Fitting lines and hyperplanes — the normal equation, coefficients, and their limits.
View all tagsComplete step-by-step solutions for the Research Methodology assignment covering Binomial & Poisson distributions, Student's t-test, One-Way ANOVA, Pearson correlation, Linear Regression, and Research Proposal preparation.
Why MAE, MSE and RMSE can report three different numbers for the same predictions, why RMSE is never below MAE, what their ratio tells you about outliers, and why scikit-learn hands back a negative mean squared error.
Complete guide to simple and multiple linear regression for CT exam with formulas, derivations, and worked examples
30 practice problems covering linear regression, multiple regression, bias-variance, and error metrics
More than one feature — the normal equations solved by hand, why a coefficient changes when a correlated feature joins it, and the measurement showing Adjusted R² fails to penalise 100 columns of pure noise while cross-validation catches them cleanly.
Settles why R² can exceed 1 or go negative, why SST = SSR + SSE only holds for a least-squares fit, why adding a junk feature never lowers R² but does lower Adjusted R², and why scikit-learn's MAPE returns 0.0296 rather than 2.96%.
Fitting a line to one feature — the two coefficients derived by hand and checked against scikit-learn, the five error measures computed from the same residuals, and why a genuinely useful feature can look exactly like noise.
Solving for every coefficient in one algebraic step — the design matrix, the column of ones, the normal equation verified against scikit-learn, and the three situations where the inverse does not exist.