Mastering Multiple Regression and ANOVA

📋 Course Outline

1. Multiple regression model
2. Regression fit and residuals
3. Regression inference and variance explained
4. Causality and multivariate relationships
5. Categorical predictors and dummy coding
6. General linear model
7. ANOVA via regression
8. One-way ANOVA example

📖 1. Multiple regression model

🔑 Key Concepts & Definitions

• Multiple regression model: A multiple regression model expresses the conditional mean of a numerical outcome as a linear function of several predictors.
• Regression predictors: Regression predictors are the multiple explanatory variables used to build the linear equation for the response’s expected value.
• Flat surface plane: In two-predictor regression, the model corresponds to a plane determined by separate slopes for each predictor.

📝 Essential Points

• The multiple regression equation is $E(y)=a+b_1x_1+b_2x_2+\dots+b_kx_k$, where $k$ is the number of predictors.
• With two predictors, the model can be visualized as a plane with two slopes, one for $x_1$ and one for $x_2$.
• To represent a model with $k$ predictors needs $k+1$ dimensions for the corresponding geometric depiction.

💡 Memory Hook

Think “plane for 2 slopes”: more predictors mean more dimensions ($k+1$).

📖 2. Regression fit and residuals

🔑 Key Concepts & Definitions