add lsline or trend line to log-log graph

i want to draw a least square line to log-log plot i am using following scripy

wet=[120 49 30 21 12 10 9 7 4];
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
scatter(x1,wet);
set(gca,'XScale','log');
set(gca,'YScale','log');
lsline

but it is not working. is their any other way to draw a line which is straight pass through the points

Answer 1

[Star Strider]

This works:

wet=[120 49 30 21 12 10 9 7 4];
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
scatter(x1,wet);
set(gca,'XScale','log');
set(gca,'YScale','log');
b = polyfit(log(x1), log(wet), 1);
wetfit = exp(b(2)) .* x1.^b(1);
hold on
plot(x1, wetfit)
hold off

producing:

[Nabeel]

thanks it worked can i extend it to x-axis

[Nabeel]

can it also be used to dry scatter plot.

[Star Strider]

My pleasure.

This code will plot (extrapolate) to intercept the x-axis (where wet=1). The x-intercept is calculated in ‘xint’:

wet=[120 49 30 21 12 10 9 7 4];
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];

b = polyfit(log(x1), log(wet), 1);
wetfit = exp(b(2)) .* x1.^b(1);
xint = (1/exp(b(2)))^(1/b(1));              % ‘x’-Intercept
x1vec = linspace(min(x1), xint, 10);        % Extrapolated ‘x1’
wetext = exp(b(2)) .* x1vec.^b(1);          % Extrapolated ‘wet’ Fit

figure(1)
scatter(x1,wet);
set(gca,'XScale','log');
set(gca,'YScale','log');
hold on
plot(x1vec, wetext)
hold off

It won’t work for ‘dry’ because ‘dry’ has zero values. Since log(0)=-Inf, you cannot do a log-log fit or plot with zero-valued data. You have to decide what you want to do about the zero values first.

[Nabeel]

thanks again if i truncate 0 values the code for wet will work for dry as well? when i remove 0 from dry first code has worked and line touches the axis because of 1

can i label only dry and wet leaving dry trend and wettrend again

lot of thanks helping me

[Star Strider]

My pleasure!

I am not certain what you want to do with your legend, but if you want to label only the points and not the lines, the easiest way is to plot them in this order:

figure(1)
scatter(x1, wet, 'ob')
hold on
scatter(x1, dry, 'or')
plot(x1vec, wetext)
plot(x1vec, dryext)
hold off

and then only include the first two in the legend:

legend('Wet','Dry','Location','NE')

You can fit all the ‘dry’ data, but not using polyfit. You have to use a nonlinear curve fitting routine.

Using fminsearch:

dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
x1dry = linspace(min(x1), max(x1));

pwrfit = @(b,x) b(2) .* x.^b(1);

OLSCF = @(b) sum((dry-pwrfit(b,x1)).^2);

B = fminsearch(OLSCF, [-2; 50]);

figure(2)
loglog(x1, dry, 'or')
hold on
plot(x1dry, pwrfit(B,x1dry), '-r', 'LineWidth',2)
hold off

You can of course do this with the ‘wet’ data as well.

[Nabeel]

it is possible to fine R-squared for wet and dry data sets Thanks

[Star Strider]

I would use the corrcoef function on the log-transformed variables.

[Nabeel]

in equations

wetfit = exp(b(2)) .* x1.^b(1);

exp(b(2)) is the slope of equation?

[Star Strider]

In the nonlinear equation, ‘b(1)’ corresponds to the slope in the log-transformed equation, and ‘exp(b(2))’ corresponds to the intercept. (In my ‘pwrfit’ function, I kept the same representation for consistency.)

[Nabeel]

there is a function of r-squared at http://www.mathworks.com/matlabcentral/fileexchange/34492-r-square--the-coefficient-of-determination i want to use this function for the code you have given to me. how can it be used.. thanks

[Nabeel]

hi, i have applied the following code to my original data. wet=[807 427 268 130 83 41 27 14 5 4 2 3 1]; x1=[1 2 3 4 5 6 7 8 9 10 11 12 13]; dry=[494 332 245 150 126 78 69 48 38 35 26 21 21 22 9 9 13 7 10 3 4 5 4 3 5 3 2 3 2 1 5 1 2 4 2 3 1 1 1 1 1 1]; x2=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 36 37 38 40 42 44 46 48 53]; bwet = polyfit(log(x1), log(wet), 1); wetfit = exp(bwet(2)) .* x1.^bwet(1); wetslope=bwet(1); xintwet = (1/exp(bwet(2)))^(1/bwet(1)); m=length(x1)+1; x1vecwet = linspace(min(x1), xintwet, m); wetext = exp(bwet(2)) .* x1vecwet.^bwet(1); figure(1) scatter(x1,wet,'filled','k'); hold on plot(x1vecwet, wetext,'r','LineWidth',2.5,'LineStyle','--') scatter(x2,dry,'d'); set(gca,'XScale','log'); set(gca,'YScale','log'); bdry = polyfit(log(x2), log(dry), 1); dryfit = exp(bdry(2)) .* x2.^bdry(1); dryslope=bdry(1); plot(x2, dryfit,'LineWidth',2.5) hold off

it has r-squared of 0 for both wet and dry :-( (This a a rainfall wet and dry days) i am not a regular programmer....

[Star Strider]

The code in the FEX contribution seems to use the same algorithm mine does for R-squared. Mine uses the nonlinear fit and the OLSCF (Ordinary Least Squares Cost Function) to generate the ‘norm(Y-X)’ data.

I didn’t run the FEX submission, but I trust my code.