How to manually perform linear regression from scratch
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My code is below. Firstly, is my linear regression actually correct?
If it's right, I want to do the same but I want to create an original code for doing the linear regression, fitting a straight line to the data.
clc
clear
%input tensile strength data
TS=[72.5 73.8 68.1 77.9 65.5 73.23 71.17 79.92 65.67 74.28 67.95 82.84...
79.83 80.52 70.65 72.85 77.81 72.29 75.78 67.03 72.85 77.81 75.33...
71.75 72.28 79.08 71.04 67.84 69.2 71.53]';
%calculate mean
meanTS=mean(TS) %using matlab function
meanTSmanual=(sum(TS))/length(TS) %calculate mean manually
%calculate standard deviation
stdTS=std(TS) %using matlab function
%calculate standard deviation manually
meandifference = (TS-meanTSmanual).^2; %find the difference between each point of the mean then square it
TSvariance=sum(meandifference)/(length(TS)-1); %divide by sample size minus 1 to get the variance
stdTSmanual=sqrt(TSvariance) %square root the variance to get the standard deviation
%ascending order
[ascend,index]=sort(TS,'ascend'); %sort the data in ascending order
ascend
%probability of survival
survival=(1-(index/(length(TS)-1))) %applying given formula
%Weibull model
reg1=real(log((log(1./survival)))) %first dataset for linear regression, real parts only
reg2=log(TS) %second dataset for linear regression
%linear regression
idx = isfinite(reg1) & isfinite(reg2); %exclude infinite values and NaNs
pwf = fit(reg1(idx),reg2(idx),'poly1')
plot(pwf,reg1,reg2)
xlim([-5,5])
ylim([-5,5])
采纳的回答
This is the code for the manual fit:
A = [ones(size(reg1(idx))),reg1(idx)];
b = reg2(idx);
% linear fit equals reg2(idx)_fitted = coeffs(1) + coeffs(2)*reg1(idx)
coeffs = A\b
2 个评论
Daniel Jordan
2022-3-14
Hi, thanks for the reply. Below is the graph that I get using this code. Figure 1 id the original matlab code, figure 2 is the one you've given. It looks like the line is trying to go directly through each point rather than a line of best fit?
Torsten
2022-3-14
As written in the comment
% linear fit equals reg2(idx)_fitted = coeffs(1) + coeffs(2)*reg1(idx)
you must plot coeffs(1)+coeffs(2)*reg1(idx) against reg1(idx):
plot(reg1(idx),coeffs(1)+coeffs(2)*reg1(idx))
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