# How to know the slope and intercept of a straight line in a log log plot and how to connect the data in log log scale by a straight line?

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DARSHAN KUMAR BISWAS on 20 Jul 2022
Answered: Star Strider on 21 Jul 2022 for this two graph, I want to do a linear regression, and find out the slope and intercept of that straight line.

dpb on 20 Jul 2022
If one is not concerned about stastical estimation but simply the coefficients, then just use
b=polyfit(log10(x),log10(y),1); % coefficients in log-log space
yhat=10.^polyval(b,log10(xNew));
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dpb on 21 Jul 2022
Edited: dpb on 21 Jul 2022
How to use coefficients (b) in log space to predict new values...
Try
x=logspace(3,5);y=logspace(2,5);
b=polyfit(log10(x),log10(y),1);
xh=(linspace(1000,100000));
yh=10.^polyval(b,xh);
hold on
plot(xh,yh,'or-')

Star Strider on 21 Jul 2022
The problem with doing regressions on logarithmic transformed variables is that they transform additive errors (that parameter estimation techniques assume) into multiplicative errors (that they do not). The result is that the parameter estimates on transformed variables are not correct.
A better approach would be to use the fminsearch (or fitnlm if you want statistics) function to estimate the parameters directly since:  coding it as:
pwrfcn = @(p,x) exp(p(1)).*x.^p(2); % Logarithmic Intercept = p(1), Logarithmic Slope = p(2)
This can be used as written in fitnlm, however the code for fminsearch requires:
P0 = rand(2,1); % Initial Parameter Estimates (Choose Appropriate Values), Necessary For ‘fminsearch’ & ‘¹fitnlm’
P = fminsearch(@(p) norm(y = pwrfun(p,x)), P0) % Estimate Parameters
yfit = pwrfcn(P,x); % Evaluate Regression
Then plot the data and ‘yfit’ on a loglog plot, as functions of ‘x’.
.

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