Learning Goals
Module 1.0Understand Why
Why we use regression for both prediction and explanation.
The Formula
Recognize the form: y = α + βx + ε (intercept, slope, error).
Level Up
Know when to move from simple to multiple regression.
Why Regression?
Regression models how a numeric outcome y changes as one or more predictors x change. It helps us quantify relationships (how strong, which direction) and make informed predictions.
Simple Regression (OLS) Lab
The Model
y = α + βx + ε
- α (alpha): Intercept — expected value of y when x=0.
- β (beta): Slope — expected change in y for one-unit increase in x.
- ε (epsilon): Random error — what the model doesn’t explain.
Drag sliders to move the line
Mini Example: Medicine
Predict carotid intima–media thickness (IMT, y) from cholesterol (x). A straight line estimates how IMT tends to change as cholesterol increases.
When do we need Multiple Regression?
Real outcomes are rarely driven by a single factor. If several variables (e.g., age, blood pressure, BMI…) also influence y, we extend to a multiple regression model.
y = α + β1x1 + β2x2 + … + βkxk + ε
Each coefficient (βj) tells you the unique contribution of predictor xj when other predictors are held constant. This lets us separate overlapping influences.
Reading SPSS Outputs
Key metrics you will encounter in your reports
Model Summary
- R: Correlation strength.
- R²: Variance in y explained.
- Adj. R²: Penalizes overfitting.
ANOVA Table
Contains the F-test for overall fit. Does the set of predictors explain a non-zero amount of variance?
Coefficients
- B: Unstandardized slope.
- Beta: Standardized slope.
- Sig. (p): Significance test.
SPSS shows both. Use Beta to compare predictor importance on a common scale (standard deviations).