data(mtcars)
model_full <- lm(mpg ~ wt + hp + disp, data = mtcars)
# optional AIC-based stepwise selection
# direction: "both" (default), "forward", or "backward"
model <- MASS::stepAIC(model_full, direction = "both", trace = FALSE)
AIC(model_full); AIC(model)
Computational Provenance & Reproducibility Record Regression Analysis · 1.0.0 · DOI 10.5281/zenodo.21318613
This Computational Provenance Record documents the statistical computing environment, software dependencies, computational provenance, and bibliographic references associated with the RAISINS Regression Analysis module. It is intended to support computational reproducibility and software transparency. Detailed statistical methodology, mathematical derivations, and user guidance are provided separately in the official module documentation.
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1 Module Metadata
| Parameter | Specification |
|---|---|
| Module | Regression Analysis |
| Module Version | 1.0.0 |
| DOI | 10.5281/zenodo.21318613 |
| Document Type | Computational workflow |
| Statistical Engine | R |
| R Version | 4.5.2 |
| Reproducibility | Execution Environment: Posit Connect · GCR · renv-locked |
2 Statistical Dependency Manifest
| Package | Version | Repository | Core Statistical Functions |
|---|---|---|---|
| MASS | 7.3-65 |
CRAN | stepAIC() |
| car | 3.1-5 |
CRAN | vif(), ncvTest() |
| lmtest | 0.9-40 |
CRAN | dwtest() |
| effectsize | 1.0.1 |
CRAN | standardize_parameters() |
| stats | 4.5.2 |
Base R | lm(), summary(), confint(), anova(), predict(), AIC(), BIC(), hatvalues(), cooks.distance(), rstudent(), shapiro.test() |
3 Statistical Function Registry
| Analytical Role | Primary Function(s) |
|---|---|
| Model fitting | stats::lm() |
| Variable selection | MASS::stepAIC() |
| Coefficient inference | base::summary(), stats::confint(), effectsize::standardize_parameters() |
| Regression ANOVA & fit | stats::anova(), stats::AIC(), stats::BIC() |
| Multicollinearity | car::vif() |
| Heteroscedasticity | car::ncvTest() |
| Residual normality | stats::shapiro.test() |
| Autocorrelation | lmtest::dwtest() |
| Influence diagnostics | stats::hatvalues(), stats::cooks.distance(), stats::rstudent(), stats::dffits() |
| Prediction | stats::predict() |
4 Default Methods & Parameters
| Analysis | Step / Parameter | Default Method / Value |
|---|---|---|
| Model Fitting | Method | Ordinary least squares multiple linear regression via lm() |
| Variable Selection | Stepwise (optional) | AIC-based MASS::stepAIC(); direction both (default), forward, or backward; initial and final AIC are reported |
| Coefficient Inference |
Estimates | Estimate, standard error, t value, and p-value from summary() |
| Significance | Star codes assigned with symnum() at cut points 0.001 / 0.01 / 0.05 |
|
| Intervals & standardised | 95% confidence intervals via confint(); standardised coefficients via effectsize::standardize_parameters(method = "refit") |
|
| Model Fit | ANOVA | Sequential (Type I) decomposition via anova() |
| Metrics | R², adjusted R², residual standard error, F-statistic and p-value, AIC, BIC, RMSE, MAE, and PRESS | |
| Regression Assumptions |
Multicollinearity | car::vif() (VIF; GVIF for categorical predictors); low < 5, moderate 5–10, high > 10; computed only when the model has more than two coefficients |
| Heteroscedasticity | car::ncvTest() non-constant error variance score test |
|
| Residual normality | Shapiro-Wilk on residuals (shapiro.test()); valid for 3 ≤ n ≤ 5000 |
|
| Autocorrelation | Durbin-Watson test (lmtest::dwtest()) |
|
| Influence Diagnostics |
Measures & thresholds | Leverage (hatvalues(), flag > 2p/n), Cook's distance (flag > 4/n), standardised and studentised residuals (|studentised| > 2 potential, > 3 extreme), and DFFITS |
| Prediction | Intervals | predict() with 95% confidence and prediction intervals |
5 R Code for Key Analytical Steps
The code blocks below demonstrate the exact computation behind each reported result using the mtcars dataset from the datasets package.
5.1 Model Fitting and Variable Selection
5.2 Coefficients, Intervals and Regression ANOVA
summary(model)$coefficients # estimate, std. error, t value, p-value
confint(model, level = 0.95) # 95% confidence intervals
effectsize::standardize_parameters(model, method = "refit") # standardised betas
anova(model) # sequential (Type I) ANOVA5.3 Model Fit Metrics
sm <- summary(model)
res <- residuals(model)
sm$r.squared; sm$adj.r.squared; sm$sigma # R2, adjusted R2, residual std. error
sqrt(mean(res^2)) # RMSE
mean(abs(res)) # MAE
AIC(model); BIC(model)5.4 Regression Assumption Tests
car::vif(model) # multicollinearity (VIF / GVIF)
car::ncvTest(model) # non-constant error variance (heteroscedasticity)
shapiro.test(residuals(model)) # normality of residuals (3 <= n <= 5000)
lmtest::dwtest(model) # autocorrelation (Durbin-Watson)5.5 Influence and Outlier Diagnostics
n <- nobs(model); p <- length(coef(model))
hatvalues(model) # leverage (flag > 2p/n)
cooks.distance(model) # Cook's distance (flag > 4/n)
rstandard(model) # standardised residuals
rstudent(model) # studentised residuals (|.| > 3 extreme)
dffits(model) # DFFITS5.6 Prediction
newdata <- data.frame(wt = 3.0, hp = 120, disp = 160)
predict(model, newdata, interval = "confidence", level = 0.95)
predict(model, newdata, interval = "prediction", level = 0.95)Explore the entire Regression Analysis module in preview mode using our demo datasets. To submit suggestions or report a workflow issue, please use the discussion section below, or visit the official RAISINS website.
6 RAISINS Native Statistical Framework
RAISINS uses R for all its statistical computations. Every package used to generate major results is listed and demonstrated with examples, so results can be reproduced independently. These results are then organized and formatted on the RAISINS website along with visualisation to make them easier to use and interpret. RAISINS also has its own custom-built statistical tools for managing workflows, validating results, and generating reports. Details of these are not fully covered here, they’re shared with outside researchers only on request, and are subject to licensing terms.
7 Package References
R Core Team. (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S (4th ed.). Springer. https://www.stats.ox.ac.uk/pub/MASS4/
Fox, J., & Weisberg, S. (2019). An R Companion to Applied Regression (3rd ed.). Sage. https://socialsciences.mcmaster.ca/jfox/Books/Companion/
Zeileis, A., & Hothorn, T. (2002). Diagnostic Checking in Regression Relationships. R News, 2(3), 7-10. https://CRAN.R-project.org/doc/Rnews/
Ben-Shachar, M. S., Lüdecke, D., & Makowski, D. (2020). effectsize: Estimation of Effect Size Indices and Standardized Parameters. Journal of Open Source Software, 5(56), 2815. https://doi.org/10.21105/joss.02815
Allaire, J. J., Xie, Y., Dervieux, C., McPherson, J., Luraschi, J., Ushey, K., Atkins, A., Wickham, H., Cheng, J., Chang, W., & Iannone, R. (2026). rmarkdown: Dynamic Documents for R (R package version 2.31). https://github.com/rstudio/rmarkdown