Statistics Quest

Correlation and Regression

Model relationships between variables, and know the limits.

Covariance and correlation, least squares, simple and multiple regression, coefficients, R-squared, residual diagnostics, inference and prediction intervals, categorical predictors, multicollinearity, influence, transformations, logistic regression and validation — fitted on real datasets in the regression workbench.

Lessons

  1. 1Covariance and correlationCalculate covariance and Pearson's correlation, test whether a correlation differs from zero, and recognise what r cannot see.35 minFree
  2. 2Rank correlationCalculate and interpret Spearman's and Kendall's rank correlations, and choose between them and Pearson's r for monotone, curved or outlier-prone data.30 minMembers
  3. 3Correlation is not causationExplain an observed association by chance, reverse causation, confounding or selection before considering a causal story, and see how adjusting for a confounder can change — even reverse — a comparison.35 minMembers
  4. 4Simple linear regressionFit the least-squares line from data or summary statistics, use it to predict, and calculate residuals.35 minMembers
  5. 5Interpreting coefficientsInterpret a regression slope and intercept in the units of the data, rescale them, and recognise when a prediction is an extrapolation.30 minMembers
  6. 6R² and residual standard errorCalculate and interpret R² and the residual standard error, and explain what a high or low R² does and does not tell you.30 minMembers
  7. 7Residual analysisUse residual plots and simple tests to check the LINE assumptions of a linear regression and decide what to do when one fails.35 minMembers
  8. 8Inference for regressionTest and estimate a regression slope with its standard error, and choose between a confidence interval for a mean response and a prediction interval for a new observation.35 minMembers
  9. 9Multiple regressionFit a regression with several predictors, interpret each slope as an association holding the other predictors fixed, and judge the model with adjusted R² and F tests.40 minMembers
  10. 10Categorical predictorsInclude categorical variables in a regression with dummy coding, interpret each coefficient against the reference level, and recognise when an interaction is needed.40 minMembers
  11. 11MulticollinearityRecognise multicollinearity, measure it with variance inflation factors, and explain why it makes individual coefficients unstable while leaving predictions intact.35 minMembers
  12. 12Outliers, leverage and influenceDistinguish outliers, high-leverage points and influential points, measure them with leverage, studentized residuals and Cook's distance, and decide what to do about them.35 minMembers
  13. 13TransformationsUse log and polynomial transformations to model skewed responses and curved relationships, and interpret the coefficients on the transformed scale as percentages, elasticities or turning points.40 minMembers
  14. 14Logistic regressionFit a logistic regression for a yes/no outcome, interpret its coefficients as odds ratios (not risk ratios), predict probabilities, and judge a classification threshold.45 minMembers
  15. 15Overfitting and validationRecognise overfitting, estimate how a model will perform on new data with a seeded train/test split or k-fold cross-validation, and choose between models on out-of-sample error.40 minMembers