REGRESSION I

Solid Propellant Rocket Engine Simple Linear Regression Exercise

Name: __________________________

The Space Transportation Program Office has tasked you with estimating production costs for a new solid propellant rocket engine to be used on the International Launch Vehicle (ILV).

Prior to collecting historical data, meetings with propulsion engineers were held. The results of the identification phase were encouraging. The experts agree that the primary driver of solid propellant rocket engine production costs is Power. For propulsion systems, Power can be measured in several ways, such as Average Thrust, Burn Time and Propellant Weight. During the specification phase, the experts all agreed that as power, burn time, and propellant weight increased, cost would also increase.

Data on twelve analogous rocket engines were gathered. The cost data is normalized to the cost at unit 100 in FY98$. The historical database is as follows:

Rocket Engines

Engine	Cost (@ Unit 100)	Average Thrust (lbs)	Burn Time (sec)	Propellant Weight (lbs)
1	9,739	1505	10.35	1003
2	6,836	2,320	11.55	2340
3	11,280	46,780	16.80	2536
4	96,334	2,465	21.52	6556
5	58,593	9,432	14.93	3,348
6	44,389	24,345	17.43	2,504
7	911,234	16,290	35.60	6,451
8	999,999	33,735	31.80	6,986
9	932,510	33,450	43.10	6,785
10	1,344,350	4,500	45.60	8,307
11	1,481,090	14,657	50.60	9,400
12	1,536,800	67,555	52.40	9,120

Tasks: Develop the best model/prediction possible, given the database provided. Document the process used and the decisions made along the way.

1. Calculate the sample mean, variance, standard deviation, and coefficient of variation for the cost data only.

2. Perform simple linear regression analysis on this data (Cost vs Average Thrust; Cost vs Burn Time; and Cost vs Propellant Weight). Analyze each regression using the Hierarchy of Regression that we used in class. Identify your preferred linear regression/CER. Indicate why you prefer the best one, and why you eliminated the other two CERs (Cost Estimating Relationships).

3. In words, state what the coefficient of determination (R2), the standard error of the estimate (SE), and the coefficient of variation (CV), are indicating about your preferred equation. Do not just give me a definition here! Use the numbers from your preferred regression.

4. Using the preferred CER, estimate the cost at unit 100 for the solid rocket motor that will be employed on the new International Launch Vehicle (ILV). Following are the specifications for the ILV rocket motor:

Average Thrust = 71,544 lbs Burn Time = 48.5 sec Propellant Weight = 9,290 lbs

5. Convert your answer to FY11$ using APN indices.