Skill: Linear Regression Modeling

Use When

• User wants to model the linear relationship between a continuous outcome and one or more predictors
• User needs coefficient estimates, confidence intervals, and p-values for each predictor
• User wants to assess model fit (R², adjusted R²) and check regression assumptions
• Use cases include: gene expression vs. age, protein concentration vs. metabolic rate, any dose-response relationship

Inputs

• Required:
  • Data table (CSV or TSV) with a numeric response variable and one or more numeric or categorical predictor columns
  • Response (outcome) variable name
  • Predictor variable name(s)
• Optional:
  • Interaction terms (e.g., var1:var2)
  • Standardize predictors: true or false (default: false)
  • Output directory (default: ./lm_output)

Workflow

1. Read data; validate that response and predictor columns exist and are appropriate types.
2. Encode categorical predictors as dummy variables (reference level = first alphabetical level).
3. Fit the linear model: response ~ predictors using ordinary least squares.
4. Report for each coefficient: estimate, standard error, t-statistic, p-value, 95% confidence interval.
5. Report model fit: R², adjusted R², F-statistic, overall p-value, AIC, BIC.
6. Generate residual diagnostic plots: (a) residuals vs. fitted, (b) Q-Q plot of residuals, (c) scale-location, (d) Cook's distance.
7. Test regression assumptions: normality of residuals (Shapiro-Wilk), homoscedasticity (Breusch-Pagan), absence of influential points (Cook's distance > 4/n).
8. Write results table (TSV), model summary (text), and diagnostic plots (PDF) to output directory.
9. Save the executable analysis script (analysis_code.py or analysis_code.R) and software version manifest (session_info.txt) used to produce results.

Output Contract

• Coefficient table (TSV): term, estimate, std_error, t_statistic, p_value, ci_lower, ci_upper
• Model fit summary (TSV): r_squared, adj_r_squared, f_statistic, f_p_value, aic, bic, n
• Residual diagnostic plots (PDF, 4-panel)
• Assumption test results (printed to stdout)
• Reproducibility artifacts: analysis_code.py or analysis_code.R, plus session_info.txt

Limits

• Assumes linearity, independence, homoscedasticity, and normality of residuals — check diagnostic plots.
• Does not handle multicollinearity automatically; check VIF (variance inflation factor) separately if many predictors.
• Not suitable for count data, binary outcomes, or data with heavy censoring — use stat-fit-glm instead.
• Common failure: near-perfect multicollinearity among predictors causes singular matrix error.