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Regression & Correlation

Pearson correlation, simple and multiple linear regression, R², and residual analysis — modelling and measuring the relationship between variables.

15 articles

Illustration: Residuals that drift together (positive autocorrelation) push d well below 2

Sep 27, 20268 min read

The Durbin-Watson Test: Detecting Autocorrelation in Regression Residuals

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Illustration: A sigmoid squeezes a linear score into a probability between 0 and 1

Sep 16, 20267 min read

Logistic Regression: Predicting Probabilities for a Binary Outcome

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Illustration: Each slope holds the other predictors constant: same slope, shifted by x₂

Sep 14, 20267 min read

Multiple Linear Regression: Modelling Several Predictors at Once

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Illustration: One high-leverage point (circled) drags the line away from where the other 14 points lead

Sep 11, 20268 min read

Leverage, Outliers, and Cook's Distance: Finding Influential Points in Regression

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Illustration: With an interaction, the slope of x depends on the group — the lines are no longer parallel

Sep 10, 20268 min read

Interaction Effects in Regression: When One Predictor's Effect Depends on Another

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Illustration: Coefficient paths: ridge shrinks every coefficient; lasso sets the weakest exactly to zero

Sep 8, 20267 min read

Ridge and Lasso Regression: Shrinking Coefficients on Purpose

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Illustration: A 0/1 dummy shifts the line up by b₂ without changing its slope

Sep 8, 20267 min read

Dummy Variables: Using Categorical Predictors in Regression

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Illustration: Three unordered outcomes: softmax turns three scores into probabilities that always sum to 1

Sep 5, 20267 min read

Multinomial Logistic Regression: Beyond Two Outcome Categories

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Illustration: The X–Y link that remains once Z, which drives both, is held fixed

Aug 25, 20267 min read

Partial Correlation: Controlling for a Third Variable

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Illustration: Does the model explain more variation than pure noise would? Compare explained to unexplained

Aug 25, 20267 min read

The F-Test for Overall Regression Significance

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Illustration: The least-squares line minimises the sum of the squared vertical gaps (dotted)

Aug 20, 20268 min read

Simple Linear Regression: The Least-Squares Line, Explained

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Illustration: The narrow band estimates the average response; the wide band predicts one new observation

Aug 13, 20267 min read

Confidence Intervals vs. Prediction Intervals in Regression

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Illustration: A straight line misses the curve (dashed); a quadratic term captures it

Aug 11, 20267 min read

Polynomial Regression: Fitting a Curve Instead of a Straight Line

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Illustration: Pearson’s r measures the strength and direction of a straight-line relationship

Aug 10, 20268 min read

Pearson Correlation: Formula, Worked Example, and Why It Isn't Causation

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Illustration: A steady but curved relationship: rank correlation sees the monotone trend that r understates

Aug 10, 20267 min read

Spearman's Rank Correlation: When the Relationship Isn't a Straight Line

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Basic probability rules, conditional probability, Bayes' theorem, expected value…

Distributions

The normal distribution, binomial distribution, t-distribution, z-scores, and th…

Sampling & Inference

Sampling distributions, the Central Limit Theorem, standard error and confidence…

Hypothesis Testing

Null and alternative hypotheses, p-values, Type I/II errors, t-tests, chi-square…

Data Science & Applications

Exploratory data analysis, data visualization, A/B testing, and Bayesian statist…

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