I am trying to fit an exponential and logistical model to a set of population data i've been given using the NonlinearFit function in the statistics toolbox. When try to find the fit for the exponential function I get an error saying "SVD of estimated Jacobian could not be computed". Furthermore, when I display the regression over the set of data points all it shows is a horizontal line. I'm not sure how to go about fixing this. My data set is only 17 points and my input function is about as simple as it gets.
When I run the program to solve for logisitcal model I do not get the error but the displayed plot still shows just a horizontal line dispite the function being non-linear.
So far I have...
regE := NonlinearFit(a*exp(b*x),year,population,x)
regLog := NonlinearFit(a/(1+b*exp(-c*x)),year,population,x)
expon := plot((regE), x = 1850..2020):
logi := plot((regLog), x = 1850..2020):
I have not tried using optimization yet but I will soon although I'm not sure if it will improve my results since my undertanding is that they both use the same process to estimate the parameters.
Anyways, Thanks for the help in advance!!
EDIT: Here is the data I am using.
year := [1850,1860,1870,1880,1890,1900,1910,1920,1930,1940,1950,1960,1970,1980,1990,2000,2010]: