Regression and Experimental Design

1. Regression Model

y = Xbeta + epsilon.

Ordinary least squares finds beta minimizing squared residuals.

2. Assumptions (Classical OLS)

• linear relation in parameters
• independent errors
• zero-mean errors
• constant variance (homoscedasticity)
• low multicollinearity

3. Diagnostics

• residual vs fitted plot
• QQ plot for residual shape
• leverage/influence points
• variance inflation factor

4. Correlation vs Causation

Regression on observational data does not imply causal effect. Need design/identification strategy.

5. Experimental Design

• randomization
• control group
• blocking/stratification
• blinding
• power and sample size

6. Worked CS Example

Model page-load time impact on bounce probability. Discuss confounders and why randomized rollout gives stronger causal claim.

Exercises

1. Fit simple linear regression and interpret coefficients.
2. Construct case where omitted variable biases estimate.
3. Design A/B test with control of one major confounder.
4. Explain why randomization supports causal inference.