What is Interpolation?

Personally, for me to understand difficult statistics procedures I find it easier to see concrete examples, things I can understand and on a rare occasion sometimes I’ll even study ugly math. So, I’m not in the mood for ugly math today, So let’s use M & M’s
The colors around these M&Ms are the interpolated colors the source.
Or maybe we could learn from some crime data from San Francisco.
The value of the data outside has been estimated with color and contour perimeters using interpolation.
Scientists use this technique because there is never enough time or money to measure every point in the area of interest.
Interpolation is based on:
Tobler’s Law of Geography, which states that everything is related to everything else, but near things are more related than distant things.
Points closer together in space are more likely to have similar values than points that are farther apart.
This is called spatial autocorrelation, by the way I Googled most of this.
Interpolation is used in many fields, from photography to geology.
There are many different computer algorithms used to interpolate data points.
Scientists choose between different algorithms based on the type of data and how the data will be used.
Here’s an example of how it’s done with software.
So Interpolation is a method for estimating the value of a function between two known data points or values.
For example, suppose we have data for temperatures and corresponding air velocity from 0 to 2000 in 200 steps. Interpolation can be used to estimate the temperature for non re-corded values such as air velocity of 250 .
First you need to know there’s different types of interpolation and here’s just 2 to get started.
Linear interpolation involves estimating a new value by connecting two adjacent known values points with a straight line.
Spline or Cubic interpolation is an approach that with a sequence of value points, and a curve is constructed whose shape closely follows this sequence.
In Graph Builder, we can see that with these data points plotted with a tight Spline allow us to visualize and forecast what the in between data points would be.
If I turn on the cross hairs I can hover over and interpolate values on the fly.
To better analyze this and attain some prediction values we’ll use the Fit Y by X. Which is a comparison of 2 variables. I’ll choose Air Velocity as the Predictor or Y , and Thermal as the X.
Here are plotted data points. Using the red triangle I’ll add a Flexible Line, under Fit Spline choose then I’ll choose 1.
Now for the prediction of data points, we don’t have.
Under the red triangle of the Fit Line. I’ll save a prediction column back to our data table.
Save Predicteds, I didn’t even now that word existed.
Now when I type in a value for Air Velocity I’ll have my interpolated or predicted value for Temperature.
So that’s Interpolation.
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And remember your homework; throw 5 M&Ms in a low clear dish with water in it. Watch the colors merge.
When you are done, do it again, empty the dish and this time uses several different arrangements of color and position.