Linear fit to log x axis scatter and correlation calculation

I have two data streams 618*1 doubles; say 'a' and 'b'

I want to plot scatter of 'a' versus 'b', 'b' in x axis in log scale

I also need a best fit line and a correlation coefficient

My code runs

scatter (a,b,10,[0.5,0.5,0.5],'filled')
set(gca,'XScale','log')
hold on;
set(gca,'Linewidth,2, FontSize',14,'FontWeight','bold');
box on;
p=polyfit(a,b,1); f=polyval(p,a);
plot(a,f,'--')

I am getting multiple fitting lines..one straight..rest curved...in same plot...I am looking for a single line. Also I require to find correlation coefficient.

PS: I even tried to replace a by log10(a) in the following lines as

p=polyfit(log10(a),b,1); f=polyval(p,log10(a));
plot(log10(a),f,'--')

NOw I am getting the multiple fitting lines away from my scatter...kindly help...I also shall require the correlation value

Answer 1

[dpb]

You forgot to attach the data so made something up...

x=1:10;
y=sort(lognrnd(10,1,1,10));
b=polyfit(x,log10(y),1);
yf=10.^polyval(b,[x(1) x(end)])
figure
scatter(1:10,y)
hLF=plot([x(1) x(end)],yf,'--');
xlim([0.5 10.5])
hAx=gca;
hAx.YScale='log';

gives

Rsq from log is fraught with danger; beware.

[Bhowmik.U]

I enclose the data.

The issue is I wish to have 'b' column as x axis, change the x axis to log scale and y axis unchanged and then obtain a straight line fit onto this and the correlation coefficient.

scatter(b,a,10,[0.5 0.5 0.5],'filled')
hold on;
set(gca,'LineWidth',2)
set(gca,'FontSize',14,'FontWeight','bold')
set(gca,'XScale','log')
 text(5,2000,str,'FontSize',14, 'FontWeight','bold');
box on;
hold on;
p=polyfit(b,a,1); f=polyval(p,b);
plot(b,f,'--')

even if I use log(b) instead of b in last two lines same issue.

[dpb]

Just reverse x,y above, excepting since it is the independent variable in log scale not the dependent (far less common); hence my misread earlier). Using the same data as previous x,y that happen to still be in my workspace:

figure
scatter(y,x)
hAx=gca;
hAx.XScale='log';
xlim([0.035 1]*1E5)
b=polyfit(y,log10(xx),1)
yf=polyval(b,log10([y(1) y(end)]))
hLF=plot([y(1) y(end)],yf,'--');

results in

Rsq is just

Rsq = 1 - SSres/SStot

SSres => Sum of Squares Residuals 
SStot => Total Sum of Squares

Again I'll caution against Rsq on logged variables; the value is generally heavily overestimated altho on semilogx with y in linear scale, not so much as other-way-round.

If have Statistics TB, the curve fitting routines in it have the calculation returned...