Overview

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BiteSize Statistics for Business: Correlation and Regression Analysis is the third and final course in the BiteSize Stats for Business specialization. It moves from testing whether two groups differ to modeling how two or more variables relate — quantifying association, fitting a predictive line, and rigorously checking whether that line can be trusted. Across five modules, learners progress from scatterplots and the Pearson correlation coefficient (with significance testing and common pitfalls), through simple linear regression and OLS estimation, to inference for the regression slope, model-fit diagnostics (R², residual plots, influential points), and finally multiple regression with multicollinearity checks. Every core lesson pairs a focused reading with a hands-on interactive notebook built around a realistic business scenario, and every module includes a fully worked demo case study and one or more student-led practice projects applying the module's tools to a new dataset.

Syllabus

Correlation
- Introduces scatterplots for visualizing linear association between two quantitative variables, then the Pearson correlation coefficient r for quantifying it. Students test whether a population correlation is statistically different from zero and learn four common pitfalls — outliers, non-linearity, confounding, and Simpson's paradox — that can make a correlation misleading.
Simple Linear Regression
- Introduces the simple linear regression model and the OLS criterion for fitting a line that minimizes the sum of squared residuals. Students interpret the slope and intercept in business terms, distinguish association from causation, and compute predictions and residuals while learning why extrapolation beyond the data range is unreliable.
Inference for Regression
- Covers the sampling distribution of the OLS slope and its standard error, then the t-test and confidence interval for the population slope. Students distinguish a confidence interval for the mean response from a prediction interval for an individual observation and learn when each is the right tool for a business decision.
Model Fit and Diagnostics
- Introduces R-squared as the proportion of variance explained by a regression model, then residual plots and Q-Q plots for checking the linearity, homoscedasticity, and normality assumptions behind regression inference. Students distinguish outliers from high-leverage and influential points using Cook's distance and learn appropriate remedies for each assumption violation.
Multiple Regression
- Extends simple linear regression to multiple predictors, introducing adjusted R-squared for comparing models fairly and the overall F-test for model significance. Students interpret partial slopes holding other predictors constant, encode categorical predictors as dummy variables, and diagnose multicollinearity using the Variance Inflation Factor.