A manufacturer produces custom metal blanks that are used by its customers for computer-aided machining. The customer sends a design via computer (a 3-D blueprint), and the manufacturer comes up with an estimated cost per unit, which is then used to determine a price for the customer. This analysis considers the factors that affect the cost to manufacture these blanks. The data for the analysis were sampled from the accounting records of 195 previous orders that were filled during the last 3 months.
(a) Create a scatterplot for the average cost per item on the material cost per item. Do you find a linear pattern?
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) What is the estimated increase in the average cost per finished item if the material cost per unit goes up by $3?
(e) One can argue that the slope in this regression should be 1, but it’s not. Explain the difference.
(f) The average cost of an order in these data was $61.16 per unit with material costs of $4.18 per unit. Is this a relatively expensive order given the material costs?
(g) Plot the residuals from this regression. If appropriate, summarize these by giving the mean and standard deviation of the collection of residuals. What does the standard deviation of the residuals tell about the ft of this equation?