📚 Introductory Econometrics with MORISTAT

A Practical Guide to Empirical Analysis

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

Chapter 3: Simple Linear Regression

🎯 Learning Objectives

Upon completing this chapter, you will be able to:

Understand the simple linear regression model
Derive and interpret Ordinary Least Squares (OLS) estimators
Use MORISTAT to estimate simple regression models
Interpret regression coefficients, standard errors, and R-squared
Understand the Gauss-Markov Theorem

3.1 Introduction to Simple Linear Regression

The Simple Linear Regression Model is:

Y = β₀ + β₁X + u

where:

Y is the dependent variable
X is the independent variable
β₀ is the intercept
β₁ is the slope
u is the error term

3.2 OLS Estimators

β̂₁ = Σ(Xᵢ − X̄)(Yᵢ − Ȳ) / Σ(Xᵢ − X̄)²

β̂₀ = Ȳ − β̂₁X̄

3.3 Simple Regression with MORISTAT

3.3.1 Complete Example: Advertising and Sales

Suppose we have data on advertising spending and monthly sales:

Advertising (X)	Sales (Y)
1.0	25
1.5	30
2.0	35
2.5	38
3.0	42
3.5	45
4.0	48
4.5	52
5.0	55

Run regression:

MORISTAT> LOAD advertising.csv
MORISTAT> LIST
MORISTAT> REGRESS Sales ~ Advertising

Interpretation:

Intercept (β̂₀): Predicted Sales when Advertising = 0
Slope (β̂₁): Each additional $1,000 in advertising increases Sales by β̂₁
R-squared: Proportion of variation explained by the model

3.4 Practice Lab

In this lab, you will:

Load the advertising.csv dataset
Run the regression of Sales on Advertising
Interpret the results

# Step 1: Load the data
LOAD advertising.csv

# Step 2: Examine the data
LIST
SUMMARY

# Step 3: Run regression
REGRESS Sales ~ Advertising

# Step 4: Confidence intervals
CI 0.95

# Step 5: Diagnostics
DIAG

3.5 Key Terms

Simple Linear Regression Dependent Variable Independent Variable Intercept (β₀) Slope (β₁) Error Term (u) OLS Residual (û) R-squared Gauss-Markov Theorem Standard Error t-statistic p-value

3.6 What's Next?

In Chapter 4, we extend the model to multiple regression.

→ Proceed to Chapter 4

🔄 Ready to connect with MORISTAT?