# Question

Companies that manufacture products that conform to a unique specifcation for each order need help in estimating their own costs. Because each order is unique, it can be hard to know for sure just how much it will cost to manufacture. Plus, the company often needs to quote a price when the customer calls rather than after the job is done. The company in this exercise manufactures customized metal blanks that are used for computer-aided machining. The customer sends a design via computer (a 3-D blueprint), and the manufacturer replies with a price per unit. Currently, managers quote prices on the basis of experience.

What factors are related to the order’s cost? It’s easy to think of a few. The process starts with raw metal blocks. Each block is then cut to size using a computer-guided tool. All of this work requires a person to keep an eye on the process.

The data for the analysis were taken from the accounting records of 200 orders that were filled during the last three months. The data have four variables of interest. These are the final cost (in dollars per unit manufactured), the number of milling operations required to make each block, the cost of raw materials (in dollars per unit), and the total amount of labor (hours per unit).

Motivation

(a) If the manufacturer can find a variable that is highly correlated with the final cost, how can it use this knowledge to improve the process that is used to quote a price?

Method

(b) What variable is the response? Which are the possible explanatory variables?

(c) How can the manufacturer use the correlation to identify variables that are related to this response?

(d) Explain why it is important to consider scatterplots as well.

Mechanics

(e) Obtain all of the scatterplots needed to understand the relationship between the response and the three explanatory variables. Briefy describe the association in each.

(f) Obtain all of the correlations among these four variables. (These are most often displayed in a correlation matrix.) Which explanatory variable is most highly correlated with the response?

(g) Check the conditions for the correlation of the response with the three predictors. Do the scatterplots suggest any problems that make these three correlations appear unreliable?

(h) Adjust for any problems noted in part (g) and recompute the correlations.

Message

(i) Which variable is most related to the response?

(j) Explain in the context of this manufacturing situation why the correlation is not perfect and what this lack of perfection means for predicting the cost of an order.

What factors are related to the order’s cost? It’s easy to think of a few. The process starts with raw metal blocks. Each block is then cut to size using a computer-guided tool. All of this work requires a person to keep an eye on the process.

The data for the analysis were taken from the accounting records of 200 orders that were filled during the last three months. The data have four variables of interest. These are the final cost (in dollars per unit manufactured), the number of milling operations required to make each block, the cost of raw materials (in dollars per unit), and the total amount of labor (hours per unit).

Motivation

(a) If the manufacturer can find a variable that is highly correlated with the final cost, how can it use this knowledge to improve the process that is used to quote a price?

Method

(b) What variable is the response? Which are the possible explanatory variables?

(c) How can the manufacturer use the correlation to identify variables that are related to this response?

(d) Explain why it is important to consider scatterplots as well.

Mechanics

(e) Obtain all of the scatterplots needed to understand the relationship between the response and the three explanatory variables. Briefy describe the association in each.

(f) Obtain all of the correlations among these four variables. (These are most often displayed in a correlation matrix.) Which explanatory variable is most highly correlated with the response?

(g) Check the conditions for the correlation of the response with the three predictors. Do the scatterplots suggest any problems that make these three correlations appear unreliable?

(h) Adjust for any problems noted in part (g) and recompute the correlations.

Message

(i) Which variable is most related to the response?

(j) Explain in the context of this manufacturing situation why the correlation is not perfect and what this lack of perfection means for predicting the cost of an order.

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