Cost Analysis 2: Piston Corporation's products are replacement automobile parts. Piston had experienced a rather stable growth in sales in recent years and had been required to increase its capacity regularly. The executive officers had been asked by Piston's directors to formulate a proposal for expansion and price adjustments. Quarterly data were obtained on manufacturing costs per unit (in hundreds of dollars), production level (a proportion of the total capacity), and the index of direct material and direct labor costs for a five-year period (These data are in the worksheet entitled "PISTON5"). Begin by fitting the linear model to predict the average cost per unit (COST) from production level (x1 = PROD) and the index of direct material and direct labor costs (x2 = INDEX).

prod2= 1/PROD

COST	PROD	prod2	INDEX
3.65	0.85	1.176471	80
4.22	0.78	1.282051	93
4.29	0.82	1.219512	107
5.43	0.64	1.5625	115
6.42	0.5	2	130
5.71	0.62	1.612903	128
5.39	0.7	1.428571	116
3.99	0.9	1.111111	92
4.08	0.94	1.06383	94
4.38	1	1	110
4.28	1.04	0.961538	115
4.42	0.82	1.219512	117
5.11	0.75	1.333333	128
4.88	0.84	1.190476	134
4.99	0.86	1.162791	135
4.57	0.9	1.111111	135
4.84	0.94	1.06383	139
5.16	0.8	1.25	142
5.67	0.72	1.388889	147
6.26	0.6	1.666667	150

Regardless of your decision above, use the Reciprocal Model to answer ALL of the questions below. Also, be sure to compute these values based on the UNROUNDED values in EXCEL.
--Predict the cost per unit for a quarter with a production level of 75% and an index of 140. (Enter your answers to two decimal places.)

 

b) State the transformed model equation (i.e., the reciprocal model equation). O 9 = Bo + B1) + B2x2 O = Bo + Biln(x1) + B2x2 O = Bo + Bix + B2ln(x2) O = Bo + Bix + O = Bo + Bix1 + B2x2 c) How does the reciprocal model compare with the original, linear model? In answering this question, fit both models and use the R2 values and the standard error of the regression in the comparisons. Provide summary measures about the two models in the table below. (Enter the R2 values as percents to two decimal places and round your standard errors to three decimal places.) R2 R'adi Model Se Linear Model 91.93 V % 90.98 % .228 Reciprocal Model 95.54 % 95.01 % .169