Breaking Strength And Alloy Compos

Chemical, civil, mechanical, aerospace, and bio medical engineers need to predict the It ten the of metal parts as  function of their alloy composition. The tension force y . required to break-a steel bar is a function of the percentage X, and X2 of each of two
‘l!! Ioying elements present in the metal. The following table gives some pertinent data. Obtain a linear model y = ao +a,x, +aix: to describe the relationship


• Solution
The script file is as follows:
xl = [0: 3 J ‘ ; x2 = [5,7,8,11)’;
y [7.1,19.2,31,45J’;
X = [ones(size(x1)), xl, x2);
a = X\y
yp = X*a;
Max_Percent_Error = 100*max(abs((yp-y) ./y))
The vector yp is the vector of breaking-strength values predicted by the model. The scalar Max_Percent_Error is the maximum percent error in the four predictions. The results are a = [0.8000, 10.2429, 1.2143]’ and Max_Percent_Error =
3.2193. Thus the model is y = 0.8 + JO.2429xl + 1.2143×2. The maximum percent error of the model’s predictions. as compared to the given data. is 3.2193 percent.

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