Problem 2 Matlab An engineer needs to make a decision between two mathematical m

Question

Problem 2 Matlab An engineer needs to make a decision between two mathematical models to represent a physical system accurately: Model A: y = a0 + a1x + a3x^3 ; model B: y = b0 + b2x^2 + b3x^3 Experiments were performed and the following data were obtained: x 3 4 5 7 8 9 11 12 y 1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6 (a) MATLAB: Write a program in a script file that uses the general least-squares regression relationship [a] = ([X ]^T [X]^-1 I[X]^T [y] to fit both models to the data, and generate a plot that shows the curve-fitting function curves (both A and B) along with the original data points. Additionally, determine the associated least-squares error E associated with each model. Hint: E = [e]^T [e] (b) CONCLUSION: Which model is more accurate based on the results in (a)?

Explanation / Answer

x=[3:5,7:9,11:12];

y=[1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6];

% Local regression using weighted linear least squares polynomial model

yy=smooth(x,y,'loess' );

yy1=polyfit(x,yy,3);

>> yy1

yy1 =

0.0467 -1.0412 7.1438 -11.4887

since coefficient of model A is more than B, so model A is more correct than B.

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