# What can be determined from an R-Squared value?

##### 1 Answer

The “goodness of fit” of a set of data to a linear equation.

#### Explanation:

The R-squared value is a mathematical calculation of the average match of real data to an equation. We hope that our equation will model the correlation of the independent and dependent variables in a study. By calculating the “error” of using the equation for actual data points, we can see how well our equation “fits” or predicts our data. Averaging the error calculation for all points to the equation gives us a single value – the R-squared value. The closer it is to 1.0, the better the equation fits our actual data.

Generally, anything less than 0.6 can be considered as having very little predictive value – the equation does NOT represent the data well. Values from 0.7 – 0.8 may be considered as showing a possible match of the equation to the data, but should be used with caution. Further caution must be emphasized for values from 0.8 to 0.95. It is ONLY math – it shows a numerical correlation, which may have meaning for the equation and your data. BUT it is never a guarantee nor a “proof” that you equation is a real description of the physical interactions.

An R-squared value of 1.0 usually means that you have over-specified the equation, essentially mapping each point to a specific variable This can happen when using multiple-dimensioned polynomial linearizations. Practically, it means that your equation is inappropriate. Do not take it as an indication that you have a “perfect” fit, as that does not happen in real life.