Lesson 19
General Linear Restrictions
Big question
What if the restriction is not just omitting variables?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain general linear restrictions in plain language.
- Use unrestricted model correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
General restrictions can combine coefficients, fix coefficients to values, or impose several equations at once.
Key terms
- unrestricted model
- The model estimated without imposing the null restrictions.
- R-squared F form
- An F statistic shortcut based on restricted and unrestricted R-squared values.
- overall significance
- A test that all slope coefficients are zero.
Core formula
Use plain-language interpretation before algebra.
Example
HPRICE1 gives students a real-data setting for general linear restrictions. The lesson emphasizes inference mechanics and interpretation, not memorized output.
Interactive visual
GeneralLinearRestrictionBuilder
Original Module 4 visual for General Linear Restrictions.
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
General Linear Restrictions Python example
General Linear Restrictions Python example
Stdout
Run Python to see results here.
Status / stderr
Ready to run Python in your browser.
Line-by-line guide
- Line 1Load a Python library needed for data work or regression.
- Line 2Load a Python library needed for data work or regression.
- Line 4Load the dataset into a pandas DataFrame.
- Line 5Add an intercept column to the regression design matrix.
- Line 6Display a result so students can inspect the output.
- Line 7Display a result so students can inspect the output.
Python walkthrough
- 1Load the real dataset and keep the variables needed for both models.
- 2Estimate unrestricted and restricted models or use statsmodels f_test.
- 3Compute or read the F statistic and p-value.
- 4Interpret the test as a joint statement about population parameters.
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.
Related dataset
HPRICE1
Estimated time
25 to 40 min
Packages
pandas, numpy
Expected output
Printed Python results that can be compared with the lesson explanation.
Learning goals
- Load and inspect HPRICE1.
- Run the Python cells connected to General Linear Restrictions.
- Interpret the output using general restrictions and f_test.
Common errors
- File not found: check that HPRICE1.DTA 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_stata("/data/HPRICE1.DTA")
df.head()Interactive activity
GeneralLinearRestrictionBuilder
Build general restrictions
Create restrictions such as beta1 equals beta2 or beta1 equals one.
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 safest inference focus in General Linear Restrictions?
Quick quiz
Which reporting habit is most important in General Linear Restrictions?
Quick quiz
Why is RETURN a reasonable practice dataset here?
Key takeaway
General Linear Restrictions turns regression output into evidence only when the hypothesis, assumptions, and magnitude are stated clearly.