## A Note on the Measurement of Cost/Quantity Relationships in the Aircraft Industry

A. R. Gallant

*Journal of the American Statistical Association*, Vol. 63, No. 324. (Dec., 1968), pp. 1247-1252.

### Abstract

Many practical applications of learning theory in the aircraft industry require
the estimation of the parameters of y_{i} = ai^{b} where y_{i} is the
cost of the i^{th} aircraft. Typically data are available by
production lot rather than by individual aircraft. The estimation procedure
usually employed is the application of least squares to
logy_{n} = loga + blogx_{n} where y_{n} is the mean cost of
a production lot and x_{n} is a quantity
"near" the mean of serial
numbers of the craft. This note presents a probability model which leads
directly to maximum likelihood estimators and avoids difficulties inherent in
the usual approach. An example of estimation employing methods of non-linear
estimation is presented.