# 2

The success of a shopping center can be represented as a function of the distance (in miles) from the center of the population and the number of clients (in hundreds of people) who will visit. The data is given in the table below:

No. Customer (x) | 8 | 7 | 6 | 4 | 2 | 1 |

Distance (y) | 15 | 19 | 25 | 23 | 34 | 40 |

1 Calculate the linear correlation coefficient.

2 If the mall is located 2 miles from the center of the population, how many customers should the shopping center expect?

3 To receive 500 customers, at what distance from the center of the population should the shopping centre be located?

x_{i} |
y_{i} |
x_{i} ·y_{i} |
x_{i}^{2} |
y_{i2 } |
---|---|---|---|---|

8 | 15 | 120 | 64 | 225 |

7 | 19 | 133 | 49 | 361 |

6 | 25 | 150 | 36 | 625 |

4 | 23 | 92 | 16 | 529 |

2 | 34 | 68 | 4 | 1,156 |

1 | 40 | 40 | 1 | 1,600 |

28 | 156 | 603 | 170 | 4,496 |

There is a very strong negative correlation.

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