Plot best fit line in log-space & get slope

I am trying to determine the slope of the best-fit line in log space, and plot the best-fit line as a visual check. It needs to be a line, not a curve (I understand that the misfits could be very large in logspace). Below is an example with xy data and polyfit attempts (and plot included). Thanks for any help

x = [7.94, 16.23, 32.92, 66.8, 135.52, 274.93, 557.78, 1131.59, 2295.72, 4657.46];
y = [134000, 102000, 31000, 11000, 2600, 990, 40, 10.41, 3.48, 1.037];
scatter(x,y, 'DisplayName', 'MyData')
set(gca,'xscale','log')
set(gca,'yscale','log')
hold on
grid on
box on
axis equal

p = polyfit(log10(x), log10(y), 1);
z = polyval(p, log10(x));
loglog(x, log10(z), 'DisplayName', 'Try1');
loglog(x, z, 'DisplayName', 'Try2');
z2 = polyval(p, x);
loglog(x, z2, 'DisplayName', 'Try3');
loglog(x, log10(z2), 'DisplayName', 'Try4');

legend

Answer 1

[Star Strider]

You are regressing ‘log10(x)’ against ‘log10(y)’ so you need to give the appropriate information to both polyfit and polyval:

Bp = polyfit(log10(x), log10(y), 1);
Yp = polyval(Bp,log10(x));

figure
plot(log10(x), log10(y), 'pg')
hold on
plot(log10(x), Yp, '-r')
hold off
grid

producing this plot:

The slope is -2.0182.

[newbie9]

the fit needs to be a straight line in logspace, not linspace

[Star Strider]

O.K., try this:

x = [7.94, 16.23, 32.92, 66.8, 135.52, 274.93, 557.78, 1131.59, 2295.72, 4657.46];
y = [134000, 102000, 31000, 11000, 2600, 990, 40, 10.41, 3.48, 1.037];
Bp = polyfit(log10(x), log10(y), 1);
Yp = polyval(Bp,log10(x));

figure
loglog(x, y, 'pg')
hold on
loglog(x, 10.^Yp, '-r')
hold off
grid
expstr = @(x) [x(:).*10.^ceil(-log10(abs(x(:))))  floor(log10(abs(x(:))))]; % Mantissa & Exponent
Bp2 = expstr(10^Bp(2));
eqn = sprintf('y = %.2f\\times10^{%d}\\cdotx^{%.2f}',Bp2(1), Bp2(2), Bp(1));
legend('Data', eqn)

Same essential code & plot, different axes scales:

Experiment to get it to look the way you want.

[newbie9]

thanks, that's what I have below

[Star Strider]

As always, my pleasure.

I was working on it as you were posting.

Answer 2

[newbie9]

Star Strider basically gave the correct answer, so I have accepted; but I wanted to show the fit in log-log space, so here's my version of code, considering Star Strider's answer, in case it is useful to anyone else:

x = [7.94, 16.23, 32.92, 66.8, 135.52, 274.93, 557.78, 1131.59, 2295.72, 4657.46];
y = [134000, 102000, 31000, 11000, 2600, 990, 40, 10.41, 3.48, 1.037];
scatter(x,y, 'DisplayName', 'MyData')
set(gca,'xscale','log')
set(gca,'yscale','log')
hold on
grid on
box on
axis equal
%
Bp = polyfit(log10(x), log10(y), 1);
Yp = polyval(Bp, log10(x));
Yp2 = 10.^(Yp);
%
plot(x, Yp2, '-r', 'DisplayName', 'Fit');
text(1.1, 10, strcat('Slope in Log-Log Space =', num2str(Bp(1))), 'Interpreter', 'none');
legend

Which yields this plot:

[Angie Brulc]

Hello,

I'm a random student working on processing data for a lab and just wanted to let you know this was incredibly helpful to me. Thank you!