What to do when "second differences" are different?

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Discussion Overview

The discussion revolves around the analysis of a set of data points to determine the nature of the underlying model based on first and second differences. Participants explore the implications of differing second differences and consider the relationship between linear, quadratic, and exponential models.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents a set of data points and calculates first and second differences, questioning the validity of their results.
  • Another participant suggests that constant first differences indicate a linear model, while constant second differences indicate a quadratic model, prompting a query about constant ratios.
  • A different participant proposes that constant ratios might indicate an exponential model.
  • Further discussion raises the question of whether the nature of the first data point affects the constancy of the ratios.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the calculated differences and ratios, with no consensus reached regarding the nature of the model represented by the data points.

Contextual Notes

Participants do not clarify the assumptions behind their calculations or the definitions of the models discussed, leaving some aspects unresolved.

MRF2
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Hey, I'm using data points:

X: -1; 0; 1; 2; 3
Y:-16; 4; 1; 1/4; 1/16

I solved for the first differences, and got:
-12; -3; -1/4; -3/16

I then solved for second differences, and got:
9; 11/4; 1/16

Is my math just wrong in a way I can't see, or...?
Thanks!
 
Last edited:
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So, if the first-level differences are the same, you've got a linear model. If the second-level differences are the same, you've got a quadratic model. What do you have if the ratios are constant?
 
Ackbach said:
So, if the first-level differences are the same, you've got a linear model. If the second-level differences are the same, you've got a quadratic model. What do you have if the ratios are constant?

Exponential model?
 
MRF2 said:
Exponential model?

I didn't find the ratios to be the same.
 
Yes, it would be exponential if the ratios are the same. Is the first data point -16 or 16?

Hmm:
4/16 = 1/4
1/4 = 1/4
(1/4)/1 = 1/4
(1/16)/(1/4) = (1/16) * (4/1) = 1/4

So, if the first data point is +16 instead of -16, would the ratios be the same?
 

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