The Coefficient of Determination, commonly known as R-squared (R²), is a fundamental statistical measure used in the Improve Phase of Lean Six Sigma to evaluate the effectiveness of regression models and understand relationships between variables.
R-squared represents the proportion of variance in…The Coefficient of Determination, commonly known as R-squared (R²), is a fundamental statistical measure used in the Improve Phase of Lean Six Sigma to evaluate the effectiveness of regression models and understand relationships between variables.
R-squared represents the proportion of variance in the dependent variable (Y) that can be explained by the independent variable(s) (X) in your regression model. The value ranges from 0 to 1, often expressed as a percentage from 0% to 100%.
When R² equals 0.85 or 85%, this indicates that 85% of the variation in your output variable is accounted for by the input variables in your model. The remaining 15% is attributed to other factors not included in the analysis or random variation.
In practical Lean Six Sigma applications, R-squared helps teams determine whether their process improvement efforts are targeting the correct factors. A higher R² value suggests a stronger relationship between the Xs and Y, indicating that controlling these input variables will have a significant impact on the output.
However, practitioners should exercise caution when interpreting R-squared values. A high R² does not guarantee causation, nor does it confirm that the model is appropriate for prediction. Additionally, R² naturally increases when more variables are added to a model, even if those variables provide minimal value. This is why Adjusted R-squared is often preferred, as it accounts for the number of predictors in the model.
During the Improve Phase, Green Belts use R-squared to validate that proposed solutions address root causes effectively. When conducting Design of Experiments (DOE) or regression analysis, R² helps confirm that the identified critical inputs genuinely influence the process output. Teams typically seek R² values above 0.70 for process improvement projects, though acceptable thresholds vary by industry and application complexity.
Coefficient of Determination (R-squared) - Complete Guide for Six Sigma Green Belt
Why is R-squared Important?
The Coefficient of Determination, commonly known as R-squared (R²), is a critical statistical measure in the Improve Phase of Six Sigma projects. It helps practitioners understand how well their regression model explains the variability in the outcome variable. This metric is essential for:
• Validating the strength of relationships between variables • Making data-driven decisions about process improvements • Determining if identified factors truly influence the output • Justifying project recommendations to stakeholders
What is R-squared?
R-squared is a statistical measure that represents the proportion of variance in the dependent variable (Y) that is explained by the independent variable(s) (X) in a regression model. It is expressed as a value between 0 and 1, or as a percentage between 0% and 100%.
• R² = 0 means the model explains none of the variability • R² = 1 means the model explains all of the variability • R² = 0.75 means 75% of the variation in Y is explained by X
How Does R-squared Work?
R-squared is calculated using the following concept:
R² = 1 - (SS Residual / SS Total)
Where: • SS Residual = Sum of Squares of Residuals (unexplained variation) • SS Total = Total Sum of Squares (total variation)
The calculation compares how much variation your model explains versus the total variation present in the data. A higher R² indicates a better fit between your model and the observed data.
Interpreting R-squared Values
• 0.90 - 1.00: Excellent fit - the model explains most variation • 0.70 - 0.89: Good fit - strong explanatory power • 0.50 - 0.69: Moderate fit - useful but other factors exist • Below 0.50: Weak fit - model may need improvement
Note: Acceptable R² values vary by industry and application context.
Exam Tips: Answering Questions on R-squared
1. Remember the Range: R² always falls between 0 and 1. If you see an answer option outside this range, eliminate it.
2. Interpretation Questions: When asked what an R² value means, focus on the percentage of variation explained. For example, R² = 0.85 means 85% of the variation in Y is explained by the model.
3. Higher is Generally Better: A higher R² indicates a stronger relationship, but be cautious of overfitting when using multiple predictors.
4. Know the Difference: R² measures correlation strength, not causation. Do not confuse explanatory power with cause-and-effect relationships.
5. Adjusted R-squared: Be familiar with Adjusted R², which accounts for the number of predictors and is more appropriate for multiple regression analysis.
6. Common Trap Questions: Watch for questions that test whether you understand R² cannot be negative and that adding more variables always increases R² (but not necessarily Adjusted R²).
7. Connect to Six Sigma Context: Remember that R² helps validate whether your identified Xs truly influence Y, which is fundamental to the Improve Phase.
8. Formula Recognition: Be prepared to identify R² from regression output tables and understand its relationship to the correlation coefficient (r), where R² = r² for simple linear regression.