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

Question

Zaki Aslam 2022-1-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1620810-how-do-i-deduce-the-function-using-linear-regression-for-a-set-of-x-and-y-values

评论： Zaki Aslam 2022-1-2

采纳的回答： Turlough Hughes

在 MATLAB Online 中打开

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?

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Answer 1

Turlough Hughes 2022-1-2

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1620810-how-do-i-deduce-the-function-using-linear-regression-for-a-set-of-x-and-y-values#answer_866525

在 MATLAB Online 中打开

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')

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Turlough Hughes 2022-1-2

在 MATLAB Online 中打开

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'

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Answer 2

KSSV 2022-1-2

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1620810-how-do-i-deduce-the-function-using-linear-regression-for-a-set-of-x-and-y-values#answer_866520

在 MATLAB Online 中打开

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')

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Zaki Aslam 2022-1-2

thank you sir, it worked

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

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

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