**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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