## Related questions with answers

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

$\begin{array}{cc}\begin{array}{c}\text { Line } \\ \text { Speed }\end{array} & \begin{array}{c}\text { Number of } \\ \text { Defective } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$

a. Develop a scatter diagram with the line speed as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Use the least squares method to develop the estimated regression equation.

d. Predict the number of defective parts found for a line speed of 25 feet per minute.

Solution

Verified**a)** For this exercise, we are to develop a scatter diagram for the given table with the line speed as the independent variable.

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

Line Speed | No. of Defective Parts Found |
---|---|

$20$ | $23$ |

$20$ | $21$ |

$30$ | $19$ |

$30$ | $16$ |

$40$ | $15$ |

$40$ | $17$ |

$50$ | $14$ |

$50$ | $11$ |

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

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