How to fit polyfit coefficients to a linear model

Hi, I've used polyfit to fit a polynomial to a set of data.

I'm trying to create a linear regression model

I have used fitlm() to create models that are straight lines, and this works very well, but I don't know how to fit a polynomial style regression to data.

Can anyone guide me?

Is there a way to force MATLAB to create a linear model using fitlm() with the polynomial I found using polyfit?

The main is I want the estimates, SE's, t-stats and Rsquared etc from fitlm()

I've attached an image to show what I've done.

Thanks

Answer 1

[Star Strider]

Try this:

x = 1950:2020;                                                  % Create Data
y = 0.07*x.^2 -300*x + 304130 + randn(size(x))*100;             % Create Data

mdl = fitlm(x(:), y(:), 'purequadratic');                       % Choose Model Specification

[ypred,yci] = predict(mdl, x(:));

figure
plot(x, y, 'p')
hold on
plot(x, ypred, '-r',  x, yci, '--r')
hold off
grid

The data I created from your polyfit coefficients do not look like the data in the plot, in spite of fitlm reproducing them reasonably well. Obviously, use your own data (that I do not have access to).

[Connor Cheema]

Hi Star Strider

I actually figured out how to get fitlm() to predict my model for me and create the coefficients itself. Didn't need to use polyfit in the end. Thanks for your answer however.

[Connor Cheema]

https://uk.mathworks.com/matlabcentral/answers/589216-how-to-bootstrap-estimated-gamma-parameters-from-sample-95-confidence

If you could, I have another question which I still need help with if you don't mind having a go at it.

[Star Strider]

As always, my pleasure!

Jeff Miller appears to have posted an Answer to your other Question that I likely cannot improve upon. (It would help for you to copy your data and paste it to your original post or to a Comment. A picture may be worth a thousand words, however the actual data is worth a thousand keystrokes attempting to reproduce it!)

[Connor Cheema]

Thanks man

I put the data in there. Gonna try my hand at the question now.

[Star Strider]

As always, my pleasure!

Jeff and I both thank you!