Old Projects: Statistical Inference and Regression in R

This repository contains archived coursework projects originally completed in 2017 as part of the Johns Hopkins Data Science Specialization (Coursera).
These early exercises illustrate foundational concepts in simulation, inference, and regression using the R programming language.
They are preserved for reference but are not part of my current professional data science portfolio.

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Contents

1. Statistical Inference, Part I — Simulation

Focus: Demonstrating the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) through simulation.
Summary:

• Simulates 1,000 exponential samples (lambda = 0.2, n = 40) to show convergence of sample means.
• Compares theoretical vs. observed means and variances.
• Illustrates that sample means of non-normal data approach normality as n increases.
• Reinforces that both the mean and variance of simulated samples are consistent with theoretical expectations.

Concepts: simulation, sampling distributions, normal approximation, consistency

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2. Statistical Inference, Part II — Inferential Data Analysis

Focus: Using t-tests for hypothesis testing on small samples.
Dataset: ToothGrowth (R’s built-in dataset).
Summary:

• Tests whether tooth growth depends on supplement type (OJ vs VC) and dosage level (0.5, 1, 2).
• Applies two-sample t-tests and interprets p-values and confidence intervals.
• Finds that tooth length increases with dose, but supplement effects depend on dosage.
• Demonstrates the logic of using the t-distribution to account for small-sample uncertainty.

Concepts: hypothesis testing, t-tests, confidence intervals, small-sample inference

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3. Cars: MPG vs. Transmission Type

Focus: Bivariate and multivariate analysis using linear regression.
Dataset: mtcars (Motor Trend, 1974).
Summary:

• Tests whether cars with manual transmissions achieve higher MPG than automatics.
• Uses t-tests and OLS regression to evaluate the relationship while controlling for confounders (e.g., weight, horsepower, cylinders).
• Finds that while manual cars appear more fuel-efficient in bivariate analysis, the transmission effect disappears once controls are added.
• Includes model selection (step()), residual diagnostics, and discussion of statistical power.

Concepts: regression modeling, confounding, model selection, residual analysis

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Tools and Environment

• Language: R
• Core Packages: datasets, knitr, stats, base R plotting
• Outputs: .Rmd, .html, .pdf
• Originally completed: September–October 2017

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Author

Samuel Shaw, PhD
Sociologist & Data Scientist
Seattle, WA
LinkedIn

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Note: These files are maintained here as part of an “old projects” archive for completeness and documentation of early R-based statistical work. They are intentionally excluded from my active portfolio repository.