In my homework, I was given the following problem:

The following data represent the population of a country. An ecologist is interested in building a model that describes the population.

$$\begin{array}{c|c}\text{Year, x} & \text{Population, y} \\ \hline 1900 & 76,212,168 \\1910 & 92,228,496\\1920 & 106,021,537\\1930&123,202,624\\1940&132,624,569\\1950&151,325,798\\1960&179,323,175\\1970&203,302,031\\1980&226,542,203\\1990&248,709,873\\2000&281,421,906\end{array}$$

(a) Treating the year as the independent variable and the population as the dependent variable, use a graphing utility to fit a logistic model from the data. Find the values for a, b, and c in a logistic model of the form $y = \frac{c}{1+ae^{-bx}}$.

As it says to use a graphing utility, I plugged it in to my graphing calculator, which is a TI-89, as follows: I went to the "APPS" button, then "Data/Matrix editor", then "new", then selected "data" and gave it the name "a", I think, or something similarly innocuous, then put all the x data (years) into column c1 and all the y data (population into column c2. Then I went to the "Calc" menu and selected "Logistic" for my calculation type, and put in "c1" and "c2" for my x and y data, respectively, and had it store the regression equation to y1. I selected "NO" for frequencies and categories.

Running this produces the error "singular matrix". I talked to my teacher and he has no idea why this is happening, and he seemed to think that I had done everything correctly (however, he said he was unfamiliar with the TI-89 so something may have missed his notice). I looked it up and it seems like that error shouldn't even be coming up for the logistical regression - they only mention it for SinReg and the polynomial regression.

Nobody else in the class seemed to be having this trouble (they mostly use TI-84s, I think). Any help would be appreciated. Thanks!


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