Simple linear regression with maximum likelihood estimation

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Melisa Akan
Melisa Akan 2019-9-17
Hello,
I have a very simple question that I couldn't find an answer to. Any guidance would be greatly appreciated.
All I have is 5 pairs of x,y values and I am trying to fit a line to these points using maximum likelihood estimation (MLE).
I have already done this using least squares estimation (code below) and came up with the parameter estimates, 0.3368 and 1.2805, for the slope and the intercept respectively. I would like to compare these with parameter estimates that the MLE method would produce.
I have already looked into the MLE function explained on MATLAB's website but I couldn't be sure how to implement it.
Thanks again!
x= [0.1 0.1 0.5 0.8 0.9];% probability values FAR
y= [0.8 0.8 0.9 0.95 0.95];% probability values HR
x = transpose(norminv(x)); % convert to z, the line will be fit to z-scores
y = transpose(norminv(y));
Xz =[ones(length(x),1) x]; % add ones before the x values to get it ready for linear regression
b=Xz\y; % returns vector with intercept and slope

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