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Engineering LibreTexts

4: Inferential Statistics and Regression Analysis

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  • 4.0: Introduction
    This page discusses the importance of inferential statistics in data science for making population conclusions from sample data. Key techniques such as confidence intervals, hypothesis testing, and correlation analysis are highlighted, particularly in finance for risk mitigation and predictions. It also explores regression analysis, which models relationships between variables, and its applications in machine learning and time series forecasting.
  • 4.1: Statistical Inference and Confidence Intervals
    This page covers inferential statistics, focusing on estimating population parameters through sample data, confidence intervals, and bootstrapping methods. It explains confidence intervals, margin of error, and sampling distributions, emphasizing the central limit theorem. The text describes calculation methods using t-distribution and normal distribution, optimal sample size determination, and verification of normal approximations.
  • 4.2: Hypothesis Testing
    This page discusses hypothesis testing in statistics, focusing on one-sample and two-sample methods. Key concepts include defining null and alternative hypotheses, calculating test statistics and p-values, and making decisions about hypotheses based on significance levels. Real-world applications are illustrated, including claims about student AI usage and medication effectiveness, with examples showing how to analyze sample data, assess claims, and interpret results.
  • 4.3: Correlation and Linear Regression Analysis
    This page covers correlation and regression analysis, focusing on understanding relationships between numeric variables and predicting outcomes. It details the calculation and interpretation of the correlation coefficient, visualizing data with scatterplots, and applying linear regression models. The page emphasizes the significance of a strong correlation, hypothesis testing, and the least squares method for fitting lines.
  • 4.4: Analysis of Variance (ANOVA)
    This page explains the one-way ANOVA process for comparing multiple means, covering hypothesis formulation, conditions, and calculations using the F-distribution. It highlights the null hypothesis of equal means versus an alternative of at least one differing mean. A practical example using Python's f_oneway function shows an F statistic of 4.388 and a p-value of 0.
  • 4.5: Key Terms
    This page offers definitions and descriptions of essential statistical concepts relevant to hypothesis testing and data analysis, including alternative hypothesis, ANOVA, correlation analysis, and the central limit theorem. It addresses methods for estimating population parameters like confidence intervals, highlights potential errors in hypothesis testing (Type I and II), and explores regression analysis, residuals, and modeling techniques that illustrate variable relationships.
  • 4.6: Group Project
    This page outlines three group projects centered around statistical analysis: Project A surveys students to analyze work hours related to sociodemographic data, creating confidence intervals; Project B formulates a hypothesis regarding the proportion of white cars, involving data collection and hypothesis testing; Project C collects data on shoe length and height, develops scatterplots and regression models, and includes a follow-up assignment on used car prices based on age.
  • 4.7: Quantitative Problems
    This page discusses statistical analysis tasks including hypothesis testing, confidence intervals, and correlation calculations. It covers creating confidence intervals, p-value calculations for mean times and smoker proportions, average meal price comparisons between two restaurants, correlation coefficients for cash flow and salary, and an ANOVA test for plant growth under different light treatments, focusing on statistical significance assessments.


This page titled 4: Inferential Statistics and Regression Analysis is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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