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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

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)

Petter Stefansson
on 20 Sep 2019

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])

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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);

Rik
on 5 Sep 2019

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
on 5 Sep 2019

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