Population Growth Model

[JB]

This is a model I've developed based on the logistic growth equation, which has been in use for over 150 years to describe population growth in a constrained environment. In our case, the constraint is land.

The population growth curve shows a rapid growth phase, followed by a steady rise to equilibrium. At equilibrium, the population will reach steady state, with natural variations above and below. However, the population will always gravitate back to the equilibrium point.

The District 204 model which was developed based on 21 years of data (1985 – 2005). The proof of any forecasting tool is its ability to predict, and this one does quite well. The equation fits the data with a correlation coefficient of 0.9997. If your wondering what this means, consider that 1.000 means perfect agreement between forecast and actual data.

Put another way, if you had this model in 1984, when the district had 3,239 TOTAL students, you would have predicted that in 2005 that enrollment would be 27, 857. You’d be off by 44 students.

The model predicts our district will come into equilibrium at 31,743 students. Into the future, we will experience natural variation about this number, much like we’ve seen in District 203.

It is interesting that this model is in agreement with the district's methodology of adding current enrollment to projected new student generation. It's also in agreement with the rather simple approach of dividing current student population by % build-out.

You'll also note that this is a total student population projection. It is an established principle of forecasting that forecasts on aggregated numbers (i.e. student population) are more accurate than forecasts based on lower level data (i.e. 3rd grade enrollment).

[rew]

JB, can one say from the data, at equilibrium, that 31,753 is about 2440 kids per class, or about 9600-9700 HSers?? And that's 95% utilization of 10200 HS seats?

[rew]

JB...can you email your growth prediction model to 204thekids??? I think people should see it!!!

[204parent]

jb,
This is a very impressive model. A correlation coefficient of 0.9997 is a very tight fit for the curve. Visually, it looks just like district 203, which is what one would expect.

It also correlates perfectly with the charts in the 'bursting the bubble' document.

[JB]

204parent said:

jb,
This is a very impressive model. A correlation coefficient of 0.9997 is a very tight fit for the curve. Visually, it looks just like district 203, which is what one would expect.

It also correlates perfectly with the charts in the 'bursting the bubble' document.

Nice one-two punch. Thanks for laying the groundwork.

[JB]

rew said:

JB, can one say from the data, at equilibrium, that 31,753 is about 2440 kids per class, or about 9600-9700 HSers?? And that's 95% utilization of 10200 HS seats?

That's how I look at it. In forecasting, it is more accurate to forecast aggregated groups, i.e. total student population, then use ratios to determine sub-group projections.

So, take the 31,750, divide by 12.9 or so to take into account the private kindergartner who enter the district in first grade, and you get about 2,461 per class / 9,845 at the HS level. That's about 93% if you estimate 400 kids also using the COD campus.

204TK has the info - wanted to give you all a sneek preview.

[Arch]

JB,

Excellent work and put together. That's into the threshold of 'extra' students above today's numbers that I said earlier would be needed to swing me over. Just waiting to hear from Dave Holm on the refinance amounts and I think you've got yourself a convert.

[admin]

JB that is great work. I also copied it over to the research area.

ETA: This is what I love about this board.

[kae]

It's a pretty graph, but can you post the model equations and the input data? Maybe you could post the Excel spreadsheet too.

[hodedo]

jb said:

This is a model I've developed based on the logistic growth equation, which has been in use for over 150 years to describe population growth in a constrained environment. In our case, the constraint is land.

The population growth curve shows a rapid growth phase, followed by a steady rise to equilibrium. At equilibrium, the population will reach steady state, with natural variations above and below. However, the population will always gravitate back to the equilibrium point.

The District 204 model which was developed based on 21 years of data (1985 – 2005). The proof of any forecasting tool is its ability to predict, and this one does quite well. The equation fits the data with a correlation coefficient of 0.9997. If your wondering what this means, consider that 1.000 means perfect agreement between forecast and actual data.

Put another way, if you had this model in 1984, when the district had 3,239 TOTAL students, you would have predicted that in 2005 that enrollment would be 27, 857. You’d be off by 44 students.

The model predicts our district will come into equilibrium at 31,743 students. Into the future, we will experience natural variation about this number, much like we’ve seen in District 203.

It is interesting that this model is in agreement with the district's methodology of adding current enrollment to projected new student generation. It's also in agreement with the rather simple approach of dividing current student population by % build-out.

You'll also note that this is a total student population projection. It is an established principle of forecasting that forecasts on aggregated numbers (i.e. student population) are more accurate than forecasts based on lower level data (i.e. 3rd grade enrollment).

Maybe I am a little slow...but where does home price, competition from surrounding suburbs, SB actions/decisions, changing demographics, age of housing stock, age of residents, mobility, private school attendance, taxes, etc. come into play in the model?

Recent Examples: 2 developments canceled, 2 new developments not selling, residential permits dropping off cliff, Plainfield building new HS facilities and more affordable vs Naperville. Carillon adult community (kid restricted) of about 900 units is only development moving forward at this time in Sector G just north of 95th (what about tail end of baby boomer kids passing thru?).

Why would the curve not flatten and/or go down from here?

Were there adult communities or high schools 150 years ago?

Do 150 year old models really work for high school student projections and is history always a predictor of the future?

[kae]

Still waiting on those model equations and data or do you want everyone to just take this at face value as being valid?

I would think by now this group would know that it takes more than a pretty picture to convince anyone of anything. Isn't this what everyone complains that CFO does all the time?

Where's the assumptions?
Where's the external factors?

We're not just growing bacteria in a petre dish under a controlled environment.

[Arch]

For me it was this as far as enrollement goes: It was never the doubt as to the eventuality.. it was always the WHEN... since there is still space to be built out eventually (now eventually is a long time, granted) we are at a point now that already has a certain number in the queue that will be hitting the HS level.. .that's 9,200.

For me, we needed about another 200+ in each class to 'justify' it from an enrollment perspecive. It's not that unreasonable to look at the overturn in older neighborhoods as the replacement... The key point was this:

I was going under the assumption that the 1:1 replacement had to maintain the year before.. But for the older neighborhoods, it really has to only maintain what was there 18 years ago (a much lower threshhold) to maintain the current numbers... and that's a far lower threshold to maintain, even *IF* faced with a slow buildout and slower growth (which I think will still happen).

(( This tidbit is not hit on by anyone's numbers or explanations here or anywhere else that I've seen ))

So, that made this chart very believable... even without the chart, with the reshift in the 1:1 replacement thinking it created a "you're both right" scenerio that was easy to see as soon as I stepped back 3 feet, cleared the head and re-looked at things.

The re-finance information that came to light recently (that it was not the full 272 million) helped to curb the fears of the triple financial whammy that would have been waiting if it were re-doing the full amount.

So, with both of those personal concerns 'at ease' it was easy to reassess my position.



(any typos, blame the d**ned boxed wine)

[admin]

Maybe he hasn't seen your post yet. why don't you PM him/her.

[admin]

Does Plainfield take in more than $0.260 billion per year in taxes like 204? I would be surprised. What I meant was less housing cost in Plainfield = less tax dollars, not what the rate is. What is the rate BTW?

I guess it is easier to complain than to actually go find the facts and report back.

[204parent]

hodedo said:

$0.260 billion per year in taxes

Wow, that sounds like a lot of money. It just made me realize that my house is worth over $0.0004 billion! Hey, I'm a fractional billionaire!!! ;D