Overview

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This course delves into regression analysis using R, covering key concepts, software tools, and differences between statistical analysis and machine learning. - You'll learn data reading, cleaning, exploratory data analysis, and ordinary least squares (OLS) regression modeling, including theory, implementation, and result interpretation. - You'll tackle multicollinearity with techniques like principal component regression and LASSO regression, and cover variable and model selection for performance evaluation. - You'll handle OLS violations through data transformations and robust regression, and explore generalized linear models (GLMs) for logistic regression and count data analysis. - Advanced sections include non-linear and non-parametric techniques such as polynomial regression, GAMs, regression trees, and random forests. Ideal for statisticians, data analysts, and machine learning practitioners with basic R knowledge, this course blends theory with hands-on practice to enhance your regression analysis skills.

Syllabus

Get Started with Practical Regression Analysis in R

In this module, we will introduce you to the essential concepts and tools for regression analysis in R. You'll learn the differences between statistical analysis and machine learning, get familiar with R and R Studio, and start working with data. We'll guide you through the steps of data cleaning and perform some initial exploratory data analysis to set a solid foundation for your future learning.

Ordinary Least Square Regression Modelling

In this module, we will delve into Ordinary Least Squares (OLS) regression, covering both theory and practical implementation in R. You will learn how to interpret OLS results, calculate and apply confidence intervals, and explore various OLS regression techniques, including models without intercepts, ANOVA, and multiple linear regression with interaction and dummy variables. Additionally, we will discuss the essential conditions that OLS models must satisfy to ensure accurate and reliable results.

Deal with Multicollinearity in OLS Regression Models

In this module, we will address the challenge of multicollinearity in OLS regression models. You will learn how to detect multicollinearity and manage regression analyses with correlated predictors. The module covers advanced regression techniques such as Principal Component Regression, Partial Least Square Regression, Ridge Regression, and LASSO Regression, providing you with a comprehensive toolkit to handle multicollinearity effectively in R.

Variable & Model Selection

In this module, we will explore the critical aspects of variable and model selection in regression analysis. You will understand why selection is essential, learn how to choose the most appropriate OLS regression model, and identify model subsets. We'll cover evaluating regression model accuracy from a machine learning perspective and assessing performance using diverse metrics. Additionally, you will implement LASSO Regression for variable selection and analyze the contribution of predictors in explaining the variation in the outcome variable.

Dealing with Other Violations of the OLS Regression Models

In this module, we will tackle common violations of OLS regression model assumptions. You will learn how to apply data transformations to correct issues, use robust regression methods to manage outliers, and address heteroscedasticity to ensure the reliability and validity of your regression models. This module equips you with essential techniques to refine your analysis and improve model performance.

Generalized Linear Models (GLMs)

In this module, we will introduce you to Generalized Linear Models (GLMs) and their various applications. You will learn the fundamentals of GLMs, including logistic regression for binary response variables, multinomial logistic regression, and regression techniques for count data. Additionally, we will cover methods to evaluate the goodness of fit for these models. This module will enhance your understanding of how GLMs extend traditional linear regression models to handle a wider range of data types and distributions.

Working with Non-Parametric and Non-Linear Data

In this module, we will explore advanced methods for working with non-parametric and non-linear data. You will learn to implement polynomial and non-linear regression techniques, use Generalized Additive Models (GAMs) and their boosted versions, and develop Multivariate Adaptive Regression Splines (MARS) models. We will also cover CART regression trees, Conditional Inference Trees, Random Forests, and Gradient Boosting Regression. Additionally, you will gain insights into selecting suitable machine learning models for complex data scenarios, enhancing your ability to handle diverse data structures in R.