Scatterplot (1, 5) (2, 10) (3, 15) (4, 20) (5, 25): 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 5, then plus 5, then plus 5, then plus 5.

We add 5 every step.

The same number.

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 5 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.