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

조회 수: 214 (최근 30일)
PARIVASH PARIDAD 2019년 9월 5일
답변: ABHILASH SINGH 2020년 8월 18일
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
##### 댓글 수: 2없음 표시없음 숨기기
Rik 2019년 9월 5일
What have you tried yourself?
PARIVASH PARIDAD 2019년 9월 5일
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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### 채택된 답변

Petter Stefansson 2019년 9월 5일
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)
##### 댓글 수: 6이전 댓글 4개 표시이전 댓글 4개 숨기기
Petter Stefansson 2019년 9월 20일
편집: Petter Stefansson 2019년 9월 20일
If you mean you want a “1/1 line", i.e. a line that increases by the same amount in both the x and y direction and just cuts the figure in a 45° angle, then you can just give the plot command the same input for both the x and y values. For example, to plot a 1/1 line between -100 and 100:
plot([-100 100],[-100 100],'displayname','1/1 line')
However, this line may not visually appear as if it has a 45° slope unless the x and y axis are displayed the same way. So you will probably have to use something like this in order for it to look right:
plot([-100 100],[-100 100],'displayname','1/1 line')
axis equal
xlim([-0.05 0.6])
ylim([-0.05 0.6])
PARIVASH PARIDAD 2019년 9월 20일
Thanks so much

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### 추가 답변 (2개)

Rik 2019년 9월 5일
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);
##### 댓글 수: 3이전 댓글 1개 표시이전 댓글 1개 숨기기
Rik 2019년 9월 5일
Do you know how to calculate the Rsquare and RMSE with pen and paper? Start there and then implement it. Wikipedia can be a great starting point for situations like this.
As for my code, there isn't really a need to fully understand how an OLS function itself works, it is just one example of a cost function. Every fitting method has some function that describes how well a function fits that data. The fitting process then consists of trying to find parameters that will minimize the cost function. (this is not specific to Matlab)
The fminsearch function tries to minimize a function. This function can have multiple inputs, but the first input must be a vector or matrix with your parameters.
Rik 2019년 9월 5일
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 2020년 8월 18일

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