As part of a pollution study, a sanitary engineer has collected some BOD data on a particular sample of water taken from a certain stream in Wisconsin. The BOD equation is
where η = mean value of BOD t = time and L0 and k are two parameters to be estimated. Her data consist of one BOD reading_ for each of several times t. She wants to estimate the parameters in the· equation.
(a) Under what circumstances would it be appropriate to use the method of least squares?
(b) Why might it be inappropriate to use the ordinary method of least squares in this situation?
(c) Assuming that appropriate circumstances exist, explain how the method of least squares could be used to solve this problem. Your explanation should be understandable to an engineer who has had no experience with statistical methods.