problem defining linear regression condition

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fima v
fima v on 12 Mar 2020
Hello, i have built the first code( the top one which uses matlabs regress command to aproximate [m10;m5] (NX1) vector with
[repmat([0.04,10],n,1);repmat([0.04,12],n,1)] NX2 matrices getting B(2X1) vector. it works great.
then i tried to do the same thing by myself using the linear regression theory and using itterations to get the same result as regress.
However I am stuck on the "fixing condition" the gradient descent. D_m(2)=(-2./n)*sum(x.*(y-y_pred));
is there some one who can help me with the gradient descent?
Thanks.
Regress function code:
n=10000;
min_value = 30+273-5;
max_value = 30+273+5;
%We need all out samples to be in the range of max_value min_value
T = min_value + (max_value - min_value) * rand(n,1);
%our emesivity samples
e_delta=0.31622*randn(n,1);
var_e=var(e_delta); %emesivity variance
mean_e=mean(e_delta); %emesivity avarage
e = 0.9+0.1*e_delta;
var(e)
mean(e)
eT = e.*T;
m10 = 0.04*eT+10*e ;
m5 = 0.04*eT+12*e ;
[B,BINT,R] = regress([m10;m5],[repmat([0.04,10],n,1);repmat([0.04,12],n,1)]);
tested_T=B(1)/B(2)
plot(T);
xlabel('Sample number');
ylabel('Temperature');
ylim([min_value-2, max_value+2]);
My itterative code:
n=100000;
x=[repmat([0.04,10],n,1);repmat([0.04,12],n,1)];
m=[0;0];
L=0.0001;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
min_value = 30+273-5;
max_value = 30+273+5;
T = min_value + (max_value - min_value) * rand(n,1);
e_delta=0.31622*randn(n,1);
e = 0.9+0.1*e_delta;
eT = e.*T;
m10 = 0.04*eT+10*e ;
m5 = 0.04*eT+12*e ;
y=[m10;m5];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%plot(x,y,'.b');
%hold;
for i=1:100
y_pred=x*m;
D_m(1)=(-2./n)*sum(x.*(y-y_pred));
D_m(2)=(-2./n)*sum(x.*(y-y_pred));
m=m-L*D_m;
end

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