# R-Squared

## What it is:

R2, pronounced R-squared, is a percentage measure of how often one variable changes when another variable changes. In statistical terms, it is a measure of how correlated a group of actual observations are to a model’s predictions.

## How it works (Example):

In the following examples, the blue dots represent the going prices for figurine collections on eBay. Collections with more figurines go for as much as \$100; collections with fewer than five figurines sell for very little. How can we predict how much a collection will sell for?

We do it using regression analysis, which essentially finds the formula for the line that most closely fits the observations. That way, we can use the line to predict what the price of the collection might be if we know how many figurines are in a collection, or we can predict how many figurines should be in a collection if we know the asking price.

In our example below, the black lines represent a regression line, which is represented by the formula in the top right-hand corner of each chart. This formula is what analysts also use to predict future values of securities based on the behavior of the actual observations.

The R2 indicates how well the formula works; statisticians call this goodness of fit. The term refers to how far apart the expected values of a financial model are from the actual values (that is, how predictive the line is).

As you can see, this regression line has a high R2 or goodness of fit; the formula for the regression line comes up with the observed values about 79% of the time.

This next chart is an example of a regression line with low R2 or goodness of fit. Here, the values are all over the place, and the formula for the regression line was virtually unable to predict anything.

## Why it Matters:

Regression is a mathematical version of a crystal ball, but a very cracked, blurry crystal ball. Goodness of fit is the key -- it's a confidence measure. This is because when you've come up with a formula that accounts for most of the variations in a group of, say, price observations, you've also come up with a formula that can be a very reliable predictor of what prices will be in the future. And that's priceless.