Linear Regression

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Coding
Theory
Quiz

    Simple Ols Fundamentals

    • Fit Single-Feature LinearRegression

      Junior

    • Simple OLS Slope And Intercept

      Junior

    • Fit A Line With np.polyfit

      Junior

    • Total Sum of Squares (SST)

      Junior

    • Fit OLS Line and Predict

      Junior

    • Pearson Correlation Coefficient

      Junior

    • Simple OLS Residual Vector

      Junior

    • OLS Slope From Correlation Identity

      Mid

    • OLS Params With statsmodels

      Mid

    • OLS Sum-of-Squares Decomposition

      Mid

    • R-squared for Simple OLS Fit

      Mid

    • Mean-Centered OLS Fit

      Mid

    • linregress Summary Tuple

      Mid

    • Regression Through The Origin

      Mid

    • Simple OLS Slope Three Ways

      Senior

    • OLS Coefficients Under Predictor Rescaling

      Senior

    • Per-Group OLS Slopes as a Series

      Senior

    • One-Pass OLS From Sufficient Statistics

      Senior

    Normal Equation Matrix Form

    • Normal Equation OLS Coefficients

      Junior

    • Solve Normal Equations for Beta

      Junior

    • OLS Design Matrix With Intercept

      Junior

    • Gram Matrix and Moment Vector

      Junior

    • Split OLS Intercept and Slopes

      Junior

    • OLS Fitted Values via Normal Equation

      Junior

    • OLS Coefficients via np.linalg.lstsq

      Mid

    • Unpack the Full lstsq Return

      Mid

    • OLS via Moore-Penrose Pseudo-Inverse

      Mid

    • OLS via QR Factorization

      Mid

    • Centered OLS Without Ones Column

      Mid

    • Multi-Target OLS In One Solve

      Mid

    • OLS Through the Origin

      Mid

    • Cholesky Solve of Normal Equations

      Mid

    • Conditioning Report: cond(XᵀX) = cond(X)²

      Senior

    • Rank-Aware OLS Solver Dispatch

      Senior

    • Minimum-Norm Solution for Wide Systems

      Senior

    • Minimum-Norm OLS For Rank-Deficient X

      Senior

    • OLS via Truncated SVD

      Senior

    Multiple Regression Fitting

    • Fit OLS With statsmodels add_constant

      Junior

    • OLS Slope Coefficients

      Junior

    • OLS Coefficients and Intercept

      Junior

    • Fit OLS, Predict New Rows

      Junior

    • OLS Regression Through the Origin

      Junior

    • Coefficient Series by Feature Name

      Junior

    • Fitted OLS Intercept

      Junior

    • sklearn vs statsmodels Coefficients

      Mid

    • Train, Split, and Predict

      Mid

    • OLS via statsmodels Formula API

      Mid

    • Regression Through the Origin

      Mid

    • OLS Predict on New Exog

      Mid

    • Mean-Centering Absorbs the Intercept

      Mid

    • Multi-Target Coefficient Matrix

      Mid

    • Predict From DataFrame Preserving Index

      Mid

    • Fit Named Feature Subset

      Senior

    • Recover Intercept From Centered Fit

      Senior

    • Non-Negative Least Squares Fit

      Senior

    Fit Metrics Evaluation

    • Compute R-squared From Predictions

      Junior

    • Compute RMSE

      Junior

    • Variance Decomposition: TSS, ESS, RSS

      Junior

    • R-squared Equals Correlation Squared

      Junior

    • In-Sample R² of OLS Fit

      Junior

    • OLS Regression Report Metrics

      Junior

    • Compute Mean Absolute Error

      Junior

    • R² Monotonicity Over Nested Fits

      Mid

    • In-Sample R² and Adjusted R²

      Mid

    • Adjusted R-Squared From Scratch

      Mid

    • Negative Out-of-Sample R-Squared

      Mid

    • Compute MAPE in Both Conventions

      Mid

    • In-Sample vs Out-of-Sample R²

      Mid

    • Verify Sum-of-Squares Decomposition

      Mid

    • Zero-Safe MAPE Metric

      Mid

    • No-Intercept R-Squared Trap

      Senior

    • Adjusted R2 Penalty for Junk Predictor

      Senior

    • Best-Subset Selection by Adjusted R²

