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Dr. Turner will provide two or three reports of multiple linear regression projects made by previous students. Using the information about planning an analysis and report, provide some criticism on what you think the authors could have done better and what aspects of their report that they did very well. This can be a combination of technical details on the modeling front as well as just how they chose to communicate and present the information to you.
Based on the video which outlines a detailed analysis of a multiple linear regression project focusing on Manufacturer’s Suggested Retail Price (MSRP) of cars, I will offer some criticism and praise for the technical modeling aspects as well as the communication and presentation of the information.
Over-Reliance on Complex Models: The project team appears to have heavily focused on advanced models like polynomial regression, gradient boosting, and k-nearest neighbors. While these techniques are powerful, there is a risk of overfitting, especially with limited discussion on cross-validation techniques or a clear rationale for parameter selection. A more thorough exploration of simpler models, alongside the complex ones, might provide a more balanced approach.
Data Cleansing Approach: The approach to handling missing data, especially for electric cars (inserting zeros), could potentially skew results. A more nuanced method, such as imputation based on similar car types or predictive modeling for missing values, might yield more accurate results.
Handling of Outliers: While the report mentions identifying outliers, it lacks a detailed discussion on how they were dealt with. Outliers can significantly impact regression models, and a clear strategy for handling them (e.g., exclusion, transformation) is crucial.
Variable Selection: The stepwise regression approach for feature selection is noted, but the rationale behind choosing certain variables over others is not fully elaborated. A more transparent discussion on why specific predictors were included or excluded would enhance the report’s credibility.
Comprehensive Data Exploration: The team conducted extensive exploratory data analysis (EDA), which is commendable. The detailed examination of variables like engine horsepower, vehicle type, and cylinders provides a solid foundation for understanding the dataset’s characteristics.
Clear Presentation of Correlation Analysis: The discussion of correlations between different variables, such as between year and MSRP or between fuel efficiency and price, is well-presented. This helps in understanding the dynamics within the dataset.
Use of Diagnostic Plots: The use of residual plots, QQ plots, and leverage plots demonstrates a thorough approach to checking model assumptions. This is a strong aspect of the report, as it provides evidence of the model’s validity.
Effective Communication: Despite the technical depth, the information in the transcript is communicated in a manner that is relatively easy to follow. The use of layman’s terms to explain complex statistical concepts is particularly effective.
Diverse Modeling Techniques: Employing a variety of models, including linear, polynomial, and gradient boosting, shows a commendable effort to explore the data from multiple angles and find the best predictive model.
Balanced Approach to Model Complexity: While advanced models are attractive, there should be a balance between model complexity and interpretability. Simpler models can sometimes provide comparable insights and are easier to interpret.
More Detailed Explanation of Model Selection and Validation: A deeper discussion on why certain models were chosen and how they were validated (e.g., cross-validation techniques, parameter tuning) would enhance the report’s technical rigor.
Broader Discussion on Implications of Findings: While the technical analysis is strong, the report could benefit from a more detailed discussion on how these findings could impact real-world scenarios, such as in manufacturing or marketing strategies.
Enhanced Visualization Techniques: While the report mentions various plots, incorporating more advanced visualization techniques could aid in better understanding and presenting the data, especially for a non-technical audience.
Incorporation of External Factors: Consideration of external economic or market trends in the analysis could provide a more holistic view of the factors influencing car prices.
During our live session we will break out into groups to discuss and then come together and share general themes.
You are working on a project to build a regression model for prediction purposes. The model should be good enough that the vast majority of future predictions will be off by no more than \(\pm100\) units. Suppose that “vast majority” is defined to be 99.7 percent. When fitting your models via 10-fold cross validation, what RMSE are you looking to see that you are within the project’s specification? Assume that prediction errors are normally distributed.
##ANSWER
In order to determine the appropriate Root Mean Square Error (RMSE) for my regression model given the specified conditions, it’s crucial to understand both the concept of RMSE and the assumption that prediction errors follow a normal distribution.
RMSE serves as a measure of the difference between the values predicted by a model and the values actually observed. It is defined as the square root of the average of the squared differences between the predicted and actual values.
With the assumption that prediction errors are normally distributed, I can utilize the empirical rule, also known as the 68-95-99.7 rule. This rule indicates that in a normal distribution:
For my project, the requirement is that a “vast majority” (99.7%) of future predictions should not deviate by more than ±100 units. This suggests that ±100 units is equivalent to three standard deviations in the distribution of prediction errors.
Therefore, under the assumption of a normal distribution, the standard deviation of these prediction errors should be one-third of 100 units, since 3σ equals 100.
This means that σ should be 100 / 3, or approximately 33.33 units.
The RMSE for my model is an indicator of this standard deviation in prediction errors. Therefore, my target RMSE should be around 33.33 units to ensure that 99.7% of the future predictions are within a margin of ±100 units from the actual values.
During my 10-fold cross-validation process, I will aim for a model that consistently shows an RMSE of about 33.33 units or less, to meet the accuracy requirements of my project.
Given the current scenario with the predictive modeler’s dissatisfaction regarding the accuracy of their multiple linear regression model, there are several suggestions and questions that could potentially lead to improvements.
Transformation of Variables: If the predictors are being used as they were originally recorded, it might be beneficial to consider transforming them. For continuous variables, transformations like log, square root, or reciprocal can sometimes linearize relationships, reduce effects of outliers, and normalize distributions, leading to improved model performance.
Interaction Terms: It’s possible that interactions between predictors are influential in predicting the outcome. The modeler can test for interaction effects between continuous and categorical variables, or among continuous variables themselves, to see if they add value to the model.
Polynomial Regression: If the relationship between the predictors and the response variable is not strictly linear, adding polynomial terms (like squared or cubic terms of predictors) might capture the curvature in the data better.
Regularization Techniques: Techniques like Ridge Regression or Lasso Regression can be applied, especially if there’s a possibility of multicollinearity or overfitting. These methods not only help in improving prediction accuracy but also in feature selection (in the case of Lasso).
Revisit Data Preprocessing: Ensuring that the data is properly cleaned and preprocessed, including checking for outliers and influential points that could skew the results, is crucial. Sometimes, a thorough data cleaning can significantly improve model accuracy.
Model Diagnostics: Conducting a comprehensive diagnostic analysis of the current model can reveal issues like non-linearity, high-leverage points, or heteroscedasticity, which, once addressed, can improve model performance.
Nature of the Data: What is the context and nature of the data being analyzed? Understanding the domain can often suggest natural transformations or interactions that might be relevant.
Model Fit and Diagnostics: How well does the current model fit the data? Have diagnostic plots been examined for any violations of linear regression assumptions?
Distribution of Predictors: Are the distributions of the continuous predictors skewed or have outliers that could affect the model?
Previous Model Adjustments: Have any transformations or interactions been tried previously? If so, what was the outcome?
Model Evaluation Metrics: Which metrics are being used to evaluate model accuracy? Different metrics can provide different insights into the model’s performance.
Target Variable’s Characteristics: Are there any peculiarities in the target variable, like a skewed distribution, that might require transformation?
Model Complexity Concerns: Is there a concern about overfitting? Understanding their position on the trade-off between model complexity and interpretability can guide the choice of techniques.
By addressing these areas and questions, the modeler can potentially uncover new avenues for improving their model’s prediction accuracy.