# How to show r square correlation and RMSE on a scatterplot

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PARIVASH PARIDAD on 5 Sep 2019
Answered: ABHILASH SINGH on 18 Aug 2020
I have 2 colmuns in my excel file and I need to make the scatterplot which I wrote:
dataset = xlsread ('data.xlxs');
x = dataset (:,1);
y = dataset (:,2);
plot (x, y, '*')
title('scatterplot')
xlable('estimated')
ylable('measured')
Now I need to fit a linear regression line on the plot and display the Y=ax+b equation along with R square and RMSE values on the plot.
Can anyone help me? Thanks
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PARIVASH PARIDAD on 5 Sep 2019
I tried the basic fit tool which exists after you plot the scatter to show R2 but I want to write a code for it and for RMSE, I do not how to do it

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### Accepted Answer

Petter Stefansson on 5 Sep 2019
Given your x and y vectors, perhaps this is what you are looking for?
plot(x, y, '*','displayname','Scatterplot')
title('scatterplot')
xlabel('estimated')
ylabel('measured')
% Fit linear regression line with OLS.
b = [ones(size(x,1),1) x]\y;
% Use estimated slope and intercept to create regression line.
RegressionLine = [ones(size(x,1),1) x]*b;
% Plot it in the scatter plot and show equation.
hold on,
plot(x,RegressionLine,'displayname',sprintf('Regression line (y = %0.2f*x + %0.2f)',b(2),b(1)))
legend('location','nw')
% RMSE between regression line and y
RMSE = sqrt(mean((y-RegressionLine).^2));
% R2 between regression line and y
SS_X = sum((RegressionLine-mean(RegressionLine)).^2);
SS_Y = sum((y-mean(y)).^2);
SS_XY = sum((RegressionLine-mean(RegressionLine)).*(y-mean(y)));
R_squared = SS_XY/sqrt(SS_X*SS_Y);
fprintf('RMSE: %0.2f | R2: %0.2f\n',RMSE,R_squared)
##### 6 CommentsShowHide 5 older comments
PARIVASH PARIDAD on 20 Sep 2019
Thanks so much

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### More Answers (2)

Rik on 5 Sep 2019
With the code below you can determine a fitted value for y. Now it should be easy to calculate the Rsquare and RMSE. Let me know if you're having any issues.
x=sort(20*rand(30,1));
y=4*x+14+rand(size(x));
plot(x,y,'.')
f=@(b,x) b(1)*x+b(2);%linear function
guess_slope=(max(y)-min(y))/(max(x)-min(x));
guess_intercept=0;
b_init=[guess_slope;guess_intercept];
OLS=@(b,x,y,f) sum((f(b,x) - y).^2);%objective least squares
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
% Use 'fminsearch' to minimise the 'OLS' function
b_fit=fminsearch(OLS,b_init,opts,x,y,f);
x_fit=x;
y_fit=f(b_fit,x_fit);
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Rik on 5 Sep 2019
Since Petter Stefansson wrote a complete answer, I'll attach a wrapper for fminsearch I sometimes use, which will also return goodness of fit parameters. I still encourage you to try to find out how it works with pen and paper, attempt to implement it yourself, and see if you get to the same code as me or Petter.

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ABHILASH SINGH on 18 Aug 2020
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