Cubic Regression: Exponential Growth & Leveling Off

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The discussion focuses on modeling population data with cubic regression and its limitations. While cubic regression shows initial exponential growth, it inaccurately predicts population decay over time due to a negative coefficient, suggesting the population could decline indefinitely. A logistic model is proposed as a more suitable alternative, as it can better represent a population leveling off at a stable value. The user seeks clarification on the appropriate function to model the data and whether their understanding of the intervals is correct. Ultimately, the conversation emphasizes the importance of selecting the right mathematical model for accurate population predictions.
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Hi,

I have the following population figures for a five year interval:

554.8, 609, 657.5, 729.2, 830.7, 927.8, 998.9, 1070, 1155.3, 1220.5

The graph has an exponential growth from the first value to the fourth value and then the population starts to decay.

I found that a Cubic Regression best illustrates these figures but I have to describe it and, since I've never worked with them I am a bit wary.

Is it correct to say that the cubic correctly illustrates the initial exponential growth of the population but also manages to reflect the leveling off of the population in the latter segment of the plot?

Thanks
 
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ProPM said:
Hi,

I have the following population figures for a five year interval:

554.8, 609, 657.5, 729.2, 830.7, 927.8, 998.9, 1070, 1155.3, 1220.5

The graph has an exponential growth from the first value to the fourth value and then the population starts to decay.

I found that a Cubic Regression best illustrates these figures but I have to describe it and, since I've never worked with them I am a bit wary.

Is it correct to say that the cubic correctly illustrates the initial exponential growth of the population but also manages to reflect the leveling off of the population in the latter segment of the plot?

Thanks
A cubic would get steeper over time, not decay. A logistic function might be the better choice.
 
Yes, a Logistic is my next step, but this function here:

-0.0056755x^3+0.4186x^2+7.35529x+555.2542

Seems to me like it's leveling off towards the end, or is that impossible? It looks like it is possible from google images but you are probably a more trustworthy source :smile:
 
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No, that one isn't leveling off. Because the coefficient of x3 is negative, the graph of this function is heading to negative infinity as x gets large.
 
Um,

Look :redface:
 

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That's a pretty good fit, but is it likely that the population will die out in another 50 years? That's what modeling this data with a cubic spline is predicting. On the other hand, if the population is more likely to approach some stable value, then a logistic model is the way to go.
 
BTW, your first post says the data is for a five-year interval, but you graph uses about a 45-year interval. I suspect that you meant that the data represent populations at five year intervals.
 
Are you just wanting a curve of good fit for these points, or do you plan on extrapolating for the next couple of years?
 
This is what my assignment says:

What types of function could model the behavior of the graph

and a bit later:

Analytically develop one model function that fits the data points on your graph

Furthermore, I am restricting the domain of my graph too.
 
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