Confounders

🔀 Confounders

🔀 Confounders

Controlling:

• Isolates relationship between two variables from the correlations with the confounder → closer to the causal effect

Remaining limitations:

📈 Multiple Regression

\(Y = \alpha + \beta \cdot \text{Height} + \gamma \cdot \text{Gender} + \epsilon\)

📈 Multiple Regression 1: No control

\(Y = \alpha + \beta \cdot \text{Height} + \epsilon\)

📈 Multiple Regression 2: Add control

\(Y = \alpha + \beta \cdot \text{Height} + \gamma \cdot \text{Gender} + \epsilon\)

📈 Multiple Regression 2: Intercepts

📈 Multiple Regression 3: Visualising continuous controls

📈 Interpreting multiple regression

\(Y= \alpha + \beta_1 X_1 + \beta_2 X_2 + \epsilon\)

• \(\alpha\): the intercept. Value of \(Y\) when all \(X\)’s = 0.
• \(\beta_1\): regression coefficient for first variable (\(X_1\))
• \(\beta_2\): regression coefficient for first variable (\(X_2\))
• \(\epsilon\): the error term

📈 Prediction with multiple regression

\(\text{Turnout}= 0.32 + 0.02 \cdot \text{Age} + -0.04 \cdot \text{Gender}\)

• Gender coded as 1 for women and 0 for men

Prediction time:

📈 Reading multiple regression tables