Making a Best Fit line with 0,0

So, I am in Engineering Physics 2. My lab partners and I have complied some data. Data is as follows

Capacitance = 1.0e-07 * [
  0.1077
  0.0669
  0.0485
  0.0379
  0.0309
  0.0272
  0.0225
  0.0194
  0.0185
  0.0164
  0.0110
  0.0081
  0.0069]

and

InvDistance = [
  20000
  10000
  6666.666667
  5000
  4000
  3333.333333
  2857.142857
  2500
  2222.222222
  2000
  1333.333333
  1000
  400]

So we plot it and then we tried doing a best fit like but our professor said the slope is incorrect and it needs have the intercept at (0,0). How do I make this best fit line change it's intercept to (0,0) so we can have a slope the professor agrees with?

Answer 1

[Star Strider]

If you want it to go through the origin, do not use an intercept term in your model. In this instance, Capacitance = InvDistance * B, so solve for parameter vector (here a scalar with only the slope) ‘B’.

See if this does what you want:

B = InvDistance\Capacitance;

Fit = InvDistance * B;

figure(1)
plot(InvDistance, Capacitance, 'pb')
hold on
plot(InvDistance, Fit, '-r')
hold off
grid
xlabel('InvDistance')
ylabel('Capacitance')

Your data have to be column vectors for this to work, but since they already are, you don’t need to do anything with them.

Answer 2

[Guillaume]

You're basically wanting to find m (the slope) in:

InvDistance = m * Capacitance;

Which you can solve in matlab with:

m = Capacitance \ InvDistance;

Answer 3

[Latasha Cable]

Thank you very much! This helped us a lot. :D