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- QUESTION
The research firm LL Research collected data from 200 client businesses. They want to determine how the businesses compare among four variables:
2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits
Two-Year Average Number of EmployeesData collected for the sample of 200 businesses is contained in the file named Businesses. Use all 200 data points.
Managerial Report
Prepare a report using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client business. Be sure to include the following three items in your report.Find descriptive sample statistics (mean, median, two quartiles Q1 and Q3, minimum, maximum, range, sample standard deviation, and coefficient of variation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the client businesses.
Compute the percent change in profit from 2015 to 2016 for each business. Then use the z-score to determine which businesses were outliers with respect to percent change in profit.
Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.
Write a report that adheres to the Written Assignment Requirements and APA Requirements. You should have in-text citations and a reference page. An example paper is provided in the Guide to Writing with Statistics (attached)Submit your Excel file in addition to your report.
Requirements:
Paper must be written in third person.
Your paper should be 3 pages in length (not counting the title page and references page) and cite and integrate at least two credible outside sources.
Include a title page, introduction, body, conclusion, and a reference page.
The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
| Subject | Business | Pages | 6 | Style | APA |
|---|
Answer
Analytical Comparisons of Businesses
Business analytics has vastly grown to influence market shifts and competition for businesses organizations that have embraced the technique in strategizing. The importance of analytics is even gaining more popularity in the entire spectrum of business that has been exponentially dynamic. Comparative analytics is a mechanism that is used by many organizations for both scenario and extrapolated business analysis, as it offers an effective platform for laying strategy in relation to competitors and in the process gaining competitive advantage (Stubbs, 2011). This paper is a report on comparative statistical analysis of 200 companies based on certain variables that define the market dynamics.
Descriptive Statistics
The description of the dataset of the client businesses is presented in the measure of central tendency and dispersion.
|
Descriptive Statistic |
2015 Profit |
2016 Profit |
Two Year avg. change in daily no. of visits |
Two Year Average Number of Employees |
|
Mean |
5695.625 |
5332.625 |
49.23 |
61.425 |
|
Median |
6116 |
5401 |
52.5 |
64 |
|
Mode |
6541 |
1063 |
83 |
79 |
|
Standard Deviation |
2440.808653 |
2653.386812 |
35.66281371 |
22.33829384 |
|
Sample Variance |
5957546.879 |
7040461.572 |
1271.836281 |
498.9993719 |
|
Kurtosis |
-1.02042965 |
-1.187707891 |
-0.363759321 |
-1.077074488 |
|
Skewness |
-.127807021 |
-0.024452848 |
-0.517402667 |
-0.13801677 |
|
Range |
8981 |
9035 |
161 |
80 |
|
Minimum |
992 |
930 |
-60 |
20 |
|
Maximum |
9973 |
9965 |
101 |
100 |
|
First Quartile |
3702.5 |
2823.75 |
19.75 |
41.75 |
|
Third Quartile |
7561.5 |
7492 |
82.25 |
79 |
|
Coefficient of Variation |
43% |
50% |
72% |
36% |
|
Upper Bound |
5355.28 |
4962.64 |
44.26 |
58.31 |
|
Lower Bound |
6035.97 |
5702.61 |
54.20 |
64.54 |
Table 1: Table of Descriptive Statistics.
The measures of central tendency (Mean, Mode and Median) are shown in the data. These describe the central values of the variables that contribute to the success of the client businesses. All the variables posted a negative skewness, meaning that all the variables in the dataset had their means smaller than the median (data has longer left tail in each case). However, the skewness can be described as approximately symmetrical due to the skewness values that fall between the -0.5 and 0.5 region. Moreover, there is 95% confidence that the confidence intervals for the variables is as indicated in the table above, meaning we are 95% confident that the population means will always fall between the lower and upper bounds of the interval.
Further, the coefficients of variation (CV) determine the ratio of the standard deviation to the mean. This is the most appropriate measure for comparing the variables, as it is dimensionless. It helps measure the volatility of the variables which are to be used in comparing the businesses. The lower the value of the coefficient of variation, the more precise the statistic/estimate (Albrecher, Ladoucette, & Teugels, 2010).
Outliers
In order to determine which businesses were outliers with respect to percent change in profit, the z score is used to determine if the computed values of the businesses fall within the 3 Standard deviation interval, with -3SD being the Lower Limit and 3SD being the Upper Limit. The values are standardized to fit the interval using the Z score where:
Z =
The computed Z score is then compared with the range of 6SD, where values below -3 and those above 3 are considered outliers. In this dataset, the client businesses tabulated with their respective Z scores were found to be outliers (based on the percentage profit change from 2015 to 2016).
|
Business |
% Profit change from 2015 to 2016 |
Z Score |
|
First Supply Group; Inc. |
542% |
4.308447726 |
|
Sears Grand |
730% |
5.874148852 |
|
Shamrock Computer |
532% |
4.224348364 |
|
Fiduciary Trust Co. Intl |
400% |
3.130355595 |
|
The Jones Shop |
682% |
5.47270064 |
|
Florida Villa Vacations Inc. |
393% |
3.071344768 |
Table 2: Businesses considered Outliers based on their Z score on Profit change between 2015 and 2016.
Relationship between Change in Profits and Change in Daily Number of Visits
The correlation between the two variables is -0.47 (p<0.05). This is a significant moderate negative correlation at 95% confidence level.
Fig 1: Scatter plot of the relationship between Change in Profits and Change in Daily Number of Visits
The moderately negative correlation indicates that with a shift in one of the variables (either change in profit or change in daily number of visits), there is likely to be a moderate shift in the other variable in the opposing direction.
Relationship between Change in Profits and Two Year Average Number of Employees
The correlation between the two variables is 0.0106 (p>0.05). Therefore, it is conclusive that the weak positive correlation between the two variables is not significant at 95% confidence interval. This means that while it is expected that shift in one of these variables will cause minimal change in the other variables (which ideally is negligible), this linear relationship is not significant.
Fig 2: Scatter plot for relationship between change in profits and two year average number of employees.
Relationship between Change in Daily Number of Visits and Number of Employees
The correlation coefficient between the two variables is a weak positive one (r = 0.0847, p > 0.05). This also means that the correlation is not significant at 95% confidence level. Therefore, there is 95% confidence that there is no relationship between the two variables.
Fig 3: Figure of correlation between the variables Change in Daily Number of Visits and Number of Employees.
Conclusion
Based on the above insights, it is important to note that some businesses made profits into 2016 that would be termed as abnormal (being outliers). Moreover, the businesses can best be compared by use of the two variables “Two Year Average Number of Employees” and “2015 Profit” as they are the variables that have the highest precision (determined by their comparatively lower CV). Moreover, it is notable that the only significant relationship among the variables is between “Two Year avg. change in daily no. of visits” and “% Profit change from 2015 to 2016” which have a moderate negative correlation.
References
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Albrecher, H. A. N. S. J. O. R. G., Ladoucette, S. A., & Teugels, J. L. (2010). Asymptotics of the sample coefficient of variation and the sample dispersion. Journal of Statistical Planning and Inference, 140(2), 358-368. Stubbs, E. (2011). The value of business analytics: Identifying the path to profitability (Vol. 43). John Wiley & Sons.
Appendix
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