因变量与自变量相关性极低的数据集建模优化咨询

Hey Maryam, let's work through how to tackle this modeling problem—low Pearson correlations and a tiny R-squared with linear regression are clear signs that linear assumptions aren't matching your data, so we need to pivot to more fitting approaches and data checks.

Linear regression relies on strict assumptions that might not hold here, even if you didn't notice:

• Check for non-linear relationships: Pearson correlation only measures linear trends. Your numerical independent variable could have a curved relationship with service time. Try plotting a scatter plot with a loess curve to spot hidden non-linear patterns.
• Test interaction effects: Binary variables often interact with each other or the numerical variable. For example, maybe the impact of your numerical var changes depending on whether a binary var is 0 or 1. Add interaction terms like num_var * binary_var1 to your linear model and see if R² improves.
• Hunt for outliers: Extreme service time values can skew the model and suppress correlations. Use boxplots or Cook's distance to identify outliers, then test removing them or transforming the dependent variable to reduce their impact.

Since linear regression isn't working, let's explore models built for non-linear patterns and mixed data:

• Tree-based models: Random Forest, XGBoost, or LightGBM are perfect here. They automatically capture non-linear relationships and variable interactions, even when Pearson correlations are low. Plus, they handle numerical and binary variables seamlessly. Use feature importance scores to see which variables actually drive service time.
• Generalized Additive Models (GAMs): GAMs let you model non-linear trends for your numerical variable while keeping linear terms for binary ones. It's a balanced choice—you get more interpretability than tree models, but more flexibility than linear regression.
• K-Nearest Neighbors (KNN): If your data has local patterns that linear models miss, KNN could work. It's simple to implement, though less interpretable. Just remember to scale your numerical variable first, since KNN uses distance metrics.

Sometimes the issue is how we're using the variables, not the variables themselves:

• Transform the dependent variable: service time is often right-skewed. Try log-transforming it (log(service_time)) or using a square root transformation—this can uncover linear relationships that were hidden in the original scale.
• Group binary variables if meaningful: If some binary vars are part of the same category (e.g., different service types), combine them into a single multi-level categorical variable. This might capture patterns that individual binary vars can't.
• Double-check data quality: Even if you think your data is clean, verify for missing values or mis-coded binary variables. A small number of errors can throw off correlations and model performance.

R-squared can be misleading for non-linear data—use metrics that matter for your use case:

• MAE or RMSE: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) tell you how far your predictions are from actual service time in real units, which is more actionable than R-squared.
• Cross-validation: Use k-fold cross-validation instead of a single train/test split to get a reliable estimate of model performance. This avoids overfitting to one specific subset of data.

内容的提问来源于stack exchange，提问作者Maryam