how do i deduce the function using linear regression for a set of x and y values?

clc
clear all
load x2.txt
load y2.txt
x=[x2]
y=log([y2])
format long
b2=x\y
yCalc1 = b2*x;
scatter(x,y)
hold on
plot(x,yCalc1)
xlabel('X_2')
ylabel('Y_2')
title('Linear Regression Relation Between X2 & Y2')

x = 25×1

70 170 10 20 100 180 200 110 130 31

y = 25×1

6.7153 8.8063 2.6804 3.7078 7.4083 8.8500 9.1882 7.6424 8.1274 4.9574

b2 = 
   0.050110078623913

This is what I am getting when i tried to use linear regression. Is there any way i can find the function this plot is tracing?

Answer 1

[Turlough Hughes]

Consider using a power fit.

Your data:

x = readmatrix('https://uk.mathworks.com/matlabcentral/answers/uploaded_files/850570/x2.txt');
y = readmatrix('https://uk.mathworks.com/matlabcentral/answers/uploaded_files/850575/y2.txt');

Power law fit:

powerFit = fit(x, y, fittype('power1'))

powerFit = 
     General model Power1:
     powerFit(x) = a*x^b
     Coefficients (with 95% confidence bounds):
       a =     0.01469  (0.001567, 0.02782)
       b =       2.525  (2.359, 2.691)

plot(powerFit, x, y);
set(gca,'YScale','log')

[Turlough Hughes]

You actually have the parameters in your question but the way you fitted the data fixes the intercept to 0 - so the slope is equal to b2 and the intercept is 0. As a point of information, you can fit the slope and intercept using matrix left division with the following modification:

x = readmatrix('https://uk.mathworks.com/matlabcentral/answers/uploaded_files/850570/x2.txt');
y = readmatrix('https://uk.mathworks.com/matlabcentral/answers/uploaded_files/850575/y2.txt');
log_y = log(y);
b = [ones(size(x)) x]\log_y; % pad the left side with ones
yCalc1 = b(2)*x + b(1);

scatter(x,log_y)
hold on
plot(x,yCalc1)

sprintf('Slope: %1.2f\nIntercept: %1.2f',b(2),b(1))

ans = 
    'Slope: 0.02
     Intercept: 4.45'

Answer 2

[KSSV]

clc
clear all
load x2.txt
load y2.txt
x=x2 ;
y = log(y2) ; 
% Use polyfit 
p = polyfit(x,y,1) ;
yCalc1 = polyval(p,x) ; 

scatter(x,y)
hold on
plot(x,yCalc1)
title(sprintf('y = %f*x+%f',p))
xlabel('X_2')
ylabel('Y_2')

[Zaki Aslam]

thank you sir, it worked