I have a question that might be easy...but has me curious
Suppose we have this set of data:
and with this we need to determine the type of growth that best describes it by finding:
-1st Differences [Arithmetic Growth]
-2nd Differences (If needed) [Quadratic Growth]
-Factors (If needed) [Geometric Growth]
Now, my question is how to use this. In order to find the differences do we need to set them up consecutively by time or by distance? Since, when writing a difference program, the array of coefficients is used, I'm assuming that the Distance would be consecutively ordered. Any way I order this the type of growth doesn't follow any of those patterns.
Ordered as shown above:
-1st differences = {5,4,5,8,5,7,1,-2,-3,-1,-10}
-2nd differences = {-1,1,3,-3,2,-6,-3,-1,2,-9}
Ordered by Time (Consecutive):
-1st differences = {1,-2,-3,-1,-10,-19,5,4,5,8,5}
-2nd differences = {-3,-1,2,-9,-9,24,-1,1,3,-3}
Ordered by Distance (Consecutive):
-1st differences = {5,4,5,5,3,5,2,1,3,1,1}
-2nd differences = {-1,1,0,-2,2,-3,-1,2,-2,0}
Does it actually fit any of these types or is some kind of curve fitting needed?
This is not HW by the way. Just a problem I found that I'm curious about.