How Model Selection Is Done on Minitab Assignment Using Regression Techniques
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- Stepwise Regression in Minitab
- How the Stepwise Method Works
- How to Interpret Stepwise Output
- Forward Selection Method in Minitab
- How Forward Selection Is Conducted
- How to Interpret Forward Selection Results
- Backward Elimination Method in Minitab
- How Backward Elimination Works
- How to Interpret Backward Elimination Results
- Best Subset Regression in Minitab
- How Best Subsets Regression Is Run
- How to Interpret Best Subsets Output
- AIC Model Selection Using Minitab Output
- How AIC Is Calculated
- How to Compare Models Using AIC
- Conclusion
Model selection is a critical step in building a reliable statistical model, particularly when multiple predictors are involved. In Minitab, several techniques such as Stepwise Regression, Forward Selection, Backward Elimination, Best Subset Regression, and model comparison using AIC help students choose the best predictive model. For those working on a Minitab assignment involving model selection, understanding these processes can significantly improve accuracy and confidence.
This blog explores how each method works within Minitab, offering structured insights through practical example outputs to help students successfully complete model selection tasks in their assignments. Whether you're analyzing real data or preparing reports, these techniques can help you solve your statistics assignment with greater clarity and precision.
Stepwise Regression in Minitab
Stepwise regression is one of the most widely used model selection techniques because it combines both forward selection and backward elimination. Understanding this method is essential when you need to complete your Minitab assignment with accuracy and statistical justification.
How the Stepwise Method Works
The Stepwise procedure starts by selecting the most significant variable using forward selection. After this, it tests whether previously included variables should be removed, using backward elimination. This iterative approach continues until no more variables can be added or removed based on predefined alpha levels.
- Alpha-to-Enter: Usually 0.05
- Alpha-to-Remove: Typically 0.10
How to Interpret Stepwise Output
Suppose we are analyzing how BMI and exercise influence blood pressure using data from 10 males aged 50. When a stepwise regression is performed with alpha-to-enter = 0.05 and alpha-to-remove = 0.10, the result includes BMI but excludes exercise.
- R-Sq: 73.94% (indicating good explanatory power)
- Adjusted R-Sq: 70.68%
- Mallows Cp: 3.3 (close to the number of predictors, indicating good model fit)
This result suggests BMI is a significant predictor of blood pressure, while exercise is not, based on the specified alpha levels.
Forward Selection Method in Minitab
Forward selection is another variable selection approach that progressively adds predictors to the model.
How Forward Selection Is Conducted
This method begins by evaluating each variable independently and selecting the one with the smallest p-value and largest t-statistic. Variables are then added one at a time as long as they improve the model significantly. The process stops when no remaining variables meet the criteria.
How to Interpret Forward Selection Results
When applying forward selection with alpha-to-enter = 0.25:
- Step 1: BMI is selected
- Step 2: Exercise is also added
- R-Sq: 80.43%
- Adjusted R-Sq: 74.84%
- Mallows Cp: 3.0 (better than stepwise regression)
This suggests that while exercise’s p-value (0.171) is marginal, it’s still included due to the more lenient alpha-to-enter threshold.
Backward Elimination Method in Minitab
Unlike forward selection, backward elimination begins with a full model and gradually removes insignificant variables.
How Backward Elimination Works
This method starts by including all variables and eliminates the one with the highest p-value if it exceeds a chosen alpha-to-remove. The model is refined until all remaining variables are statistically significant.
How to Interpret Backward Elimination Results
Using the same dataset, backward elimination first includes both BMI and Exercise. But since Exercise has a p-value of 0.171 (above the 0.10 threshold), it is removed in the second step.
- R-Sq: 73.94%
- Adjusted R-Sq: 70.68%
- Mallows Cp: 3.3
Although this model is simpler, it has slightly lower explanatory power compared to the model generated using forward selection.
Best Subset Regression in Minitab
Best Subset Regression compares all possible combinations of predictors to determine the best-performing model.
How Best Subsets Regression Is Run
How to Interpret Best Subsets Output
Example output shows three model options:
| Vars | R-Sq | R-Sq(adj) | Cp | S | Predictors |
|---|---|---|---|---|---|
| 1 | 73.9 | 70.7 | 3.3 | 12.85 | BMI |
| 1 | 55.8 | 50.3 | 9.8 | 16.73 | Exercise |
| 2 | 80.4 | 74.8 | 3.0 | 11.91 | BMI, Ex. |
Key things to look for:
- Highest R-Sq and R-Sq(adj)
- Lowest S
- Cp closest to number of predictors + 1
The best subset model includes both BMI and Exercise, with strong explanatory power and the best overall statistics.
AIC Model Selection Using Minitab Output
Although Minitab does not directly calculate AIC (Akaike Information Criterion), it can be computed manually using regression output.
How AIC Is Calculated
Where:
- n = sample size
- RSS = residual sum of squares
- k = number of model parameters
Use the ANOVA table from Minitab to find RSS and plug it into the formula. This allows comparison between models even when the number of predictors differs.
How to Compare Models Using AIC
| Model | AIC |
|---|---|
| Blood Pressure ~ BMI | 52.842 |
| Blood Pressure ~ Exercise | 58.117 |
| Blood Pressure ~ BMI + Ex. | 51.978 |
The model with both BMI and Exercise has the lowest AIC, making it the best among the three, despite exercise having a weaker individual p-value. AIC balances model complexity with fit, so a lower AIC implies a better overall model.
Conclusion
Minitab offers multiple tools for model selection, each providing a different lens through which to assess predictor significance and model performance. Whether you use stepwise regression, forward selection, backward elimination, best subset regression, or compute AIC manually, each method contributes to selecting the most appropriate model for your dataset.
When working on Minitab assignments involving model selection, students should:
- Set meaningful thresholds for alpha-to-enter and alpha-to-remove
- Use Mallows Cp, Adjusted R-Sq, and S to evaluate model efficiency
- Try multiple methods and compare outcomes
- Use AIC as a balancing tool between complexity and model fit
Understanding these methods not only helps complete your assignments effectively but also equips you with statistical decision-making skills crucial for real-world data analysis. As you work with Minitab, remember that the best model is not just the one that fits best statistically—but the one that balances simplicity, significance, and predictive power for your given data.