## Answers

using excel>data analysis>regression

we have

Regression Statistics | ||||||

Multiple R | 0.724953 | |||||

R Square | 0.525556 | |||||

Adjusted R Square | 0.494947 | |||||

Standard Error | 5.517757 | |||||

Observations | 100 | |||||

ANOVA | ||||||

df | SS | MS | F | Significance F | ||

Regression | 6 | 3136.483 | 522.7472 | 17.16985 | 2.9E-13 | |

Residual | 93 | 2831.445 | 30.44564 | |||

Total | 99 | 5967.928 | ||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |

Intercept | 74.08432 | 7.985766 | 9.277046 | 6.93E-15 | 58.22617 | 89.94247 |

Rooms | -0.00797 | 0.001249 | -6.38667 | 6.61E-09 | -0.01045 | -0.0055 |

Nearest | -1.56552 | 0.632113 | -2.47665 | 0.01507 | -2.82077 | -0.31027 |

Ofice | 0.019463 | 0.003417 | 5.695413 | 1.43E-07 | 0.012677 | 0.026249 |

College | 0.199082 | 0.137898 | 1.443691 | 0.152186 | -0.07476 | 0.47292 |

Income | -0.42306 | 0.143796 | -2.94211 | 0.004115 | -0.70861 | -0.13751 |

DISTTwn | 0.229487 | 0.173906 | 1.319599 | 0.190208 | -0.11586 | 0.57483 |

the coefficient of multiple determination is 0.5256

the adjusted coefficient of multiple determination is 0.4950

the only College and DiSSTWN variable is insignificant at 10% level of significance because p value 0.152 and 0.190 are >0.10

the f test statistic is 17.20. the p-value of f test statistic is 0.0000. at 5 % level of significance, these variable are significant , therefore you choose this model as your final model.

characterstics | Ann Arbor | Bloomington | Champaign |

Rooms | 2672 | 2500 | 2300 |

Competitor distance | 1.3 | 1.2 | 0.5 |

Office Space | 952 | 604 | 1430 |

Students | 42 | 21 | 45 |

Income | 35 | 37 | 33.5 |

Disst to downtown | 3.4 | 4.5 | 1.4 |

predicted profit margin | 63.61236 | 53.593 | 77.90432 |

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