Logistic Population growth... w. linear regression and polyfit

i've been giving the following initial data.

t=0:14; n=[105 118 139 164 189 214 240 265 290 316 330 348 363 369 373];

and have been asked to model. the following equation. and compare it to the curve produced by the above data set.

Nt+1=Nt+Nt(r-(r/K)*Nt) % for anyone unfamiliar this is an FDE.

i've also figured out that the above equation can be broken down into the equation below.

(Nt+1-Nt)/Nt=r-r/K*Nt ... where the left hand side can be identifed as the y axis and the RHS can be identified as the x- axis and that r and r/K can be determined through linear regression... and then K can be solved.

I've tried inputting coeff=polyfit(t,n,1) and get 21.1250 and 106.9917 as output. i feel like what i'm doing is right but my number don't make any sense. can anyone give me any feed back. any help is appreciated! thanks!

[Kyle]

any ideas anyone?

[John D'Errico]

Do you mean n in the model?

[John D'Errico]

(Nt + 1 - Nt)/(Nt) == 1/(Nt)

When t = 0, I wonder what happens? Very often when you have something that looks algebraically correct, it is still a poor thing to do using a computer.

[Kyle]

its an FDE. so when t=0, n=105.

Answer 1

[Paul]

I dont understand what you want to do with the fit but the numbers are correct:

    coeff=polyfit(t,n,1)
    n_fit = polyval(coeff,t)
    figure;plot(t,n)
    hold on;
    plot(t,n_fit,'r')
    legend('data','fit')

As you can see the fit is the best linear fit you'll get. The first value of coeff is the slope and the second is the constant.