Course Level: Intermediate

Course Objectives

• Calculate a confidence interval for a proportion
• Conduct an A-B test
• Calculate the correlation coefficient and test its statistical significance
• Fit a simple regression line via least squares
• Use the regression equation for predicting
• Fit a multiple regression model
• Distinguish between explanation and prediction in regression
• Assess regression model fit (R-squared, goodness-of-fit, RMSE)
• Interpret regression coefficients
• Explain the use of k-nearest neighbors for prediction
• Use a hold-out sample to assess performance of models

Course Outline

Module 1: Review of Basic Statistical Concepts

• Recap of descriptive statistics (mean, median, mode)
• Introduction to probability theory
• Overview of sampling distributions
• Understanding the central limit theorem
• Case Study: Review and analyze a dataset to summarize key descriptive statistics and discuss the implications of the central limit theorem.

Module 2: Hypothesis Testing Fundamentals

• Formulating null and alternative hypotheses
• Understanding Type I and Type II errors
• Setting significance levels (α) and interpreting p-values
• Performing and interpreting one-sample and two-sample tests
• Case Study: Conduct a hypothesis test on a real dataset to determine if there is a significant difference between two groups.

Module 3: Confidence Intervals

• Constructing and interpreting confidence intervals for means and proportions
• Understanding margin of error and confidence levels
• Comparing confidence intervals to hypothesis testing results
• Impact of sample size on confidence intervals
• Case Study: Calculate and interpret confidence intervals for a dataset, and assess the precision of the estimates.

Module 4: Comparing Means: ANOVA

• Introduction to Analysis of Variance (ANOVA)
• Understanding between-group and within-group variability
• Performing one-way ANOVA and interpreting results
• Post-hoc tests and multiple comparisons
• Case Study: Perform one-way ANOVA on a dataset with multiple groups and interpret the results, including post-hoc comparisons.

Module 5: Correlation Analysis

• Understanding correlation coefficients (Pearson, Spearman)
• Interpreting the strength and direction of relationships between variables
• Limitations of correlation and potential pitfalls
• Visualizing correlations with scatter plots
• Case Study: Analyze the correlation between two variables in a dataset and discuss the implications for relationship strength and direction.

Module 6: Simple Linear Regression

• Basics of linear regression models
• Estimating regression coefficients and interpreting results
• Assessing model fit (R-squared, residual analysis)
• Understanding assumptions of linear regression
• Case Study: Fit a simple linear regression model to a dataset and evaluate the model’s effectiveness and assumptions.

Module 7: Multiple Regression Analysis

• Introduction to multiple regression models
• Estimating and interpreting multiple regression coefficients
• Assessing multicollinearity and model diagnostics
• Model selection and improvement techniques
• Case Study: Build and interpret a multiple regression model using a dataset with several predictor variables.

Module 8: Logistic Regression

• Understanding logistic regression and its applications
• Estimating and interpreting odds ratios
• Assessing model fit and performance (ROC curves, confusion matrix)
• Comparing logistic regression with linear regression
• Case Study: Apply logistic regression to analyze binary outcomes and interpret the results.

Module 9: Chi-Square Tests for Association

• Introduction to chi-square tests and their applications
• Performing chi-square tests for independence and goodness-of-fit
• Interpreting chi-square test results and understanding limitations
• Visualizing categorical data relationships
• Case Study: Conduct a chi-square test to assess the relationship between categorical variables in a dataset.

Module 10: Advanced Topics in Inference and Association

• Introduction to non-parametric tests (e.g., Mann-Whitney U test)
• Understanding interaction effects in regression models
• Exploring techniques for handling complex data structures
• Practical considerations for inference and association in real-world data
• Case Study: Apply non-parametric tests and analyze complex data relationships in a given dataset, including interaction effects.