Producing a Reproducible Regression Report from Raw Data

From a Raw File to a Report

A regression report is reproducible when a reader can trace its numbers and figures from the data through the analysis steps that produced them. That means more than saving a final table: the raw file, preparation rules, model specification, and output-generating code must agree. A scripted workflow also makes errors easier to find. If a variable is converted to the wrong unit, for example, the issue can be corrected in one documented step and all dependent outputs regenerated.

This tutorial follows a hypothetical housing dataset from a comma-separated values file (CSV) to a multiple-regression report. The model specification is fixed in advance. The purpose is to show how to connect each reported result to its source, not to find the best possible model or to make a causal claim about housing prices.

State the Model Before Running It

Suppose the file contains one row per home sold in a fictional city. The outcome is sale price in thousands of dollars. The predictors are living area in units of 100 square feet, number of bedrooms, home age in years, and distance from downtown in miles. The fixed model is:

Here, \(\epsilon_i\) is the difference between home \(i\)'s observed price and the model's conditional mean. Each slope describes the modeled change in mean sale price associated with a one-unit increase in that predictor, holding the other listed predictors fixed. For instance, \(\beta_1\) is in thousands of dollars per 100 square feet.

For the usual coefficient standard errors, confidence intervals, and t-tests to have their standard model-based interpretation, the conditional mean must be correctly represented by this linear specification, the errors must have mean zero conditional on the predictors, observations must be independent, and error variance must be constant. Normal errors are also assumed for exact t-based inference in a finite sample. The predictor columns must not be exact linear combinations of one another, so the coefficients can be estimated. These assumptions are not established just because software returns estimates. A residual diagnostic figure can reveal some problems, but it cannot prove that all assumptions hold.

Prepare the Data Without Hiding Decisions

The hypothetical raw file is named homes.csv. It has 120 rows and includes the columns house_id, sale_price_usd, living_area_sqft, bedrooms, age_years, and distance_miles. For illustration, a few rows might look like this:

Assume that, in the full hypothetical file, four rows have a missing value in at least one model variable. The analysis uses complete cases for the outcome and all four predictors, leaving \(n=116\) homes. It does not silently treat missing values as zero. The script should report the raw and analysis sample sizes and identify which variables had missing entries. A data check should also confirm that house IDs are unique and that recorded sale prices and living areas are positive. If a check fails, the script should stop for review rather than quietly continue with questionable input.

A readable script can implement these decisions in sequence. For example, using R, the core operations are to read the file with `readr::read_csv("data/homes.csv")`, count missing values in the outcome and predictor columns, check `!anyDuplicated(raw$house_id)`, create `price_k = sale_price_usd / 1000` and `area_100 = living_area_sqft / 100`, and retain rows complete on `price_k`, `area_100`, `bedrooms`, `age_years`, and `distance_miles`. The script should explicitly check positive prices and areas and record the number of retained rows. It should not edit the original CSV in place.

Next, fit the stated specification to the prepared analysis data, explicitly requiring complete records for those variables (in R, `na.action = na.fail` makes an unexpected missing value an error). Save the script alongside the project, record the software and relevant package versions, and use stable project-relative file paths. Because this workflow involves no random sampling step within the script, it does not need a random seed. A seed would be needed if a later procedure used randomness, such as randomly splitting data.

Generate Results From the Fitted Model

The coefficient table should be generated from the fitted model object, rather than typed separately and allowed to drift from the analysis. It should identify the outcome and predictor units, the sample size, the coefficient estimates, standard errors, confidence intervals, and p-values. The following values are hypothetical output from the 116-home example; they illustrate how the pieces fit together.

The model has 116 observations and five estimated coefficients, including the intercept, so the residual degrees of freedom are \(116-5=111\). For example, the age t-statistic is \(-0.62/0.18=-3.44\). Its two-sided p-value is below 0.001 with 111 degrees of freedom, and its 95% interval uses the form estimate \(\pm t^* SE\), where \(t^*\) is the 97.5th percentile of the t distribution with 111 degrees of freedom. Rounded to two decimal places, this gives \(-0.62\pm1.982(0.18)\), or approximately \((-0.98,-0.26)\). The table's estimate, interval, and p-value therefore tell a consistent story under the model assumptions.

A corresponding diagnostic figure can be created from the same model object. A residual-versus-fitted plot places each fitted price on the horizontal axis and its residual on the vertical axis, with a horizontal reference line at zero. In R, `broom::augment(fit)` supplies fitted values and residuals; a plotting command can map `.fitted` to the horizontal axis and `.resid` to the vertical axis, add points and the zero line, label both axes in thousands of dollars, and save the figure to a specified output directory. The script should create that directory if needed and write the figure rather than relying on a manually edited image.

Turn the Outputs Into a Report

For this hypothetical output, suppose the residual-versus-fitted figure shows no strong curve but does show somewhat greater vertical spread at larger fitted values and one relatively large positive residual. A concise diagnostic statement should report those observations and their consequence: the mild increase in spread raises concern about constant error variance, so conventional standard errors and intervals may be less reliable than they would be under constant variance. The plot does not establish why the spread changes, and the unusual point should be checked against the source record rather than deleted automatically. Any additional diagnostic, sensitivity analysis, or correction would need to be reported as such, not substituted invisibly into the original analysis.

A results paragraph can now connect the model, sample, estimates, uncertainty, and diagnostic context. For example:

Hypothetical results paragraph: “Among 116 homes with complete values for sale price, living area, bedrooms, age, and distance, we fit the prespecified linear regression of sale price (thousands of dollars) on area (per 100 square feet), bedroom count, age (years), and distance from downtown (miles). Adjusting for the other listed predictors, each additional 100 square feet was associated with an estimated \$18,400 higher mean sale price (95% CI \$15,920 to \$20,880; p<0.001). Each additional year of age was associated with an estimated \$620 lower mean sale price (95% CI \$260 to \$980 lower; p<0.001). The diagnostic plot showed somewhat greater residual spread at higher fitted prices; this raises concern about the constant-variance assumption and may limit the reliability of conventional standard errors and intervals.”

The statements about area and age are conditional associations, not effects caused by changing a home's area or age. The p-values describe how incompatible the observed estimates are with zero coefficients under the specified model and its assumptions; they are not probabilities that the coefficients are zero. A report should also state the limitations tied to this particular dataset and model. Here, the data are hypothetical and limited to one city, complete-case analysis excludes four homes with missing model variables, the model assumes a linear conditional mean, and the diagnostics raise a variance concern. The fitted relationships do not establish that changing a predictor would change sale price, because unmeasured differences between homes may also be related to both predictors and price.

Why the Scripted Chain Matters

Each output should have a traceable source: the analysis sample comes from documented preparation rules, the coefficient table comes from the fitted model, the figure comes from its fitted values and residuals, and the prose uses the same units and sample as those outputs. Re-running the analysis from the unchanged raw file provides a practical check that the workflow is complete. If the report says \(n=116\) but a clean run produces a different sample size, the mismatch needs investigation before the report is considered final.

Common Mistake: Treating a Saved Table as Reproducibility

A polished table is not enough if someone must guess how the data were cleaned, which units were used, or which model was fitted. Conversely, a script alone is not a complete report if it hides exclusions or presents output without interpretation. The correction is to make the analysis chain explicit: preserve the raw data, state the preparation and model decisions, regenerate outputs directly from code, and check the rendered report against the fresh results. Hand-editing a coefficient or figure after the run breaks that chain and can produce contradictions that are difficult to detect.