📚 Introductory Econometrics with MORISTAT

A Practical Guide to Empirical Analysis

Naguib Lallmahomed · naglal@linux-mauritius.com · 2026-06-14

Chapter 5: Multiple Regression Analysis (Inference)

🎯 Learning Objectives

Upon completing this chapter, you will be able to:

Test single hypotheses using t-tests in multiple regression
Test multiple hypotheses using F-tests
Construct and interpret confidence intervals
Understand restricted vs unrestricted models
Use MORISTAT's TEST command for F-tests

5.1 Introduction to Inference in Multiple Regression

We are typically interested in questions like:

Does βⱼ = 0? (Is Xⱼ individually significant?)
Does β₁ = β₂? (Do two variables have the same effect?)
Does β₁ = β₂ = β₃ = 0? (Are a group of variables jointly insignificant?)

5.2 Testing Single Hypotheses: The t-Test

t = β̂ⱼ / SE(β̂ⱼ) ∼ t_n−k−1

5.3 Testing Multiple Hypotheses: The F-Test

F = [(SSE_R − SSE_UR) / q] / [SSE_UR / (n − k − 1)]

5.4 MORISTAT's TEST Command

MORISTAT> TEST Size = 0
MORISTAT> TEST Bedrooms = 0, Age = 0

5.5 Complete Example: Housing Prices

Run regression and tests:

MORISTAT> LOAD houses.csv
MORISTAT> REGRESS Price ~ Size Bedrooms Age
MORISTAT> TEST Size = 0
MORISTAT> TEST Bedrooms = 0
MORISTAT> TEST Age = 0
MORISTAT> TEST Bedrooms = 0, Age = 0

5.6 Practice Lab

In this lab, you will:

Load the houses.csv dataset
Run the multiple regression
Test individual coefficients
Test joint hypotheses

# Step 1: Load the data
LOAD houses.csv

# Step 2: Run regression
REGRESS Price ~ Size Bedrooms Age

# Step 3: Individual tests
TEST Size = 0
TEST Bedrooms = 0
TEST Age = 0

# Step 4: Joint test
TEST Bedrooms = 0, Age = 0

5.7 Key Terms

t-Test F-Test Confidence Interval Joint Hypothesis Restricted Model Unrestricted Model Exclusion Restriction Overall Significance Omitted Variable Bias

5.8 What's Next?

Congratulations! You have completed Chapters 1-5.

You now have a solid foundation in econometrics with MORISTAT.

📚 Return to Table of Contents

🔄 Ready to connect with MORISTAT?