**FORTS 7 QUESTIONS – CORRELATION AND REGRESSION**

- The management of Huddwink Hessian Ltd believes that the cost of servicing and delivering an order varies in direct proportion to the size of the order.

The following data which has been randomly sampled from recent orders is considered typical:

Size of order (units) |
Order handling cost
£ |

36 | 929 |

85 | 2215 |

69 | 1679 |

57 | 1224 |

95 | 1988 |

76 | 2002 |

72 | 1857 |

74 | 1580 |

You are required to:

(a) Find the sample correlation coefficient (r).

(b) Test, at the 5% level of significance, the null hypothesis that there is no linear relationship between order handling cost and size of order.

(c) Calculate the “Goodness of Fit” for the data.

(d) Calculate the equation of the least squares regression line:

Order handling cost = A + (B × Size of order).

(e) Estimate from your equation the order handling cost for an order of 79 units.

- For the period 19X0 to 19X9, the coal production, number of coalminers killed underground and average weekly earnings of underground workers were as follows:

Year |
Coal production(million tons) |
Persons killedunderground |
Average weeklyearnings (£) |

19X0 | 123 | 87 | 234 |

19X1 | 120 | 70 | 266 |

19X2 | 100 | 75 | 306 |

19X3 | 114 | 79 | 381 |

19X4 | 100 | 70 | 407 |

19X5 | 110 | 63 | 470 |

19X6 | 110 | 60 | 528 |

19X7 | 159 | 113 | 584 |

19X8 | 96 | 55 | 642 |

19X9 | 99 | 45 | 959 |

(i) With respect to the relationship between coal production and number of persons killed:

(a) Find the sample correlation coefficient (r).

(b) Test, at the 10% level of significance, whether there is a linear relationship between coal production and number of persons killed.

(c) Calculate the “Goodness of Fit” for the data.

(d) Calculate the equation of the least squares regression line:

Persons killed = A + (B × Coal production (million tons)).

(ii) With respect to the relationship between coal production and average weekly earnings:

(a) Find the sample correlation coefficient (r).

(b) Test, at the 1% level of significance, whether there is a linear relationship between coal production and average weekly earnings.

(c) Calculate the “Goodness of Fit” for the data.

(d) Calculate the equation of the least squares regression line:

Average weekly earnings = A + (B × Coal production (million tons)).

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