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.