Use factorial plots in conjunction with regression. Factorial plots include the Main Effects Plot and Interaction Plot.

A main effect is the change in the mean response from the low level to the high level of a variable. Use this plot for these purposes:

·    examine the level means for each variable

·    compare the level means for several variables

·    compare the relative strengths of the effects across variables

An interaction occurs when the effect of one variable depends on the value of another variable. Each plot displays the interaction between two variables. Use interactions plots to compare the relative strength of the effects across variables.

A forest products laboratory tested the effects of certain variables in the production of plywood. To make plywood, chucks are inserted at each end of a log. The log is then spun while a saw blade cuts off a thin layer of wood. These layers are glued together to form plywood. The laboratory measured the torque that could be applied to the chucks before they spun out of the log, under different conditions of log diameter, log temperature, and chuck penetration. These are the three variables in the study: diameter, temperature, and penetration. A table of the data set is shown below:

Data for Plywood Experiment

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|         |      |            Penetration              |

|Diameter | Temp |     1.00     1.50     2.25     3.25 |

|---------|------|-------------------------------------|

|         |  60  |   17.300   18.050   17.400   17.400 |

|4.5      | 120  |   16.700   17.950   18.600   18.550 |

|         | 150  |   15.750   16.650   15.250   15.850 |

|---------|------|-------------------------------------|

|         |  60  |   29.550   31.500   36.750   41.200 |

|7.5      | 120  |   23.200   25.900   35.650   37.600 |

|         | 150  |   22.550   22.900   28.900   35.200 |

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Data: Plywood_model.MTW (available in the Sample Data folder).