Am I using corrcoef correctly?

I want to find R^2 for my polyfit approximation and I read on this form that corrcoef can be used to find R^2. I am however not sure if I have the correct inputs or if I interpret the output correctly? Can someone confirm if I have correctly used corrcoef in this code and that R^2 equals 0.6327 for my polyfit approximation?

H=log([0.01 0.02 0.03 0.04 0.05]);

T=log([0.645 0.647 0.646 0.646 0.647]);

p=polyfit(H,T,1);%derivative=0.0013

f=polyval(p,H);

plot (H,T,'o',H,f,'-');

%legend('data','linear fit')

axis([-4.8 -2.8 -0.45 -0.42])

xlabel("ln(h/m)")

ylabel ("ln(T/s)")

grid on

[R1,P1] = corrcoef(H,T) %R^2=0.6327

Answer 1

[Star Strider]

‘Am I using corrcoef correctly?’

Yes, except for squaring the result, and that will produce .

H=log([0.01 0.02 0.03 0.04 0.05]);
T=log([0.645 0.647 0.646 0.646 0.647]);
p=polyfit(H,T,1);%derivative=0.0013
f=polyval(p,H);
plot (H,T,'o',H,f,'-');
%legend('data','linear fit')
axis([-4.8 -2.8 -0.45 -0.42])
xlabel("ln(h/m)")
ylabel ("ln(T/s)")
grid on

[R1,P1] = corrcoef(H,T) %R^2=0.6327

R1 = 2×2

1.0000 0.6327 0.6327 1.0000

P1 = 2×2

1.0000 0.2520 0.2520 1.0000

Rsq = R1.^2

ans = 2×2

1.0000 0.4003 0.4003 1.0000

And fitlm agrees —

mdl = fitlm(H,T)

mdl = 
Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate         SE         tStat       pValue  
                   _________    __________    _______    __________

    (Intercept)     -0.43194     0.0033633    -128.43    1.0409e-06
    x1             0.0012893    0.00091105     1.4152       0.25196


Number of observations: 5, Error degrees of freedom: 3
Root Mean Squared Error: 0.00116
R-squared: 0.4,  Adjusted R-Squared: 0.2
F-statistic vs. constant model: 2, p-value = 0.252

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[Oliver Lundblad]

ooh nice, thanks for correcting me. By the way, this “fitlm” function does not work for me. “Undefined function 'fitlm' for input arguments of type 'double'.” any idea why?

[Star Strider]

My pleasuire!

The fitlm function is part of the Statistics and Machine Learning Toolbox. It must be licensed and installed in order to use its functions. (There are at least three other Toolboxes that can do parameter estimation, those being the Optimization, Global Optimization, and Curve Fitting Toolboxes.)

.

[Oliver Lundblad]

It works now. thanks for telling me which product to install.

[Star Strider]

As always, my pleasure!

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