## Related questions with answers

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

$\begin{array}{cc}\text{Distance to Work} & \text{Number of Days}\\\text { (miles) } & \text { Absent } \\ 1 & 8 \\ 3 & 5 \\ 4 & 8 \\ 6 & 7 \\ 8 & 6 \\ 10 & 3 \\ 12 & 5 \\ 14 & 2 \\ 14 & 4 \\ 18 & 2\end{array}$

a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.

b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.

c. Predict the number of days absent for an employee that lives 5 miles from the hospital.

Solution

Verified**a)** For this exercise, we are to develop a scatter diagram for the given table.

$\small \text{Table 1. Given values.}$

Distance to Work (miles) | Number of Days Absent |
---|---|

$1$ | $8$ |

$3$ | $5$ |

$4$ | $8$ |

$6$ | $7$ |

$8$ | $6$ |

$10$ | $3$ |

$12$ | $5$ |

$14$ | $2$ |

$14$ | $4$ |

$18$ | $2$ |

*What are the relationships of the variables to the coordinates of a point?*

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