Scatterplot (0, 200) (1, 150) (2, 113) (3, 84) (4, 63): linear or… Step by Step

Step by step

The question

Question: does a linear or an exponential model fit this scatterplot better?

linear or exponential?

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.

x: 0, 1, 2, 3, 4 same step: + 1

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: minus 50, then minus 37, then minus 29, then minus 21.

The changes are getting smaller and smaller.

They are not about the same.

So it is not linear.

= − 50, − 37, − 29, − 21: not the same

Careful!

Going down each step does not make it linear.

Linear needs about the same number added every step.

Careful: it goes down each step, but that is not linear

3 Check the ratios

Exponential means: we multiply by about the same number each step.

So we divide each y by the one before.

150/200 is about 0.75.

113/150 is about 0.75.

84/113 is about 0.74.

63/84 is about 0.75.

= 150200 ≈ 0.75, 113150 ≈ 0.75, 84113 ≈ 0.74, 6384 ≈ 0.75

All close to 0.75.

y is multiplied by about 0.75 each step.

So an exponential model fits better.

= about × 0.75 every step → exponential

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 0.75 each step goes through the points, or very close.

So the exponential model is right!

the curve passes close to every point; the line does not

Let's look back.

First: look at the points.

Then: check the differences.

Then: check the ratios.

Last: check.

Answer