Fit Polynomial Model to Data

This example shows how to fit a polynomial model to data using the linear least-squares method.

Load the patients data set.

load patients

The variables Diastolic and Systolic contain data for diastolic and systolic blood pressure measurements, respectively. Fit a third-degree polynomial to the data with Diastolic as the predictor variable and Systolic as the response.

polymodel = fit(Diastolic,Systolic,"poly3")

polymodel = 
     Linear model Poly3:
     polymodel(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =   -0.001061  (-0.003673, 0.001551)
       p2 =      0.2844  (-0.3701, 0.9389)
       p3 =      -24.72  (-79.2, 29.76)
       p4 =       821.1  (-685.5, 2328)

polymodel contains the results of the fit. Display the least-squares method used to estimate the coefficients by using the function fitoptions.

opts = fitoptions(polymodel);
opts.Method

ans = 
'LinearLeastSquares'

The output shows that polymodel is fit to the data with the linear least-squares method. Evaluate polymodel at the values in Diastolic, and display the result together with a scatter plot of the blood pressure data.

plot(polymodel,Diastolic,Systolic)

The plot shows that polymodel follows the bulk of the data.