linear: constant difference
quadratic: constant 2nd differences
exponential: constant ratio over equal intervals
Considering linear, quadratic, and exponential lines of best fit:
If you're studying a set of data, how can you decide which of those three types of model would be most appropriate for the data?
3 answers
Steve, thank you, but what do you mean constant 2nd differences? And constant ratio over equal intervals? For me, the difference between linear and exponential is that linear go up/down at a constant amount by adding that same constant amount. Exponential goes up/down by multiplying that same constant amount.
x _y____y(n)-y(n-1) ___ next diff
1__0______
2__5______ 5
3__10_____ 5____________0
4__15_____ 5____________0
5__20_____ 5____________0
6__25______5____________0
THAT is constant diff
now
x _y____y(n)-y(n-1) ___ next diff
1__1______
2__4______ 3
3__9_______5____________ 2
4__16 ____ 7____________ 2
5__25_____ 9_____________2
6__36______11____________2
THAT is constant difference of difference - Get it?
1__0______
2__5______ 5
3__10_____ 5____________0
4__15_____ 5____________0
5__20_____ 5____________0
6__25______5____________0
THAT is constant diff
now
x _y____y(n)-y(n-1) ___ next diff
1__1______
2__4______ 3
3__9_______5____________ 2
4__16 ____ 7____________ 2
5__25_____ 9_____________2
6__36______11____________2
THAT is constant difference of difference - Get it?