putting a trendline on a semi-log plot in MatLab.

The values are as following,

avgspeed = [27.7846701084929; 31.1385896602218; 33.3643634350556; 37.0654321948195; 38.5042712877777; 41.3807720015859] ;

height = [13; 33; 55; 155; 245; 519];

semilogy(avgspeed, height)

How do I code to find the equation of trendline for this semi-log plot?

Answer 1

[William Rose]

@Shinichiro Shimata,

To add the trendline quation to the plot, see last two lines of the code below.

avgspeed = [27.78; 31.14; 33.36; 37.07; 38.50; 41.38];  %the x values
height = [13; 33; 55; 155; 245; 519];       %the raw y values
%next: make a matrix with a column of ones and a column of the x values
X=[ones(length(avgspeed),1) avgspeed];    %X=(column of ones,column of x values)
Y=log10(height);        %log(height), for the regression
%next line: the standard matrix equation for a linear regression
b=inv(X'*X)*X'*Y;       %b(1)=intercept, b(2)=slope
predheight=10.^(X*b);   %the heights predicted by the linear regresison
semilogy(avgspeed,height,'rx',avgspeed,predheight,'r-');
xlabel('Avg.Speed'); ylabel('Height');
textstr=sprintf('Pred.Height=\n10^{(%.3f+%.3f*AvgSpeed)}',b(1),b(2));
text(27,520,textstr);

The code above produces the plot below.

Answer 2

[William Rose]

@Shinichiro Shimata,

Here is the solution. Your question demonstrates Matlab's power and code efficiency: it takes only 6 lines of code, after the data is specified, and no toolbox functions are needed. Most of the text below is just comments.

avgspeed = [27.78; 31.14; 33.36; 37.07; 38.50; 41.38];  %the x values
height = [13; 33; 55; 155; 245; 519];       %the raw y values
%next: make a matrix with a column of ones and a column of the x values
X=[ones(length(avgspeed),1) avgspeed];    %X=(column of ones,column of x values)
Y=log10(height);        %log(height), for the regression
%next line: the standard matrix equation for a linear regression
b=inv(X'*X)*X'*Y;       %b(1)=intercept, b(2)=slope
predheight=10.^(X*b);   %the heights predicted by the linear regresison
semilogy(avgspeed,height,'rx',avgspeed,predheight,'r-');
xlabel('Avg.Speed'); ylabel('Height');

And the output is below:

If you need to report the equation for the predicted height, it is:

predheight=10^(b1 + b2*avgspeed)

where b=[b1;b2] is calculated in the code.

[Shinichiro Shimata]

Thank you so much!

I am still having a hard time displaying equation of the trendline. Could you help me further?

Thanks,

Answer 3

[Shinichiro Shimata]

Man, thank you again!!