Article(s) Based upon research for work in UCLAs Stats Dept.

Visualizing 3D Regressions Plots & Integrating

This code processes and visualizes California COVID-19 data by county. First, it loads statewide COVID-19 data and displays basic info, then loads and filters FIPS codes to focus on California’s 58 counties. For each county, COVID-19 data is downloaded using FIPS codes, combined into a single dataset, and verified. Next, it reduces feature size by removing unnecessary columns, combines longitude and latitude to ensure location accuracy, and visualizes county data with ggplot2. Elevation data is added, creating an elevation map layered with county boundaries and centroids. Finally, cleaned datasets are saved as CSV files for further analysis.

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Network Analysis in R provides a comprehensive introduction to representing, analyzing, and visualizing networks using the `igraph` package in R. It covers fundamental concepts such as creating graph objects from data, adding attributes to nodes and edges, and utilizing centrality measures like degree and betweenness to identify influential nodes. The guide also delves into advanced topics like community detection, network randomization, and interactive visualizations to uncover patterns and structures within complex networks.

Project-Objective: This project aims to analyze user sentiments in Reddit comments on an R-related post to determine how positive and negative sentiments correlate with mentions of R and Python. By applying sentiment analysis techniques and leveraging machine learning models—k-Nearest Neighbors (kNN) and Naive Bayes—this project seeks to classify the overall sentiment of the community and identify trends related to each programming language. The project includes data collection, preprocessing, exploratory analysis, and model comparison, providing insights into user preferences in a structured and data-driven manner.

This R function decompose_and_identify_transformations analyzes a 2x2 matrix to identify specific linear transformations, such as scaling, reflection, shearing, and their combinations. It checks the matrix against various patterns, including simple scaling, reflections about axes, and horizontal/vertical shearing, providing a verbal explanation and the general form of the transformation. The function also computes the transformed vector and its polar coordinates, comparing it with the original vector to determine changes in magnitude and direction. Each identified transformation is explained with a standardized output format, including the matrix, the transformation type, and polar coordinate differences. The code is designed to handle a wide range of transformations, providing clear and concise explanations for each case.

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This chapter focuses on linear transformations and their geometric and algebraic properties. Section 2.1 introduces the concept of linear transformations, highlighting their relationship with matrices and inverse transformations. Sections 2.2 and 2.3 explore the geometric interpretations, including rotations, reflections, and scaling, and the algebraic properties of matrix multiplication. Section 2.4 discusses the inverse of linear transformations, detailing the conditions under which a transformation is invertible and the significance of the determinant in this process

This document explores solutions of linear systems using matrix algebra. It explains that consistent systems have at least one solution, with possible outcomes including a unique solution or infinitely many solutions, while inconsistent systems have no solutions. The rank of a matrix determines the number of leading variables and the nature of the solutions, with matrix-vector multiplication discussed as a linear transformation. Additionally, linear combinations of vectors are introduced, emphasizing their role in representing systems of linear equations.