# What does it mean to interpolate a data?

May 18, 2018

Using a best-fit line to estimate the value of one thing given the value of another.

Say you had a scatter graph and the values had a fairly good linear shape with little scattering, you could estimate (or given the data and a means of calculating, work it out) what the best-fit line. The best-fit line is the linear line which shows the relationship between two sets of data while reducing the amount of scattering on the graph.

Most likely, the best-fit line will have values on either side that will be slightly off the line, and we may not have data for one value.

For example, say a best-fit line followed the equation $y = 1.4 x + 3.5$, we could use this equation to estimate values within a range of data.

So, say we had values of $y$ from $x = 10$ to $x = 40$ and we wanted what $x = 32$ was despite not having it, we could use the equation to estimate what it might be.

We only use interpolation to estimate values within a range of data because extreme values, like $x < 0$ or $x > 100$ might follow a different pattern..