Plot best fit line in log-space & get slope

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newbie9
newbie9 2019-7-27
评论： Angie Brulc 2022-3-7
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
Capture.JPG

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采纳的回答

Star Strider
Star Strider 2019-7-27
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.
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Star Strider
Star Strider 2019-8-3
As always, my pleasure.
I was working on it as you were posting.

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更多回答（1 个）

newbie9
newbie9 2019-8-3
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:
untitled.jpg
  1 个评论
Angie Brulc
Angie Brulc 2022-3-7
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!

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