predictors and how it relates back to each city. f. Use what you have learned in the course and analyze all the data not just what you see on the surface. g. You must use the numbers and the output to justify your answers. Do not use any outside resources to justify your answer. Only use Significant Predictors AND Descriptive Statistics.
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Explanation & Answer

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Executive Summary
This report uses a multiple linear regression model to analyze the Cost of Living using Rent
(in City Centre), Monthly Pubic Trans Pass, Loaf of Bread, Milk, Bottle of Wine (mid-range), and
Coffee as the predictor variables for 17 different countries. Out of the six predictor variables in the
model, only two variables are significant in predicting the index of cost of living. The two variables
of significance are the price of a one-pound loaf of bread and that of the monthly transportation
pass because both have p-values lower than 0.05. The coefficient of determination, 0.8758, shows
that the model predicts approximately 87.58% of the variation in the index of cost of living. Since
the model explains a large proportion of the dependent variable, it is applicable in predicting the
cost of living index. The monthly transportation pass has a coefficient of 0.2997, while the price
of a loaf of bread has a coefficient of 16.59. An increase in the monthly transportation pass by a
dollar is estimated to increase the living cost index by 0.2997. Similarly, an increase in the price
of a one-pound loaf of bread by a dollar will raise the cost of living index by 16.59. These
predictors make sense because both variables are essential. A worker is bound to use both a
tra...

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