10
Quantitative MethodsModule 10 of 11

Simple Linear Regression

5

Concepts

5

Formulas

1

Decisions

3

Quiz Questions

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Key Concepts

5 concepts covered in this module.

Regression Equation

Ŷ = b0 + b1X. b0 = intercept, b1 = slope (change in Y per unit change in X).

R-squared

Coefficient of determination = proportion of Y's variation explained by X. R² = correlation². Range: 0 to 1.

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Formulas

5 essential formulas for this module.

Slope Coefficient

b1 = Cov(X,Y) / Var(X) = Σ(X-X̄)(Y-Ȳ) / Σ(X-X̄)²

Where: OLS estimator

Intercept

b0 = Ȳ - b1X̄

Where: Regression line passes through (X̄, Ȳ)

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Decision Frameworks

1 decision frameworks to guide your analysis.

How to assess regression quality?

  • R² for goodness of fit
  • SEE for prediction accuracy
  • t-test on b<sub>1</sub> for statistical significance
  • F-test for overall model significance

Mind Map

Visual overview of how concepts connect in this module.

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Regression Equation

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Answer
Ŷ = b0 + b1X. b0 = intercept, b1 = slope (change in Y per unit change in X).
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