Publications by Alexander Ng
DATA 621 HW3 Logistic Regression
Introduction This assignment explores, analyzes and models a data set containing information on crime and demographic details of the neighborhoods of a city. Each record show a target variable indicating whether the crime rate is above(1) or below(0) the city median crime rate. We build a set of binary logistic regression models using only the pr...
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DATA 621 Blog 4 Lowess Regression
Introduction In this blog, we examine lowess, a statistical curve-fitting technique. We will provide some mathematical preliminaries, then give an example calculation followed by an example in R. Lastly, we describe a commonly used R graphical function where lowess is the underlying curve fitting methodology. Mathematical Overview Lowess regress...
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DATA 621 Blog 3 Leverage for Logistic and Linear Regression Are Different
Introduction In this blog, we compare the diagonal elements of the hat matrix used in multiple linear regression and logistic regression. As we know, the standardized residuals of a multiple linear regression require dividing by a function of leverage numbers \(h_{ii}\), the diagonal elements of the hat matrix \(\mathbf{H}\). We will show theoret...
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Data 621 Homework 2 Classification Metrics
1 Introduction This assignment explores classification metrics in data science using R. The assignment has 13 items to be completed. The deliverables include a report in PDF, the R code and functions and the supporting RMarkdown file. This report is divided into 5 subsequent parts. In the second section, we solve items 1-9 which require implement...
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Data 621 Datasaurus and Anscombe Quartet
Data 621 Blog 1 Alexander Ng 02/11/2020 Introduction This blog demonstrates the importance of graphical visualization in addition to using statistical summaries to understand a data set. Begin With the Familiar The most famous example of how different data sets can have the same statistical summaries but different graphical structure is Anscombe...
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Data 605 Fall 2019 Assignment Week 15
Data 605 Assignment Week 15 Alexander Ng 12/06/2019 Problem 1: Equation of the Regression Line Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. \[ (5.6, 8.8), (6.3, 12.4), (7, 14.8), (7.7, 18.2), (8.4, 20.8) \] The solution can be obtained by organizing the data points i...
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Data 605 Fall 2019 Discussion Week 15
Data 605 Discussion Week 15 Alexander Ng 12/4/2019 Chapter 12.8 Exercise 17 Find the absolute maximum and minimum of the function subject to the given constraint. \[f(x,y) = x^2 + 2x + y^2 + 2y \] constrained to the region bounded by the circle \[x^2+y^2=4\]. Solution The region is a circle of radius 2 centered at the origin. By the Extreme Valu...
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Data 605 Fall 2019 Assignment Week 14
Data 605 Assignment Week 14 Alexander Ng 11/28/2019 Problem 1: Taylor Series of \(\frac{1}{(1-x)}\) The Taylor Series centered at \(x=0\) is \[ \frac{1}{(1-x)} = 1 + x + x^2 + x^3 + \ldots + x^n + \ldots = \sum_{n=0}^{\infty} x^n\] defined on the interval \(\lvert x \rvert < 1\) with radius of 1. Obviously, \(f(0) = 0\). \[\begin{align} f^{(0)}(x...
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Data 605 Fall 2019 Discussion Week 14
Data 605 Discussion Week 14 Alexander Ng 11/24/2019 Chapter 8.8 #32 Approximate the definite integral by using the first 4 nonzero terms Approximate the value of the given definite integral by using the first 4 non-zero terms of the integrand’s Taylor series. \[\int_{0}^{\pi^2/4 } \cos( \sqrt{x}) dx \] Solution First, we obtain the exact answ...
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Data 605 Fall 2019 Final Week 16
Data 605 Final Project Week 16 Alexander Ng 12/06/2019 knitr::opts_chunk$set(echo = TRUE) library(tidyverse) ## ── Attaching packages ──────────────────────────────────────────────────────────────────────�...
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