Given Data | |

Gift Card Sales (millions) | Revenue (millions) |

5.41 | 28.49 |

5.52 | 32.45 |

5.00 | 30.69 |

5.01 | 28.49 |

5.57 | 32.89 |

4.28 | 32.89 |

6.49 | 33.99 |

6.16 | 31.79 |

18.06 | 93.39 |

15.91 | 91.19 |

6.41 | 39.49 |

5.83 | 34.65 |

6.90 | 34.1 |

6.56 | 33.99 |

5.56 | 33 |

6.16 | 31.79 |

9.07 | 40.59 |

7.37 | 46.09 |

8.56 | 44.55 |

9.94 | 48.29 |

6.59 | 41.25 |

8.30 | 41.69 |

9.67 | 48.95 |

6.70 | 41.69 |

9.20 | 42.79 |

8.95 | 40.59 |

10.06 | 50.38 |

13.2 | 45.1 |

2. Star Barista Coffee is an international coffeehouse chain operating over 27,000 stores worldwide. Recently gift cards were introduced as a way to encourage coffee sales and it is of interest to a local area manager to investigate the relationship between the sales of gift cards per store (millions) versus revenue per store.

(a) Identify what should be the dependent and the independent variable for this scenario. Then use Excel to produce an appropriate scatter diagram that contains the trendline, least squares model and the coefficient of determination R2 . In addition:

• Comment on the relationship between Gift Card Sales (millions) and Revenue (millions), based on the scatter diagram.

• Use the Excel CORREL function to compute the correlation coefficient between Gift Card Sales (millions) and Revenue (millions). Include the EXCEL command you used including the Excel cell references as part of your solution below.

• Comment on the correlation coefficient and the coefficient of determination (R² ) and explain the difference between what each one tells you about regression. For both include an interpretation in the context of the data.

• Are there any data points that you think might have an undue influence on the coefficient of determination? Explain briefly.

(14 Marks)

(b) Interpret the meaning of the slope in this problem. In addition, interpret the intercept and explain if it is meaningful in the context of this problem? (6 Marks)

(c) Use the model described in the scatterplot to predict revenue if gift card sales are 7 million. Explain whether this prediction likely to be accurate. (4 Marks)

(d) Based on the regression line in the scatterplot, would the model be likely to over- or under-predict the revenue in part (c)? Explain briefly. (2 mark

**Note! Take particular care in interpreting the value of R-squared and in assessing the accuracy of prediction.**

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