Scatterplot (0, 12) (1, 19) (2, 25) (3, 33) (4, 40): linear or…

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 7, then plus 6, then plus 8, then plus 7.

The changes are not exactly the same, but they are all close to plus 7.

Real data is never perfect.

Careful!

The y numbers grow, but that does not make it exponential.

What we add each step stays about the same.

So it is linear.

So a linear model fits better.

3 Check

Let's check on the picture.

A straight line that adds about 7 each step goes through the points, or very close.

So the linear model is right!

Let's look back.

First: look at the points.

Then: check the differences.

Last: check.