Step by step
The question
Question: does a linear or an exponential model fit this scatterplot better?
1 Look at the points
Each dot is one point of the data: across is x, up is y.
x goes up by 1 each time, the same step.
So we can compare each point with the one before.
We write the points in a table.
2 Check the differences
Linear means: about the same number is added each step.
So we look at the change from one y to the next: plus 2, then plus 6, then plus 18, then plus 54.
The changes are getting bigger and bigger.
They are not about the same.
So it is not linear.
Careful!
Going up each step does not make it linear.
Linear needs about the same number added every step.
3 Check the ratios
Exponential means: we multiply by about the same number each step.
So we divide each y by the one before.
3/1 is 3.
9/3 is 3.
27/9 is 3.
81/27 is 3.
The same number.
y is multiplied by 3 each step.
So an exponential model fits better.
4 Check
Let's check on the picture.
A straight line from the first point to the last one misses the points in the middle.
A curve that multiplies by about 3 each step goes through the points, or very close.
So the exponential model is right!
Let's look back.
First: look at the points.
Then: check the differences.
Then: check the ratios.
Last: check.