Goodness of Fit Calculator

Formula

To calculate the goodness of fit:

\[ GoF = 1 - \left( \frac{SSR}{SST} \right) \]

Where:

\( GoF \) is the goodness of fit
\( SSR \) is the sum of squares of the residuals
\( SST \) is the total sum of squares

What is Goodness of Fit?

Goodness of fit refers to a statistical measure that shows how well-observed outcomes match the expected outcomes. It is used in various fields such as economics, psychology, and biology to test the validity of a specific model or theory. The test compares the observed data with the expected data according to a certain model, with a smaller difference indicating a better fit. This helps in determining whether the model or theory being tested provides an accurate representation of the reality it’s supposed to describe.

Example Calculation

Let's assume the following values:

Sum of Squares of the Residuals \( SSR \) = 50
Total Sum of Squares \( SST \) = 200

Step 1: Divide the sum of squares of the residuals by the total sum of squares:

\[ \frac{SSR}{SST} = \frac{50}{200} = 0.25 \]

Step 2: Subtract the result from 1:

\[ GoF = 1 - 0.25 = 0.75 \]