Lesson 16

Controls for Precision

Big question

When can a control improve precision without changing the target coefficient?

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain controls for precision in plain language.
  • Use bootstrap standard error correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

A control can reduce residual variation and make estimates more precise, even if it is not the main causal variable. The key is whether it is safe for the research design.

Key terms

Bootstrap standard error
A standard error estimated by repeatedly resampling the data and re-estimating the statistic.
Exact percent effect
A log-model conversion using the exponential function rather than the small-change shortcut.
Adjusted R-squared
A fit measure that penalizes adding regressors.

Core formula

precisionimproveswhenresidualvariancefallsprecision improves when residual variance falls

Use plain-language interpretation before algebra.

Example

M6_POLICY_CONTROLS is a synthetic teaching dataset for controls for precision. It is designed to practice precision controls without presenting fabricated real-world empirical findings.

Interactive visual

Compare standard errors before and after adding a safe baseline control.

Original Module 6 visual for Controls for Precision.

wage_sample.csv

y variable

wage

The dependent variable. It is the outcome students want to explain.

x variable

education

The explanatory variable. It is used to describe changes in wage.

Live Python

Controls for Precision Python example

Controls for Precision Python example

Stdout

Run Python to see results here.

Status / stderr

Ready to run Python in your browser.

Line-by-line guide

  1. Line 1Load a Python library needed for data work or regression.
  2. Line 2Load a Python library needed for data work or regression.
  3. Line 4Load the dataset into a pandas DataFrame.
  4. Line 5Add an intercept column to the regression design matrix.
  5. Line 6Add an intercept column to the regression design matrix.
  6. Line 7Display a result so students can inspect the output.
  7. Line 8Display a result so students can inspect the output.

Python walkthrough

  1. 1Load the synthetic teaching dataset from the Module 6 public data folder.
  2. 2Create transformed variables only after checking their meaning and valid support.
  3. 3Fit a regression that matches the lesson's interpretation target.
  4. 4Print coefficient or prediction summaries that students can connect to the formula.
  5. 5Use comments and output labels so no empirical result is presented without context.

Live notebook

Run this lesson as a notebook

Open an editable notebook cell-by-cell, run Python in the browser, and download the `.ipynb` file for later.

Open live notebookDownload .ipynbDownload .py

Related dataset

M6_POLICY_CONTROLS

Estimated time

25 to 40 min

Packages

pandas, numpy, statsmodels, patsy

Expected output

A regression or inference table with coefficients, uncertainty, and short interpretation notes.

Learning goals

  • Load and inspect M6_POLICY_CONTROLS.
  • Run the Python cells connected to Over-Control and Bad Controls.
  • Interpret the output using bad controls and precision controls.

Common errors

  • File not found: check that M6_POLICY_CONTROLS.csv is installed or use the course data folder.
  • Package import error: use the browser notebook first, then download for local Jupyter if your local packages differ.
  • Column name error: compare your variable names with the dataset variables listed for this notebook.

Dataset path helper

import pandas as pd

df = pd.read_csv("/data/module-6/M6_POLICY_CONTROLS.csv")
df.head()

Interactive activity

PrecisionControlSimulator

Use safe controls for precision

Compare standard errors after adding a safe baseline control.

M6_POLICY_CONTROLS

Inputs

Try it yourself

Write one plain-English sentence explaining the main idea from this lesson.

Common mistakes

Check these before you move on.

A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.

Quick quiz

What is the main mistake to avoid in Controls for Precision?

Quick quiz

What is the main mistake to avoid in Controls for Precision?

Quick quiz

Why is M6_SALES_ADVERTISING a reasonable practice dataset here?

Key takeaway

Controls for Precision helps students make multiple regression more flexible while keeping interpretation precise and honest.

Download dataDownload resultsDownload interpretation