Measures of Variation and Goodness-of-fit-measure
Objective “to find SSR, SSE, SST, Coefficient Determination(R²) and Correlation(R)”
SSR/RSS ( Sum of Squared Regression): SSR Describes the explained variation in the model. It is the sum of the squared difference between the predicted value and mean of the observed value.
SSE/ESS ( Sum of Squared Errors ): SSE describes the unexplained variation in the model. It’s the sum of the squared difference between the observed value and predicted value.
SST/TSS ( Total sum of Squares): It describes the total variance in the model. The sum of SSR and SSE gives SST. i.e SST = SSR + SSE. In other words, it’s the sum of the squared difference between the observed value and mean of the observed value.
Coefficient of Determination (R²): It measures the goodness-of-fit. R² explains the percentage of variation in the model. The higher the percentage better the model. It is always between 0 and 1. It can never be negative — since it is a squared value.
Correlation Coefficient ( R): It measures the direction and the strength of the model. The values range between -1.0 and 1.0. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.
Note: The statistical point of view on covariance and correlation ( Frequently asked question in the interview )
