Special Problem 4C - Math 50



Coffee and Doughnuts

|Krispy-Kreme |

| |# of Stores |

| |Opened |

|Year | |

|1985 |1 |

|1986 |2 |

|1987 |1 |

|1988 |1 |

|1989 |1 |

|1990 |1 |

|1991 |4 |

|1992 |3 |

|1993 |2 |

|1994 |7 |

|1995 |10 |

|1996 |17 |

|1997 |7 |

|1998 |15 |

|1999 |23 |

|2000 |36 |

In this problem your task is to investigate and compare the impressive growth of Starbucks Coffee and Krispy-Kreme Doughnuts companies, as measured by the number of stores open. The table below shows the number of new Krispy-Kreme stores opened each year from 1985 through 2000. Refer to the company’s web site, for more information.

You will need to extend this table to include the total number of Starbucks stores open each year. The total number of stores open for selected years for the Starbucks Company can be found at their web site . There will be some gaps in the Starbucks data but the data available will be sufficient for our purposes. Your assignment is to construct a linear model comparing the growth of Starbucks and Krispy-Kreme by using what you have learned in Chapters 4-5.

In a report - Type up the following.

1. Title page with an appropriate title, your name and IB number and your pledge. [5 points]

2. Individual Analysis [34 points total]

Either by computer or by hand (label completely) plot the total number of stores opened by year for each company. [5 points each graph]

Describe the growth that each company has experienced. [2 points each company]

Give the linear regression equation for each (to three significant figures). [3 points each]

Either by computer or by hand, sketch the linear equations for each. [2 points each]

Report the correlation and the R2 value for each. Interpret these numerical results. [4 points each]

Use your final model to predict the number of stores in 2003? in 2010? How far into the future are you willing to make a prediction, using your model? Explain why. [5 points each company]

3. Comparative Analysis [20 points total]

Either by computer or by hand (label completely) plot the total number of stores opened by year for Starbucks against Krispy-Kreme. [5 points]

Give the linear regression equation for your plot (to three significant figures). [3 points]

Either by computer or by hand, include the sketch of the linear equation. [3 points]

Report the correlation and the R2 value. Interpret these numerical results. [4 points]

Comment on the scatterplot, the linear equation you found and describe the relationship between the two companies. [6 points]

The Report. Describe your investigation in a report. Your paper should not consist of a list of answers, but rather a free-flowing, sequential, logical description of the steps you took and the results you got from beginning to end. Tell the story, from the introduction to the analysis to the conclusions with all of the necessary supporting calculator screen shots or computer plots and numerical summaries. In particular, write your report so that the reader can follow your reasoning as you proceed through your investigation. Follow the IB project criteria as general guidelines for writing it up. You will be graded on both the accuracy of your work and the quality of your written communication.

Deadline. This Special Report will be due no later than ______May 22, 2015_______________.

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