Regression-Analysis-in-R

This repository contains basics strategies, codes, and scripts of regression analysis learnt in the class Statistics 501 by Prof. Lynn Lin at Penn State. It focused on tools and techniques for performing regression analysis in R.

The textbook used in this course is "A Modern approach to regression with R" by Dr. Simon Sheather and the Datasets for this course are available at http://www.stat.tamu.edu/~sheather/book/data_sets.php

Chapter 1. Introduction

This chapter included introduction to RStudio (IDE), R basics, vectors, matrices, data structures,conditional statements, loop statements, function.

Chapter 2. Statistical Data Analysis

This chapter included basics of plotting graphs in R, altering the size of plot margins, plotting character, color, type, labels on axis, title fot the graph, hostograms, scatter plots, boxplot, and quantile functions.

Chapter 3. Simple Regression Analysis

This chapter introduced concept of simple regression analysis and its uses. Regression analysis is the most widely used statistical tool for understanding relationships among variables. Prediction and forecasting can be performed using regression analysis.

Regression models conditional distribution of Y given X=x, i.e., P(Y=y|X=x). Given a specific value of X (i.e., X=x), we can predict the value of Y. Simple linear regression models relationship between two variables, X as explanatory variable (or Predictor) and Y as response (or Dependent) variable. Linear relationships are easy to work with and are a good approximation in lots of real word problems.

Chapter 4. Diagnostics and Transformations for Simple Linear Regressions

This chapter introduces the analysis of simple linear regression models for accuracy and shortcomings. Regression functional form can be invalid if some explanatory variables are missing, presence of non-linear terms and outliers, faulty residual assumptions, etc.

This chapter includes:

a. Residual plots

b. Leverage Points

c. Outliers

d. R-squared

e. Standardized residuals

f. Cook's Distance

g. Diagnostics Plots for Regression model

h. Transformation

Chapter 5. Multilinear Regression

This chapter introduced concept of Multilinear regression analysis and its advantages. Multiple linear regression is an extension of simple linear regression. It is used to describe scenarios of product demand models with demand variable depending on competitors' prices, advertising, demographics, etc or Multi-factor asset pricing models, Fama-French three-factor model, many variables used to describe the returns of a portfolio or stock.

This chapter includes:

a. F-test

b. Anova

c. Ancova

Chapter 6. Diagnostics and Transformation for MLR

This chapter introduces the analysis of fiited Multilinear regression model. The model can be assessed for the effects of one or more predictors on the model, outliers, leverage points, transformation of predictor or response variable or both if invalid model has been fit, etc.

This chapter includes:

a. Added variable plots

b. Transformation of predictor variable

c. Transformation of response variable

d. Inverse response plots

e. Boxcox Procedure

f. Pairs plot

g. Marginal Plots