Coefficient of Determination: Now that we have values of SSR, SSE, and SST. Let’s go ahead and find the coefficient of determination represented as \(R^2\). It is a statistical technique to measure the goodness of fit.
R-squared is generally interpreted as the percentage. If SSR is large, more SST is used and thus, SSE is smaller relative to the total. This ratio acts as a percentage.
Mathematically, it’s the sum of squares regression divided by the Total Sum of Squares.
\(R^2 = \frac{Sum of Squared Regression}{Total Sum of Squares} = \frac{SSR}{SST} \)
Note-1: The value is always between 0(0%) and 1(100%).
Note-2: Larger values of \(R^2\) suggest that our linear model is a good fit for the data we provided.
In our case,
\(R^2 = \frac{119872.9743}{124337.5} = 0.9641\) or 96.41%
Conclusion: We can conclude that 96.41% of the total sum of squares can be explained by our regression equation to predict house prices. Thus the error percentage is less than 4% which implies a GOOD FIT for our model.
While coding in S2, we include the following line to print the coefficient of determination.