..... Observations, r, were made at various levels of x and y in an experiment.

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Observations, r, were made at various levels of x and y in an experiment. A model is proposed to describe these data: r = k xayb (1 -y) c Determine the model parameters k , a, b and c using the method of least-squares. Although this equation is nonlinear, it can be transformed into a linear equation in two explanatory variables. This problem serves as an example of multiple linear least-squares regression. Although you can use Excel Solver to perform the least-squares fit I'd like you to derive the least-squares equations and solve them for this problem. The data were produced by r = 150 x 0.5 y 2 (1-y) 2 + random fluctuations. r= kxayb(1-y)c Taking the logarithm of the equation and let p = ln(r),s=ln(k),t=ln(x), etc.. transforms the equation into a linear model:p = s + at + bu + cv The objective is to find a, b. and c that minimize the sum of square of errors between the observations and the model calculated values.See how it's done with a polynomial. Think of t as the first-degree term, u as the second- degree term, and v as the third-degree term. Or, conversely, you can think of a polynomial f = a0 + a1 x + a2x2 + a3 x3 Being a linear equation f = a0 +a1x + a2y+a3z Where y =x 2 an d z =x3.

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actually its quite lengthy...but i have a found similar problem...hope you are satified...

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..... Observations, r, were made at various levels of x and y in an experiment.

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