Fit log10 function to data and determine the intercept

Hi!

I have data that x is in log10 scale and y is normal. I want to fit a function that should follow the function: y = log10(1/x) + b, where b is the intercept or off set. How do I determine b here?

Sample data here:

x = 0.24. 0.6, 1.2, 2.4, 6, 12, 24

y = 17.2499, 9.8872, 5.6918, 2.7402, 0.6857, 0.1537, 0.0224

The function has be in the form of y = log10(1/x) + b.

Thank you in advance

Answer 1

[Star Strider]

If ‘b’ is the y-intercept, the easiest way is to interpolate:

x = [0.24, 0.6, 1.2, 2.4, 6, 12, 24];
y = [17.2499, 9.8872, 5.6918, 2.7402, 0.6857, 0.1537, 0.0224];

b = interp1(log10(1./x), y, 0);

figure
plot(log10(1./x), y)
hold on
plot(0, b, 'rs')
hold off
grid
legend('Data','b', 'Location','best')
text(0, b, sprintf('b = %.4f \\rightarrow ',b), 'Horiz','right', 'Vert','middle')

.