Pay attention to the diagram and note that smaller the value of SSE, smaller is the value of (SSE/SST) and hence greater will be value of R-Squared. R-Squared can also be represented using the following formula: Pay attention to the diagram and note that greater the value of SSR, more is the variance covered by the regression / best fit line out of total variance (SST). Diagrammatic representation for understanding R-Squared Here is a visual representation to understand the concepts of R-Squared in a better manner. If the value of R-Squared is 1, the model fits the data perfectly with a corresponding MSE = 0. For the training dataset, the is bounded between 0 and 1, but it can become negative for the test dataset if the SSE is greater than SST. R-Squared is also termed as the coefficient of determination. This would be discussed in one of the later posts. This is where adjusted R-squared concept comes into picture. Greater the value of R-Squared, better is the regression model. R-squared value is used to measure the goodness of fit. Sum of Squares Regression is amount of variance explained by the regression line. R-Squared is the ratio of Sum of Squares Regression (SSR) and Sum of Squares Total (SST). Mean Squared Error Representation What is R-Squared? Here is the diagrammatic representation of MSE: Fig 2. In the above equation, Y represents the actual value and the Y’ is predicted value. When you take a square root of MSE value, it becomes root mean squared error (RMSE). An MSE of zero (0) represents the fact that the predictor is a perfect predictor. A value close to zero will represent better quality of the estimator / predictor (regression model). The value of MSE is always positive or greater than zero. This is how it is represented mathematically: Fig 1. It is also termed as mean squared deviation (MSD). Mean squared error (MSE) is the average of sum of squared difference between actual value and the predicted or estimated value.
These are used for evaluating the performance of regression models such as linear regression model. In this section, you will learn about the concepts of mean squared error and R-squared.
Introduction to Mean Square Error (MSE) and R-Squared Difference between Mean Square Error & R-Squared.Introduction to Mean Square Error (MSE) and R-Squared.