# Linear regression on a semi-log scale

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James Mathew on 11 Jun 2013
Hi,
I'm trying to plot a linear regression line on a semi-log scale.
Y-axis Linear Received power in dB
X-axis Log distance in m
The program and data I'm using as as follows:
Inc=1;
D=10; %Max meaurement distance
d1=(1:Inc:D); %1m to max measurment distance (D) in Increments (Inc)
RXPdata1=[-45.0983; -53.3746; -54.4132; -56.8286; -59.2905; -60.2743; -60.6919; -59.4938; -64.0525; -62.6163]; %Measured data in dB
semilogx(d1,(RXPdata1(:,1)),'-or') %Plot measured data
hold on
%Graph Set up
title ('Plot showing measured data')
xlabel('Distance (m) [Log scale]')
ylabel('Recieved Power (dB)')
legend ('Measured Data','Location','EastOutside')
axis([0 10 -70 -35]);
hold on
grid on
Can anyone help?
James

Miroslav Balda on 11 Jun 2013
The following code solves your problem:
% James.m
% JAMES Linear regression on a semilog scale
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2013-06-11
%
% Miroslav Balda
% miroslav AT balda DOT cz
%
Inc=1;
D=10; % Max meaurement distance
%
d1=(1:Inc:D); % 1m to max measurment distance (D) in Increments (Inc)
RXPdata1=[-45.0983; -53.3746; -54.4132; -56.8286; -59.2905; -60.2743;...
-60.6919; -59.4938; -64.0525; -62.6163]; % Measured data in dB
%
semilogx(d1,(RXPdata1(:,1)),'-or') % Plot measured data
hold on
%
% % Graph Set up
%
title ('Plot showing measured data','FontSize',14, 'FontWeight','bold')
xlabel('Distance (m) [Log scale]','FontSize',10, 'FontWeight','bold')
ylabel('Recieved Power (dB)','FontSize',10, 'FontWeight','bold')
%
axis([0 10 -70 -35]);
hold on
grid on
%
% Regression
%
logd1 = log10(d1');
A = [ones(size(RXPdata1)),logd1];
c = A\RXPdata1
y = A*c;
plot(d1,y,'o-', d1,y,'*-')
%
legend ('Measured Data','Lin. Regression','Location','EastOutside')
It is all. Good luck!
Mira
James Mathew on 11 Jun 2013
Mira,
Many many thanks, this has saved me hours of work!!!
James
James Mathew on 18 Jun 2013
Mira,
Me again, any chance you could help me out again. If trying to find the following variables for the line:
- where the line intersects 0 (or it is 1?) - the gradient - the regression coefficient
James