Most of the material properties used in engineering design and analysis were obtained from experiments.

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PROJECT EXPLANATION:

Most of the material properties used in engineering design and analysis were obtained from experiments. For example, material elasticity curve is needed in the stress analysis for designing a new product. Such curve is obtained from a function that best fits the experimental data. The method that can be used to derive an approximate function from a given set of data points is least-square regression. There are several least-square regression methods, one of them is called Polynomial Regression Method.

POLYNOMIAL REGRESSION METHOD

The polynomial regression method is suitable to derive a function for fitting a set of data scattered in a polynomial pattern. Given a set on n data at point (x1, y1), (x2, y2), …, (xn, yn) and a polynomial of order m that can be fitted to the data can be written in the form

𝑔(𝑥) = 𝑎0 + 𝑎1𝑥 + 𝑎2𝑥2 + ⋯ + 𝑎𝑚𝑥𝑚

Where a0, a1, a2, … , am are the unknown coefficients. These coefficients are determined by first writing the total error E as the sum of the error squares for all data points as

𝑛

𝐸 = ∑[𝑦𝑖 − 𝑔(𝑥𝑖)]2

𝑖=1

The total error E is minimized with respect to the unknown coefficients leading to a set of

m+1 simultaneous equations as

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