      Senior

    Coefficient Inference Significance

    • OLS Coefficient Confidence Intervals

      Junior

    • OLS Coefficient t-Statistics

      Junior

    • OLS Coefficient Standard Errors

      Junior

    • Overall F-Test for OLS

      Junior

    • OLS t-Statistics and p-Values

      Mid

    • OLS Standard Errors From Scratch

      Mid

    • Unbiased Error Variance From OLS

      Mid

    • OLS Confidence Intervals From Scratch

      Mid

    • Overall F-Test From Scratch

      Mid

    • OLS Coefficient Covariance Matrix

      Mid

    • Named P-Value Series From OLS

      Mid

    • Significant Predictor Screening at Alpha

      Mid

    • Joint F-Test on Coefficient Subset

      Senior

    • Partial F-Test for Nested Models

      Senior

    • T-Test Against a Non-Zero Null

      Senior

    • Through-the-Origin OLS Inference

      Senior

    • Inference on a Linear Combination of Coefficients

      Senior

    • Standard Errors via Design-Matrix Pseudo-Inverse

      Senior

    Residuals Fit Inspection

    • Signed Residual Sum With Intercept

      Junior

    • OLS Residual Vector

      Junior

    • OLS Fitted Values With Intercept

      Junior

    • Residual Sum of Squares from OLS

      Junior

    • Index of Largest Absolute Residual

      Junior

    • Leverage From the Hat Matrix

      Mid

    • Internally Studentized Residuals

      Mid

    • Residual Orthogonality to Design Matrix

      Mid

    • Hat Matrix Trace Identity

      Mid

    • Hat Matrix From Predictors

      Mid

    • OLS Pearson Residuals

      Mid

    • Fitted Values Orthogonal to Residuals

      Mid

    • Intercept and the Residual Zero-Sum Identity

      Senior

    • Highest-Leverage Point Index

      Senior

    • High-Leverage Observations via Hat Matrix

      Senior

    • Leverage Scores via Economy QR

      Senior

    Categorical Interactions Polynomial Terms

    • Fit a Quadratic as a Linear Model

      Junior

    • Two-Way Interaction Coefficient

      Junior

    • One-Hot Encode Regression Predictors

      Junior

    • Dummy Coefficient as a Contrast

      Junior

    • Quadratic Design Matrix With PolynomialFeatures

      Junior

    • Dummy-Variable Trap as Rank Deficiency

      Mid

    • Interaction Model Group Slopes

      Mid

    • Categorical Contrasts vs Chosen Reference

      Mid

    • Fit Additive Formula Model Params

      Mid

    • Quadratic Fit With patsy I()

      Mid

    • Mean-Centering and OLS Coefficients

      Mid

    • Interaction-Only Design Matrix

      Mid

    • Polynomial Feature Names

      Mid

    • Centering Under an Interaction

      Senior

    • Saturated Interaction Equals Separate Fits

      Senior

    • Dummy Reference Level Invariance

      Senior

    • Group Means From Dummy Coefficients

      Senior

    • Coefficients on a Standardized Predictor Scale

      Senior

    Weighted Robust Prediction Intervals

    • HC3 Robust Standard Errors

      Junior

    • Mean Response Confidence Interval

      Junior

    • Weighted Least Squares Fit

      Junior

    • Confidence vs Prediction Interval at x0

      Mid

    • WLS With Inverse-Variance Weights

      Mid

    • Classical vs HC3 Robust Standard Errors

      Mid

    • Robust Regression With Huber T

      Mid

    • RLM IRLS Observation Weights

      Mid

    • WLS vs OLS Inverse-Variance Fit

      Mid

    • OLS Prediction Summary Frame

      Mid

    • Weighted Least Squares Closed Form

      Mid

    • Prediction Interval From Scratch

      Senior

    • Manual HC0 Robust Standard Errors

      Senior

    • OLS vs Robust Regression Slope

      Senior

    • Confidence vs Prediction Interval Widths

      Senior

    • HC0–HC3 Robust Standard Errors

      Senior

    • HC3-Robust Coefficient Confidence Intervals

      Senior

    • WLS Equals Transformed OLS

      Senior