The production manager of American Tool and Castings Company is conducting a study regarding.

The production manager of American Tool and Castings Company is conducting a study regarding the relationship between the number of alloy caps milled on a lathe versus the measure of distance from specification of outside cap diameters. The lathe uses a sharp steel cutting tool in a milling process to cut and shape raw alloy bars into caps. The lathe tool turns at a high speed while cutting into the alloy, in essence, cutting the alloy down to size and shaping it to resemble a round cap. A similar lathe tool cuts into the inside of the cap. The caps are later fit with interior gaskets and permanently sealed onto airtight canisters. After the steel cutting tool is used repeatedly, the tool begins to wear, hence cutting a larger outside cap diameter than desired. If the outside cap diameter is too large the cap can’t be properly affixed and sealed to the canister. The production manager would like to build a model to estimate/predict how many caps a tool can mill until it wears down too much, hence milling caps that are too large in diameter and unusable. Each cap costs approximately $400 to mill, so defective caps are expensive. The main variable of interest (y) is “distance from specification” of outside cap diameter.

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