The correct relationship between SST, SSR, and SSE is given by
a.
SSR = SST + SSE
b.
SST = SSR + SSE
c.
all of the options
d.
none of these options
e.
SSE = SSR + SST
The correct answer and explanation is :
The correct relationship between SST (Total Sum of Squares), SSR (Sum of Squares for Regression), and SSE (Sum of Squares for Error) is:
b. SST = SSR + SSE
Explanation:
In the context of regression analysis, SST, SSR, and SSE are key components used to assess the variability in the dependent variable.
- SST (Total Sum of Squares): This represents the total variation or total sum of squared differences between each observed value and the mean of the observed values. It measures the overall variance in the dataset before any model is applied.
- SSR (Sum of Squares for Regression): SSR represents the part of the total variation that can be explained by the regression model. It measures the variability explained by the independent variables (predictors) used in the regression model.
- SSE (Sum of Squares for Error): SSE measures the variation that cannot be explained by the regression model. It represents the residual or error variance, which is the difference between the observed values and the predicted values based on the regression model.
The relationship among these components is based on the fact that the total variation (SST) in the observed data can be partitioned into two parts:
- Explained Variation (SSR): The part of the total variation explained by the regression model.
- Unexplained Variation (SSE): The part of the total variation that remains unexplained by the regression model.
Mathematically, this relationship is expressed as:
[
SST = SSR + SSE
]
This equation states that the total variability in the dependent variable (SST) is equal to the sum of the explained variability (SSR) and the unexplained variability (SSE).
This partitioning helps assess the goodness-of-fit of a regression model by comparing how much of the variability is explained (SSR) versus unexplained (SSE).