Question

solve part B

Note: Do not use MATLAB (or other programming languages) build-in functions for regression. (a) Write a MATLAB (or other programming languages) function that accepts n values of xi and Yi, perform Linear Regression and returns values of rand, the model parameters ao and a. (6) Write another MATLAB (or other programming languages) function that accepts n values of X, and y(provided as arrays), checks for Linear, Power (y = axBx) and Saturation growth- rate (y = a*) models, and estimate the values of parameters do and a (or a and B. whichever is applicable). In all three methods, the function should use the function developed in part (a) to perform the linear regression part. The function should plot the given data and the three models (one linear and two non-linear) on the same graph (use distinct colors/shades of lines to differentiate). The function should return a number from 1-3 indicating the model with the best fit, its r2, and the estimated values of parameters; Now call the function in part (b) from the command window with the data given in the table below, capture the image of the output showing the returned values, and the graph, and include these in the Word document for submission, along with comments on the results. x 0.75 2 3 4 6 8 8.5 y 1.2 1.95 2 2.4 2.4 2.7 2.6

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
format long
x=input('Enter x vector: ');
y=input('Enter y vector: ');
[a03,a13,R3_2,a01,a11,R1_2,a02,a12,R2_2]=regression(x,y)

function [a0,a1,R_2]=LinearRegression(x,y)
A=[x(:) ones(numel(x),1)];
b=y(:);
C=A\b;
a0=C(2)
a1=C(1)
SSR=sum((y-a0-a1*x).^2);
SST=sum((y-mean(y)).^2);
R_2=1-SSR/SST;
end

function [a03,a13,R3_2,a01,a11,R1_2,a02,a12,R2_2]=regression(x,y)
[c1,c2,R1_2]=LinearRegression(x.*log(x),log(y));
a01=exp(c1);
a11=(c2);
f1=@(x) a01*x.^(a11*x);
[c1,c2,R2_2]=LinearRegression(x,(x./y));
a02=1/c2;
a12=a02*c1;
f2=@(x) a02*x./(a12+x);
[a03,a13,R3_2]=LinearRegression(x,y);
f3=@(x) a03+a13*x;
xx=linspace(min(x),max(x));
plot(xx,f3(xx),xx,f1(xx),':',xx,f2(xx),'--',x,y,'o');
legend('Linear','Power','Saturation','data points');
end

- 5 x Pradeep Figure 1 - 0 X 56 Search Documentation Edit View Insert Tools APPS EDITOR Insert B fx - Go To - Comment % 9 Find Indent 5 NAVIGATE EDIT PRADEEP KALRA Documents File 0 Desktop Window Help W. COE - I A MATLAB R2018 HOME PLOTS D E L Find Files 3 Compare - New Open Save Print FILE a C: Users Current Folder Name - codegen convertFinal directory1 example first googleLinks mathlab mynewdir Linear Power - Saturation data points a X | O egg2.m x testc. mxahk. mx nse_filt. mx + T ......... IL New folder questions old simple_gui2 1.png 2.png 3.png . Details 0 1 2 3 4 5 6 7 8 9 Workspace Name Value a01 1.196408461802969 a02 a03 a11 a12 a13 R1_2 1.6688 2.9983 1.4653 0.0298 1.1964 0.1548 0.6226 0.9935 0.8028 R2_2 = 0.993491404622254 R2_2 R3_2 LinearRegression / regression 20 Ln 22 Col CAENG 7:29 PM " IN 04/07/20 a Type here to search

Kindly revert for any queries

Thanks.