Linear Regression

Linear regression (simple linear regression)

👉 1 predictor → 1 outcome

  • One independent variable (X)

  • One dependent variable (Y)

  • Asks: Does X predict Y?

Example:

  • Does stress predict sleep quality?

Equation:

Y=b0+b1XY = b_0 + b_1XY=b0​+b1​X

Think: one line, one predictor

Multiple regression

👉 2 or more predictors → 1 outcome

  • Multiple independent variables (X₁, X₂, X₃…)

  • One dependent variable (Y)

  • Asks: How well do several variables together predict Y?

  • Also tells you the unique contribution of each predictor (while controlling for the others)

Example:

  • Do stress, exercise, and caffeine intake predict sleep quality?

Equation:

Y=b0+b1X1+b2X2+b3X3Y = b_0 + b_1X_1 + b_2X_2 + b_3X_3Y=b0​+b1​X1​+b2​X2​+b3​X3​

Think: many predictors, one outcome