Lesson 2

What Consistency Means

Big question

What does it mean for an estimator to get the right answer eventually?

Lesson progress

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain what consistency means in plain language.
  • Use large sample properties correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Consistency means the estimator becomes tightly concentrated around the true population parameter as sample size grows.

Key terms

large sample properties
Approximate properties that become accurate with enough observations.
asymptotic bias
The large-sample gap between the estimator target and the true parameter.
asymptotic standard error
A standard error justified by large-sample theory.

Core formula

plim(betahatj)=betajplim(beta_hat_j) = beta_j

Use plain-language interpretation before algebra.

Example

What Consistency Means uses simulated data so students can see the large-sample mechanism without inventing empirical results.

Interactive visual

ConsistencyDistributionSimulator

Original Module 5 visual for What Consistency Means.

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

What Consistency Means Python example

What Consistency Means 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 3Load a Python library needed for data work or regression.
  4. Line 5Run this Python instruction as part of the lesson workflow.
  5. Line 6Create or update a Python object used in the analysis.
  6. Line 7Create or update a Python object used in the analysis.
  7. Line 9Run this Python instruction as part of the lesson workflow.
  8. Line 10Create or update a Python object used in the analysis.
  9. Line 11Create or update a Python object used in the analysis.
  10. Line 12Create or update a Python object used in the analysis.
  11. Line 13Add an intercept column to the regression design matrix.
  12. Line 15Create or update a Python object used in the analysis.
  13. Line 16Run this Python instruction as part of the lesson workflow.
  14. Line 17Create or update a Python object used in the analysis.
  15. Line 18Run this Python instruction as part of the lesson workflow.
  16. Line 19Display a result so students can inspect the output.

Python walkthrough

  1. 1Load libraries and data or set a simulation seed.
  2. 2Build the model or simulation that matches the lesson question.
  3. 3Compute the statistic, graph, or summary table.
  4. 4Interpret the result as large-sample evidence, not automatic causality.

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

SIMULATION

Estimated time

25 to 40 min

Packages

pandas, numpy, scipy

Expected output

Simulation output showing how estimates or test statistics behave as sample size changes.

Learning goals

  • Load and inspect SIMULATION.
  • Run the Python cells connected to What Consistency Means.
  • Interpret the output using consistency and simulation.

Common errors

  • File not found: check that WAGE1.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-5/WAGE1.csv")
df.head()

Interactive activity

ConsistencyDistributionSimulator

Watch consistency tighten

Increase n and explain why estimates concentrate around the population parameter.

Simulation

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 does consistency require students to focus on?

Quick quiz

Which reporting habit is most important in What Consistency Means?

Quick quiz

Why is GPA2 a reasonable practice dataset here?

Key takeaway

What Consistency Means helps students separate large-sample approximation from valid research design.

Download dataDownload resultsDownload interpretation