MATLAB: Adding log-linear trend to scatterplot

add trendlinelog-linear trendscatterplot

Hi. I am trying to add a log-linear trend to a scatterplot with log y axis, but I cant seem to figure out how to do it. It is a very simple plot like this:

>> scatter(data1,data2)
>> set(gca, 'yScale', 'log')

Any suggestions on how to add a log-linear trend? Thanks in advan[c]e.

Best Answer

Fit the log(y), compute the fitted result and add...

b=polyfit(data1,log(data2),1);  % ln y = mx + b
yhat=exp(polyval(data1));       % compute fitted result
hold all                        % prepare to add the fittted line
hLyhat=plot(data1,yhat);        % add to the plot; save handle to make fixups as wanted

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You may want to look at How can I do log-linear de-trending in data?

MATLAB: How to apply exponential and logarithmic curve fitting

The nlinfit function requires that the first argument of the objective function is the parameter vector and the second the vector of independent variables. Using anonymous functions,

y = a*exp(b*x)+c

becomes

y = @(B,x)  B(1).*exp(B(2).*x) + B(3);     % B(1) = a,  B(2) = b,  B(3) = c

For the logarithmic fit, all logs to various bases are simply scaled by a constant. Consider:

a^y = b^x

Taking the log to base a (denoted by loga()) of both sides gives:

y = x*loga(b)

so the log to any base will work.

The anonymous function for your logarithmic regression is then:

y = @(B,x) log(x) + B;     % B = b

or alternatively,

y = @(B,x) B(1).*log(x) + B(2);

Those should work with nlinfit.

Best Answer

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