Getting the equation of a line

So I used polyfit to create a trendline for a data set and that worked great. Now I am trying to get the equation of that trendline but I am a little stuck so any direction on that would be great. The code I used can be found here:

subplot (2,1,2)
time = (0:.00274:21.3644); %time in years to be able to plot the NAVD88 data
% Fit a polynomial p of degree 1 to the NAVD88 data. This will give a
% trendline and allow to solve a projection
x = (0:.00491814:21.3644);
y = Hclean;
p = polyfit(x,y,1);
% Evaluate the fitted polynomial p and plot:
projection = polyval(p,x);
plot(time,H,x,projection,'-')%Plot of all the waves over 21 years
title ('NAVD88 Low-High Daily Water Height for 21 year data set')
xlabel ('Years since Jan. 18 2000')
ylabel ('NAVD88 (ft)')
 

Answer 1

[John D'Errico]

You did the fit, with the estimates of the coefficients in p. p is a vector, of length 2.

The line equation is simple.

y = p(1)*x + p(2)

Had you just read the help for polyfit,

help polyfit

 POLYFIT Fit polynomial to data.
    P = POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of
    degree N that fits the data Y best in a least-squares sense. P is a
    row vector of length N+1 containing the polynomial coefficients in
    descending powers, P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1).
 
    [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a
    structure S for use with POLYVAL to obtain error estimates for
    predictions.  S contains these fields:
 
          R  -  Triangular R factor (possibly permuted) from a QR
                decomposition of the Vandermonde matrix of X
         df  -  Degrees of freedom
      normr  -  Norm of the residuals
 
    If the data Y are random, an estimate of the covariance matrix of P is
    (Rinv*Rinv')*normr^2/df, where Rinv is the inverse of R.
 
    [P,S,MU] = POLYFIT(X,Y,N) finds the coefficients of a polynomial in
    XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
    centering and scaling transformation improves the numerical properties
    of both the polynomial and the fitting algorithm.
 
    Warning messages result if N is >= length(X), if X has repeated, or
    nearly repeated, points, or if X might need centering and scaling.
 
    Example: simple linear regression with polyfit
 
      % Fit a polynomial p of degree 1 to the (x,y) data:
        x = 1:50;
        y = -0.3*x + 2*randn(1,50);
        p = polyfit(x,y,1);
 
      % Evaluate the fitted polynomial p and plot:
        f = polyval(p,x);
        plot(x,y,'o',x,f,'-')
        legend('data','linear fit')
 
    Class support for inputs X,Y:
       float: double, single
 
    See also POLY, POLYVAL, ROOTS, LSCOV.

    Documentation for polyfit
       doc polyfit

    Other functions named polyfit

       codistributed/polyfit    gpuArray/polyfit    tall/polyfit

you would have learned exactly that.

[Ben Komita]

great thank you so much. I was trying to do that but rather than p(1) and p(2) I was doing projection(1) and projection(2) which is where I ran into problems. Thanks!

[darova]