How to calculate the standard error of my linear regression coefficient?

I want to create a linear regression for my data through the origin. My code works fine, but I also need to determine the error of the coefficient K. My y data also has an error of ±0.001 (the x data has not) which have to be taken into account.

x=[-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7];
y=[-9 -7.65 -6.35 -5.05 -3.8 -2.6 -1.2 0 1.1 2.4 3.7 4.9 6.2 7.25 8.35]*0.01;

% Computing fitted line
K = x(:)\y(:);                  
yfit = x(:)*K;           

scatter(x, y)
hold on
plot (x, yfit, '-r')
hold off
K

Answer 1

[Star Strider]

You can certainly look this up and calculate it on your own, however using fitlm and predict is easier —

x=[-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7];
y=[-9 -7.65 -6.35 -5.05 -3.8 -2.6 -1.2 0 1.1 2.4 3.7 4.9 6.2 7.25 8.35]*0.01;

% Computing fitted line
K = x(:)\y(:);                  
yfit = x(:)*K;           

mdl = fitlm(x,y,'Intercept',false)

mdl = 
Linear regression model:
    y ~ x1

Estimated Coefficients:
          Estimate        SE        tStat       pValue  
          ________    __________    ______    __________

    x1    0.012436    9.7275e-05    127.84    7.0505e-23


Number of observations: 15, Error degrees of freedom: 14
Root Mean Squared Error: 0.00163

[ypred,yci] = predict(mdl,x(:));

figure
scatter(x, y)
hold on
plot (x, yfit, '-r')
plot(x, yci, '-g')
hold off

K

K = 0.0124