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Regression Analysis
Undergraduate
Definition
A statistical method to model and predict the relationship between dependent and independent variables.
Formulas
y = β₀ + β₁ x + ε
Simple linear regression model
\hatβ₁ = \frac∑(xᵢ - \barx)(yᵢ - \bary)∑(xᵢ - \barx)²
Slope estimate
R² = 1 - \fracSS_resSS_tot
Coefficient of determination
Examples
Example 1
Interpret R² = 0.75.
Applications
Economics
Demand forecasting
Marketing
Sales prediction
Machine Learning
Foundation of predictive models
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