1. Find mean, median, mode, range, variance and standard deviation separately for every type

of business

2. For every business type construct

a. frequency and relative frequency distributions starting from class 0 to 30

b. a relative frequency histogram

3. Discuss the results obtained in parts 1 and 2

4. Test if there significant difference in the starting costs for these types of business.

The data for Task 2 in the data file for Assignment represents the following variables for franchisees of All Greens Pty Ltd: annual sales ($’000), the floor area (sq.ft.’000), inventory ($’000), advertising expenditure ($’000), the size of the area where the business operates (number of families, ‘000) and the number of competitors in the area.

1. Present the MS Excel output and write down the estimated regression equation

2. How well the model fits the data

3. Test the hypothesis that there is no significant relationship between the dependent and any of the independent variables

4. Interpret individual slope coefficients

5. Construct a 95% confidence interval for the slope coefficients of individual variables

6. Test the estimated slope coefficients for individual variables for significance

7. Remove all insignificant variables and re-estimate the model

8. Using the model from part (g), predict annual sales for a franchisee with 1,000 sq ft floor area, $150,000 inventory, $5,000 spent on advertising, 5,000 families in the area of operation and 2 competitors.

## Answer:

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The following data represent business startup costs (thousands of dollars) for shops. | ||||

X1 | X2 | X3 | X4 | X5 |

80 | 150 | 48 | 100 | 25 |

125 | 40 | 35 | 96 | 80 |

35 | 120 | 95 | 35 | 30 |

58 | 75 | 45 | 99 | 35 |

110 | 160 | 75 | 75 | 30 |

140 | 60 | 115 | 150 | 28 |

97 | 45 | 42 | 45 | 20 |

50 | 100 | 78 | 100 | 75 |

65 | 86 | 65 | 120 | 48 |

79 | 87 | 125 | 50 | 20 |

Source: https://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/owan/frames/frame.html | ||||

X1 | X2 | X3 | X4 | X5 |

231 | 3 | 294 | 8.199999809 | 8.2 |

156 | 2.2 | 232 | 6.900000095 | 4.1 |

10 | 0.5 | 149 | 3 | 4.3 |

519 | 5.5 | 600 | 12 | 16.1 |

437 | 4.4 | 567 | 10.60000038 | 14.1 |

487 | 4.8 | 571 | 11.80000019 | 12.7 |

299 | 3.1 | 512 | 8.1 | 10.1 |

195 | 2.5 | 347 | 7.699999809 | 8.4 |

20 | 1.2 | 212 | 3.299999952 | 2.1 |

68 | 0.6 | 102 | 4.900000095 | 4.7 |

570 | 5.4 | 788 | 17.39999962 | 12.3 |

428 | 4.2 | 577 | 10.5 | 14 |

464 | 4.7 | 535 | 11.30000019 | 15 |

15 | 0.6 | 163 | 2.5 | 2.5 |

65 | 1.2 | 168 | 4.699999809 | 3.3 |

98 | 1.6 | 151 | 4.599999905 | 2.7 |

398 | 4.3 | 342 | 5.5 | 16 |

161 | 2.6 | 196 | 7.199999809 | 6.3 |

397 | 3.8 | 453 | 10.39999962 | 13.9 |

497 | 5.3 | 518 | 11.5 | 16.3 |

528 | 5.6 | 615 | 12.30000019 | 16 |

99 | 0.8 | 278 | 2.799999952 | 6.5 |

0.5 | 1.1 | 142 | 3.099999905 | 1.6 |

347 | 3.6 | 461 | 9.6 | 11.3 |

341 | 3.5 | 382 | 9.800000191 | 11.5 |

507 | 5.1 | 590 | 12 | 15.7 |

400 | 8.6 | 517 | 7 | 12 |

startup costs for pet stores | MS | F | ||

Classes | Frequency | Relative Frequency | 190507.7883 | 611.5904 |

91 to 120 | 1 | 6.25 | t Stat | P-value |

Total | 16 | 100 | -0.63 | 0.54 |

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