The National Institute of Standards and Technology (NIST) has created a Web site that contains a variety of estimation problems, with data sets, designed to test the accuracy of computer programs. (The URL is http://www.itl.nist.gov/div898/strd/.) One of the five suites of test problems is a set of 27 nonlinear least squares problems, divided into three groups: easy, moderate, and difficult. We have chosen one of them for this application. You might wish to try the others (perhaps to see if the software you are using can solve the problems). This is the Misralc problem (http://www.itl.nist.gov/div898/strd/nls/data/misra1c.shtml). The nonlinear regression model is 

The data are as follows:

For each problem posed, NIST also provides the “certified solution” (i.e., the right answer). For the Misralc problem, the solutions are as follows:

Finally, NIST provides two sets of starting values for the iterations, generally one set that is “far” from the solution and a second that is “close” to the solution. For this problem, the starting values provided are B¹ = (500, 0.0001) and B² = (600, 0.0002). The exercise here is to reproduce the NIST results with your software. [For a detailed analysis of the NIST nonlinear least squares benchmarks with several well-known computer programs, see McCullough (1999).]

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Y₁ = h(x, B) + ε 1 = B (1 - V₁ + 2x) * V1 + Ei.