The Coefficient of Alienation Calculator helps determine the proportion of variance in a dependent variable that cannot be explained by the independent variable(s) in a statistical model. It is a complementary measure to the Coefficient of Determination (R²) and provides insights into the level of unexplained variance, offering a clear view of the limitations of a predictive model.
This calculator is essential for researchers, data analysts, and statisticians who want to understand the strength and weaknesses of their models. By quantifying unexplained variance, it helps identify areas where the model might need improvement or refinement.
Formula of Coefficient Of Alienation Calculator
The Coefficient of Alienation is calculated using the following formula:

Where:
- R²: Coefficient of Determination, representing the proportion of variance in the dependent variable explained by the independent variable(s).
Interpretation:
- Value = 0: All variance is explained, indicating a perfect model.
- Value = 1: None of the variance is explained, indicating no relationship.
- Values between 0 and 1: Represent the proportion of unexplained variance, with higher values indicating a weaker model.
The Coefficient of Alienation is a straightforward and valuable metric for evaluating the predictive power of statistical models.
Reference Table for Quick Use
The table below provides an overview of common R² values and their corresponding Coefficient of Alienation:
R² Value | Coefficient of Alienation | Interpretation |
---|---|---|
0.9 | 0.1 | Very strong relationship |
0.8 | 0.2 | Strong relationship |
0.5 | 0.5 | Moderate relationship |
0.3 | 0.7 | Weak relationship |
0.1 | 0.9 | Very weak or negligible relationship |
This table serves as a quick reference to assess model performance based on R² and the Coefficient of Alienation.
Example of Coefficient Of Alienation Calculator
Let’s calculate the Coefficient of Alienation for a model with an R² value of 0.75.
Step 1: Apply the Formula
Coefficient of Alienation = 1 – R²
Coefficient of Alienation = 1 – 0.75
Step 2: Perform the Calculation
Coefficient of Alienation = 0.25
Interpretation
The model explains 75% of the variance in the dependent variable, while 25% of the variance remains unexplained. This indicates a reasonably strong model but highlights room for improvement.
Most Common FAQs
The Coefficient of Alienation quantifies the unexplained variance in a model, helping researchers understand its limitations and identify areas for improvement.
While R² measures the proportion of variance explained by the model, the Coefficient of Alienation focuses on the unexplained variance, providing a fuller picture of model performance.
No, the Coefficient of Alienation ranges from 0 to 1. A value of 0 indicates a perfect model, while a value of 1 indicates no relationship between variables.