Publications by Don Padmaperuma
DATA 605 - Final Project
library(kableExtra) Problem 1 Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to N, where N can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of (N+1)/2. set.seed(123) N <- 10 X <- runif(10000, min=0...
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DATA 605 - Kaggle Submission
library('ggplot2') library('ggthemes') library('scales') library('dplyr') ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union library('mice') ## Warning: package 'mice' wa...
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DATA 605 - Week 16
Chapter 12 Exercise 12.1 Describe in words and sketch the level curves for the function and given c values. We will study the level curve, \(c = x^2 - y^2\) \(f(x,y) = x^2 - y^2\); \(c = -1,0,1\) Let’s take the case \(c = 0\), \(f(x,y) = x^2 - y^2 = c = 0\) factors to , \((x-y)(x+y) = 0\) This equation satisfies either \(x = y\) or \(y = -x...
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DATA 605 - Week 15
Chapter 8 Exercise 8.8 8. Find a formula for the \(n^{th}\) term of the Taylor series of \(f(x)\), centered at \(c\), by finding the coefficients of the first few powers of \(x\) and looking for a pattern. \(f(x) = \frac{1}{x}\); \(c = 1\) # Reference: https://www.math.ucla.edu/~anderson/rw1001/library/base/html/curve.html fct_exp <- function(...
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DATA 605 - Homework 15
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 ) Step 1: Section points to x and y variables x = c( 5.6, 6.3, 7, 7.7, 8.4) y = c( 8.8, 12.4, 14.8, 18.2, 20.8) Step 2: Generate regression model reg...
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DATA 605 - Discussion 14
Task: Using R, provide the solution for any exercise in either Chapter 4 or Chapter 7 of the calculus textbook. If you are unsure of your solution, post your concerns. Book: APEX Calculus Version 4 Chapter 7 - Applications of Integration Exercise 7.1- Page 360 19. The functions \(f(x) = cos(x)\) and \(g(x) = sin x\) intersect infinitely many tim...
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DATA 605 - Discussion 13
Task: Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? What is Multiple Regression Model A...
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DATA 605 - Assignment 14
Taylor Series \(f(x) = \sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^n\) \(= f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^2+\frac{f'''(a)}{3!}(x-a)^3+...\) Equation 1 \(f(x) = \frac{1}{(1-x)}\) \(f'(x) = \frac{1}{(1-x)^2}\) \(f''(x) = \frac{2}{(1-x)^3}\) \(f'''(x) = \frac{6}{(1-x)^4}\) can be generalized as, \(f^{(n)}(x) = \frac{n!}{(1-x)^{n+1}}\) sub...
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DATA 605 - Assignment 13
Use integration by substitution to solove the integration below. \(\int4e^{-7x}dx\) Solution: Let \(u = -7x\) by defferentiation on both sides we get this: \(\frac{du}{dx}=-7\) \(dx=\frac{-1}{7}du\) Therefor this can be written in a different way. \(4e^u . \frac{-1}{7}du\) \(\frac{-4}{7}\int e^u du\) \(\frac{-4}{7}(e^u+C)\) By substituting the v...
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Data 605-Discussion 12
library(MASS) library(corrplot) ## corrplot 0.84 loaded library(ggplot2) library(knitr) Task: Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? Data Set: Boston Housing Dataset that comes with MASS library includes Housing Values in Suburbs of Boston. The da...
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