Case Study 14.2: Sapphire Coffee—Part 1 – Guidance and Further Instructions
Jennie Garcia could not believe that her career had moved so far so fast. When she left graduate school with a master’s degree in anthropology, she intended to work at a local coffee shop until something else came along that was more related to her academic background. But after a few months, she came to enjoy the business, and in a little more than a year, she was promoted to store manager. When the company for which she worked continued to grow, Jennie was given oversight of a few stores.
Now, eight years after she started as a barista, Jennie was in charge of operations and planning for the company’s southern region. As a part of her responsibilities, Jennie tracks store revenues and forecasts coffee demand. Historically, Sapphire Coffee based its demand forecast on the number of stores, believing that each store sold approximately the same amount of coffee. This approach seemed to work well when the company had shops of similar size and layout, but as the company grew, stores became more varied. Now, some stores had drive-thru windows, a feature that top management added to some stores believing that it would increase coffee sales for customers who wanted a cup of coffee on their way to work but were too rushed to park and enter the store to place an order.
Jennie noticed that weekly sales seemed to be more variable across stores in her region and was wondering what, if anything, might explain the differences. The company’s financial vice president had also noticed the increased differences in sales across stores and was wondering what might be happening. In an e-mail to Jennie, he stated that weekly store sales are expected to average $5.00 per square foot. Thus, a 1,000-square-foot store would have average weekly sales of $5,000. He asked that Jennie analyze the stores in her region to see if this rule of thumb was a reliable mea-sure of a store’s performance.
The vice president of finance was expecting the analysis to be completed by the weekend. Jennie decided to randomly select weekly sales records for 53 stores. The data are in the file Sapphire Coffee-1. A full analysis needs to be sent to the corporate office by Friday.
Required Tasks:
Identify the major issues (two) of the case.
Briefly summarize the data (include an explanation of the results of descriptive statistics of the data, variables included, how the data was collected, and any pertinent information about the data available in the case study)
Develop a scatter plot of the variables store size vs. weekly sales. Identify the dependent variable. Briefly describe the relationship between the two variables. Students must include the scatter plot in their report.
Fit a linear regression equation to the data.
Please note, consistent with the emphasis on understanding, interpretation, and application of statistical results in this course, the results of fitting a regression based on the data has been provided below. Students are encouraged to try to reproduce these results for their own benefit and to gain additional insight.
In your report explain the method by which such a regression table is obtained.
In your report, explain whether the variable store size is statistically significant in explaining the amount of the variation in weekly sales?
Include in your report, and based on the estimated regression equation, an explanation of whether it appears that the $5.00 per square foot weekly sales expectation the company currently uses is a valid one.
Comment on any other statistically and practically significant values in the results table (for example R-square, F-statistic and P-value, etc.)
Summarize your analyses and findings in a report which may also include any practical recommendation(s) for the attention of the company’s vice president of finance.
Excel output.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.810106516
R Square 0.656272568
Adjusted R Square 0.649532814
Standard Error 277.115539
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 7477595.91 7477596 97.37338 2.02652E-13
Residual 51 3916444.12 76793.02
Total 52 11394040.03
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 1612.466723 294.3407005 5.478232 1.33E-06 1021.553565 2203.38
Store Size (Sq. Ft.) 3.110896951 0.315257559 9.867795 2.03E-13 2.477991479 3.743802
