Linear best fit model

Hello Community,

I have a query about best fit model.

From a large data set, I could generate a linear best fit line, which has a specific slope.

Now, now I want to compare how deviated this best fit is from another line having a different slope.

How can I force a specific slope value to draw another fit to this dataset?

Thanks in advance,

Ani

[William Rose]

@Aniruddha Das

I am glad that helped. I moved my comment to the Answer section, which is what I had originally intended.

[Adam Danz]

> How can I force a specific slope value to draw another fit to this dataset?

What do you mean to draw another fit? There is only 1 best fit for a set of data.

[Aniruddha Das]

Thank you @William Rose. That helps.

Hi @Adam Danz, let me rephrase my question. That should not be the best fit, but a linear 'fit' which has a different slope compare to the best fit line.

[Adam Danz]

Thanks for the follow-up. Looks like @William Rose nailed it.

[William Rose]

@Adam Danz, thank you. Means a lot, coming from you!

Answer 1

[William Rose]

@Aniruddha Das

Here is an example in which the fixed slope is 1.3 and the best fit slope is approximately 1.0.

x=0:1:100;
N=length(x);        %number of data points
y=x+5*randn(1,N);  %noisy data
% Find best-fit straight line
P = polyfit(x,y,1);
y1=P(1)*x+P(2);
rmse1=sqrt(sum((y-y1).^2)/N);
% Fit straight line with fixed slope
% The straight line should pass through the mean of the data
fixedslope=1.3;
xm=mean(x); ym=mean(y);
intercept=ym-fixedslope*xm;
y2=fixedslope*x+intercept;
rmse2=sqrt(sum((y-y2).^2)/N);

%% Display results on console
fprintf('Fit 1 (best fit)   : y1=%.3fx%+.3f.  RMS Error=%.2f\n',P(1),P(2),rmse1)

Fit 1 (best fit)   : y1=1.014x-0.274.  RMS Error=4.48

fprintf('Fit 2 (fixed slope): y2=%.3fx%+.3f.  RMS Error=%.2f\n',fixedslope,intercept,rmse2)

Fit 2 (fixed slope): y2=1.300x-14.588.  RMS Error=9.47

%% Plot results
figure; plot(x,y,'rx',x,y1,'-g',x,y2,'-b')
xlabel('X'); ylabel('Y'); grid on; legend('data','fit 1','fit 2')