# Is this code for plotting linear regression in loglog scale and confidence intervals correct?

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Gianluca Regina on 18 Dec 2020
Commented: Gianluca Regina on 29 Dec 2020
Dear MatLab users,
I have a bunch of data x and y, I want to do a linear regression of the natural logarithm of my data. Then, I want to plot the original data, the linear fit, and the linear fit plus the standard deviation (i.e. the condifence intervals). I tried several solutions that I found in other answers, but in the end I had to mix a bit of all of them. I THINK I did it correctly, but I would like your opinion. Is my code correct? N = 1 ;
x = 100*rand(20,1);
y = 100*rand(20,1);
ln_x = log(x) ;
ln_y = log(y) ;
fit_ln_xy = fitlm( ln_x, ln_y ) ;
p = polyfit( ln_x, ln_y , 1) ;
y_fit = polyval( p , ln_x );
loglog( x , y , '*' )
hold on
loglog( x , exp(y_fit) , 'k' , 'linewidth', 1.5)
loglog( x , exp(y_fit + N*fit_ln_xy.RMSE ) , 'b--' , 'linewidth', 1.2)
loglog( x , exp(y_fit - N*fit_ln_xy.RMSE ) , 'r--' , 'linewidth', 1.2)
legend('Original data ' , 'linear fit' , 'linear fit + 1 std' , 'linear fit - 1 std')

Gaurav Garg on 29 Dec 2020
Hi Gianluca,
Yes, the code seems to be correct.
Moreover, you can look at the documentation on how to train/test data using linear regression and some other functions you can use here.
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Gianluca Regina on 29 Dec 2020
Thank you, Gaurav! The link you sent me is indeed interesting, I'll have a look at it!