Unit 9 of 12
Regression and Prediction
- 10 lessons
- Videos 61 to 70
Regression describes how the mean of a response changes with one or more predictors. This unit fits, checks and tests regression models and uses them for inference and prediction.
Least squares fits a line, and R-squared gives the share of the sample variation in the response that the line accounts for. Residual plots and influence measures check the model before inference about the slope, and confidence and prediction intervals answer different questions. In multiple regression a coefficient describes an association adjusted for the other predictors, which is not automatically a causal effect. Categorical predictors, interactions, curves, model comparison and logistic regression extend the model, and data not used for fitting test its predictions.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Simple Linear Regression
Least Squares and R-Squared
How a least-squares line describes a response with one predictor, how to read its slope, intercept, fitted values and residuals, and what R-squared says about the residual sum of squares.
Video 61
Regression Assumptions, Residuals and Influence
How residual plots and Q-Q plots check a fitted line's assumptions of a linear conditional mean, constant variance and independent normal errors, and how hat values and Cook's distance measure leverage and influence.
Video 62
Inference for a Regression Slope
How the simple linear regression model separates errors from residuals, and how the residual standard deviation and the standard error of the slope give a t test and a confidence interval for the slope.
Video 63
Confidence and Prediction Intervals
How a confidence interval for a mean response differs from a prediction interval for one new observation in simple linear regression, why the prediction error adds variance, and why extrapolation is risky.
Video 64
Multiple Regression and Model Building
Multiple Regression and Adjusted Associations
How multiple regression describes one response with several predictors, how a partial regression coefficient gives an adjusted association, and how indicator variables, a reference group and omitted variables shape that reading.
Video 65
Categorical Predictors and Interactions
How to code a categorical predictor with a reference category, how an interaction term lets slopes differ by group, why a group coefficient is then a conditional effect at one predictor value, and why model hierarchy matters.
Video 66
Transformations and Curved Relationships
How polynomial terms and log transformations let linear regression fit curved relationships, and why back-transformation of a log model gives a conditional median unless the lognormal error is taken into account.
Video 67
Comparing Regression Models and Multicollinearity
How to compare nested models with the partial F test and adjusted R-squared, how the variance inflation factor measures coefficient uncertainty due to multicollinearity, and what identifiability and model selection mean.
Video 68
Logistic Regression and Validation
Logistic Regression
How logistic regression models the log odds of a binary outcome, how the logit and logistic function move between scales, what an odds ratio for a predictor says, and what complete separation and calibration mean.
Video 69
Validation, Overfitting and Honest Prediction
How to judge predictions on data not used to fit them, with training and test data, loss functions and cross-validation, and how overfitting, data leakage and distribution shift can make a score misleading.
Video 70