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Statistics & Regression

Inference, hypothesis testing, OLS, and MLE.

Prerequisites: Linear Algebra + Probability

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  1. 1Sampling and Standard ErrorThe sample mean as a random variable, its standard error σ/√n, and why the sample variance divides by n − 1.
  2. 2Hypothesis Tests, p-values and Confidence IntervalsHow to decide whether a result is real or luck: null hypotheses, p-values, confidence intervals, the two kinds of error, power, and why the best of many traders is usually lucky.
  3. 3Least Squares as a ProjectionThe linear model y = Xβ + ε, the normal equations as a perpendicular drop onto the column space, R² as Pythagoras, and why the simple-regression slope is ρ times sd(y)/sd(x).
  4. 4Maximum LikelihoodPick the parameter that makes the observed data most probable, read its standard error off the curvature of the log-likelihood, and see how a prior turns MLE into MAP.
  5. 5Regression Inference: Standard Errors, t and FHow precise a regression coefficient is: standard errors, t-tests and intervals for one coefficient, F-tests for several at once, and the residual checks that decide whether to trust any of them.
  6. 6Multicollinearity and InteractionsWhat a regression coefficient means when predictors are correlated, how the variance inflation factor measures the damage, and how interaction terms let one variable's slope depend on another.
  7. 7Logistic RegressionWhy a line fails on yes/no outcomes, how logistic regression models the log-odds, reading coefficients as odds ratios, fitting by Newton's method, and judging a classifier with ROC and AUC.
  8. 8Bias, Variance and RegularizationWhy extra predictors make out-of-sample fit worse, how ridge and lasso trade a little bias for less variance, and how cross-validation picks the penalty.
  9. 9Time Series: AR(1) and StationarityAutocorrelation, the AR(1) model and its mean, variance and half-life, what stationarity means, why a unit root breaks ordinary inference, and how serial correlation shrinks your effective sample size.

Practice

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