Data, Statistics & Probability

Advanced statistics, distributions, regression and probability models

Explanation

Regression & Correlation

  • Correlation coefficient r: ranges −1 to 1; |r| close to 1 = strong relationship.
  • Line of best fit: minimises the sum of squared residuals.
  • r² (coefficient of determination): % of variation in y explained by x.
  • Correlation ≠ causation.

Distributions

  • Normal: symmetric, bell-shaped; mean = median = mode
  • Skewed right: long tail to the right; mean > median
  • Skewed left: long tail to the left; mean < median
  • Binomial distribution: P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ

Advanced Probability

  • Bayes' theorem: P(A|B) = P(B|A)P(A)/P(B)
  • Independence test: A and B are independent iff P(A∩B) = P(A)·P(B)
  • Geometric probability: favourable region/total region
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