Question

Use nonlinear regression to estimate α4 and β4 based on the following data.

y= α4Xe^(β4X)

x    0.1 0.2 0.4 0.6 0.9 1.3 1.5 1.7 1.8

y 0.75 1.25 1.45 1.25 0.85 0.55 0.35 0.28 0.14

If you were to use linear regression to find α4 and β4, how would you make the model linear? Plot the data points, the fit to the data using linear and nonlinear regression. What method produces the better estimate

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clc
clear all
x=[0.1,0.2,0.4,0.6,0.9,1.3,1.5,1.7,1.8]';
y=[0.75,1.25,1.45,1.25,0.85,0.55,0.35,0.28,0.14]';

disp('Values using non linear regression');
f=@(rx) sum((rx(1)*x.*exp(rx(2)*x)-y).^2);
[S,fval]=fminsearch(f,[1,1]);
al14=S(1)
be14=S(2)
A=[ones(length(x),1) x];
b=log(y./x);
S=A\b;
disp('Values using linear regression');
disp('Alpha4=')
al4=exp(S(1))
disp('Beta4=')
be4=S(2)
xx=0.1:0.01:1.8;
yy=al4*xx.*exp(be4*xx);
yy1=al14*xx.*exp(be14*xx);
plot(xx,yy,xx,yy1,x,y,'o');
legend('Linear regression','Nonlinear regression','data points');
disp('Sum of square of error using non linear is ');
disp(fval)
disp('Sum of square of error using linear is ');
disp(sum((al4*x.*exp(be4*x)-y).^2))

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Kindly revert for any queries

Thanks.