How can one display fitting equations (with t stat and R^2) on a scatter plot

I use

scatter(x,y)

for a scatter plot. Then I run

fitlm(x,y)

Then I want to display the result of regression equations, t-stat, and R^2 on a scatter plot. Please advise.

[alpedhuez]

Relatedly, starting from

https://www.mathworks.com/help/stats/linearmodel.plot.html

(1) how can one display data with circles (like scatter)?

(2) again, how can one display tstat, R^2 etc?

Answer 1

[Star Strider]

Try this example:

load carsmall
X = [Weight,Horsepower,Acceleration];
mdl = fitlm(X,MPG)
Tst = mdl.Coefficients.tStat;
Rsq = mdl.Rsquared;
Formula = mdl.Formula;

figure
plot(MPG, X, 'o')
xlabel('MPG')
legend('Weight','Horsepower','Acceleration', 'Location','Best')
text(10, 2000, sprintf('R^2 = %.4f\n\nt-Stats:\nIntercept = %.5f\nWeight = %.5f\nHorsepower = %.5f\nAcceleration = %.5f\n',[Rsq.Ordinary;Tst]))

.

[alpedhuez]

will work on it!

[Star Strider]

Thank you!

That is simply prototype code to demonstrate how to get — and display on the plot — the information you requested.

[alpedhuez]

Let me proceed step by step. I want to have a one-variable regression

mdl=fitlm(x,y)
Tst = mdl.Coefficients.tStat;
Rsq = mdl.Rsquared;
Formula = mdl.Formula;

and want to have a box

----------------------------

y=1.0+2.7x

t-stat: 3.0

R^2: 0.97

------------------------------

How can one proceed?

[Star Strider]

That should work with what I already provided.

The one exception is the ‘Formula’. You would have to create that yourself, since I can find no way to get that from the fitlm results in that format.

Using my example code, you would need to do something like this:

Est = mdl.Coefficients.Estimate;
FormStr = sprintf('y = %.4f %.4f*x1 %.4f*x2 %.4f*x3', Est);

crafting it for your own regression function.

Here is an approach for the example I posted:

load carsmall
X = [Weight,Horsepower,Acceleration];
mdl = fitlm(X,MPG)
Tst = mdl.Coefficients.tStat;
Rsq = mdl.Rsquared;
Formula = mdl.Formula;
Est = mdl.Coefficients.Estimate;
FormStr = sprintf('y = %.4f %.4f*x1 %.4f*x2 %.4f*x3\nt-Stat: %.2f\nt-Stat: %.2f\nR^2 : %.2f', Est,Tst([1 2]),Rsq.Adjusted);

figure
plot(MPG, X, 'o')
xlabel('MPG')
legend('Weight','Horsepower','Acceleration', 'Location','Best')
% text(10, 2000, sprintf('R^2 = %.4f\n\nt-Stats:\nIntercept = %.5f\nWeight = %.5f\nHorsepower = %.5f\nAcceleration = %.5f\n',[Rsq.Ordinary;Tst]))
annotation('textbox', [0.2 0.01 0.4 0.4], 'String', FormStr, 'FitBoxToText','on')

You will have to experiment with respect to your model and plot. This should get you started.

.

[alpedhuez]

Let me work on it. Thank you.

[Star Strider]

As always, my pleasure!