# Homework help.

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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

##### 6 Comments

Walter Roberson
on 27 Apr 2012

In that case you will not be able to find a unique answer.

If you consider

a * e^b * x^c

then for every 1 that "b" increases, if you decrease "a" by a factor of "e", then the numeric result will be the same. (a*exp(b)) effectively becomes a single constant and you cannot separate the effect of "a" and "b" -- not unless you have a bunch of constraints that force the constant to be broken down a particular way.

Image Analyst
on 27 Apr 2012

Just to further explain what Walter is saying:

y = a * exp(b) * x^c <== your original equation.

log(y) = log(a) + log(exp(b) + * log(x^c)

log(y) = log(a) + b + c * log(x)

newY = c2 + c1 * newX

with c1 being equal to c, and c2 being equal to log(a)+b.

So now you have two coefficients you can use polyfit to solve for.

But there are lots of combinations of a and b that might give c2.

So no unique solution, at least if you use linear regression.

### Answers (3)

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

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.

##### 3 Comments

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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