For AI agents: use /llms.txt for the Nakafa content index.
After finding the best-fit linear regression line for our data, the next question is: how well does that line actually represent or explain our data?
The measure that answers this question is the Coefficient of Determination, denoted as (read: r-squared).
Simply put, tells us the of the variation (ups and downs in values) in the dependent variable (Y) that by the variation in the independent variable (X) using our linear regression model.
The value of is closely related to how tightly the data points cluster around the regression line:
High (approaching or )
See how the data points above are very tightly packed and close to the regression line? This indicates a high value (for example, maybe around or ). This means that most of the variation in values can be explained well by the regression line (or by variable ).
Low (approaching or )
The easiest way to calculate is by squaring the Correlation Coefficient () that we learned about earlier.
So, if you've already calculated the value of , just square it!
Since the value of is always between and (), the value of will always be between and .
Mathematically (using Sum of Squares):
The value of can also be calculated directly using the Sum of Squares values used to calculate :
The value of is often converted into a percentage (by multiplying by ) for easier interpretation.
The higher the percentage of , the better our linear regression model is at explaining the relationship between and .
Compare this with this diagram. The points are more spread out from the regression line (the residual lines are longer). This indicates a low value (for example, maybe around or ). This means that this regression line is not very good at explaining the variation in values; only a small portion of the variation in can be explained by through this model.
