Asked by rachel
on 26 Apr 2012

You are given a data set (data2.mat) that must be fit to an equation for your lab assignment. You know that the data has the form y = a *e^bx^c . Find the coefficients a, b and c using a MATLAB function that you have written. Display a plot with a logarithmic y scale that shows the data as points and the line as a fit.

Can anyone help me figure this out. I tried using an exponential function program that used linear regression program in it but that didn't work because it didn't deal with the double power factor. So I really don't know how to go about solving this. I'm in a matlab class for the first time and it's week 3 and he's dropping these sort of things on after not really teaching us how to do this. He clearly knows his stuff but he's very bad at reiterating it to his students so we end up lost all the time. Any help would be great!

here's the data

5.1000000e+001 -9.8614120e+000

4.0800000e+002 -9.3766162e+000

1.3770000e+003 -9.4949558e+000

3.2640000e+003 -9.2442098e+000

6.3750000e+003 -9.0007595e+000

1.1016000e+004 -8.8766913e+000

1.7493000e+004 -9.0074649e+000

2.6112000e+004 -8.9332435e+000

3.7179000e+004 -8.8126032e+000

5.1000000e+004 -8.8844865e+000

6.7881000e+004 -8.7144287e+000

8.8128000e+004 -8.3825442e+000

1.1204700e+005 -8.4576726e+000

1.3994400e+005 -8.5157210e+000

1.7212500e+005 -8.4781113e+000

2.0889600e+005 -8.2878923e+000

2.5056300e+005 -8.3766055e+000

2.9743200e+005 -8.2561491e+000

3.4980900e+005 -8.2137268e+000

4.0800000e+005 -8.0925150e+000

4.7231100e+005 -7.9257422e+000

5.4304800e+005 -7.9381544e+000

6.2051700e+005 -7.9537322e+000

7.0502400e+005 -7.8015010e+000

7.9687500e+005 -7.8356798e+000

8.9637600e+005 -7.6697667e+000

1.0038330e+006 -7.5605739e+000

1.1195520e+006 -7.8521843e+000

1.2438390e+006 -7.6577670e+000

1.3770000e+006 -7.6843260e+000

1.5193410e+006 -7.4819766e+000

1.6711680e+006 -7.4679223e+000

1.8327870e+006 -7.3088850e+000

2.0045040e+006 -7.3311661e+000

2.1866250e+006 -7.2934343e+000

2.3794560e+006 -7.1592624e+000

2.5833030e+006 -7.2461091e+000

2.7984720e+006 -7.0129888e+000

3.0252690e+006 -7.0599327e+000

3.2640000e+006 -6.9684428e+000

3.5149710e+006 -6.7472645e+000

3.7784880e+006 -6.8237334e+000

4.0548570e+006 -6.9460063e+000

4.3443840e+006 -6.8844682e+000

4.6473750e+006 -6.8276870e+000

4.9641360e+006 -6.7922145e+000

5.2949730e+006 -6.8443137e+000

5.6401920e+006 -6.7642609e+000

6.0000990e+006 -6.7283737e+000

6.3750000e+006 -6.5985129e+000

6.7652010e+006 -6.8035724e+000

7.1710080e+006 -6.6019244e+000

7.5927270e+006 -6.5038275e+000

8.0306640e+006 -6.5811262e+000

8.4851250e+006 -6.3259601e+000

8.9564160e+006 -6.6594903e+000

9.4448430e+006 -6.2945521e+000

9.9507120e+006 -6.3241126e+000

1.0474329e+007 -6.2211186e+000

1.1016000e+007 -6.2944763e+000

1.1576031e+007 -6.1571240e+000

1.2154728e+007 -6.0425808e+000

1.2752397e+007 -6.2450068e+000

1.3369344e+007 -6.0584327e+000

1.4005875e+007 -6.0119037e+000

1.4662296e+007 -5.9192135e+000

1.5338913e+007 -6.0227574e+000

1.6036032e+007 -5.9185951e+000

1.6753959e+007 -6.0416041e+000

1.7493000e+007 -5.8492313e+000

1.8253461e+007 -6.0539742e+000

1.9035648e+007 -5.8733411e+000

1.9839867e+007 -5.8752898e+000

2.0666424e+007 -5.7343361e+000

2.1515625e+007 -5.8322730e+000

2.2387776e+007 -5.7831574e+000

2.3283183e+007 -5.5679345e+000

2.4202152e+007 -5.6356530e+000

2.5144989e+007 -5.7559464e+000

2.6112000e+007 -5.7025321e+000

2.7103491e+007 -5.6388418e+000

2.8119768e+007 -5.6041841e+000

2.9161137e+007 -5.4867117e+000

3.0227904e+007 -5.4993242e+000

3.1320375e+007 -5.6516519e+000

3.2438856e+007 -5.4882504e+000

3.3583653e+007 -5.5297368e+000

3.4755072e+007 -5.3379112e+000

3.5953419e+007 -5.2417512e+000

3.7179000e+007 -5.1143483e+000

3.8432121e+007 -5.2538556e+000

3.9713088e+007 -5.2262771e+000

4.1022207e+007 -5.1662034e+000

4.2359784e+007 -5.2907350e+000

4.3726125e+007 -5.1033225e+000

4.5121536e+007 -5.0992933e+000

4.6546323e+007 -5.2062895e+000

4.8000792e+007 -5.1410342e+000

4.9485249e+007 -5.0594874e+000

5.1000000e+007 -5.1098396e+000

Answer by Sean de Wolski
on 26 Apr 2012

doc semilogy

doc lsqcruvefit

doc nlinfit

Some places to look...

Answer by Richard Willey
on 26 Apr 2012

Couple quick questions / comments

1. are you sure you typed in the model correctly? This looks very close to a Gompertz function (however some terms are missing)

2. The following example on the Statistics Toolbox page address should give you some useful ideas as to different approaches to solve this problem

rachel
on 27 Apr 2012

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Answer by Walter Roberson
on 27 Apr 2012

Your expression simplifies to y = d * x^b for unknown values "d" and "b" and x known. log() both sides to get

log(y) = log(d) + b * ln(x)

and then this becomes a linear regression.

Image Analyst
on 27 Apr 2012

Walter Roberson
on 27 Apr 2012

Right, this is an explication of how you would proceed after wrapping the variables together, but you cannot separate "a" and "b".

My suspicion is that the expression to fit against was not given to us correctly.

Image Analyst
on 27 Apr 2012

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