Publications by Marley Myrianthopoulos
DATA 605 Final Exam
#Load necessary libraries and data library(tidyverse) ## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ── ## ✔ dplyr 1.1.2 ✔ readr 2.1.4 ## ✔ forcats 1.0.0 ✔ stringr 1.5.0 ## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1 ## ✔ lubridat...
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DATA 605 Discussion 15
Page 711 Problem 10 Find \(f_x\), \(f_y\), \(f_{xx}\), \(f_{yy}\), \(f_{xy}\), and \(f_{yx}\) of \(f(x,y)=y^3+3xy^2+3x^2y+x^3\) Solution \(f_x=3y^2+6xy+3x^2\) \(f_y=3y^2+6xy+3x^2\) \(f_{xx}=6y+6x\) \(f_{yy}=6y+6x\) \(f_{xy}=6y+6x\) \(f_{yx}=6y+6x\)...
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DATA 605 HW 15
Task 1 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 ) Solution 1 I will use R to determine the regression equation. x <- c(5.6, 6.3, 7, 7.7, 8.4) y <- c(8.8, 12.4, 14.8, 18.2, 20.8) linreg <- lm(y ~...
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DATA 605 Discussion 14
For this discussion post, I’ve chosen to demonstrate how a problem from the homework can be solved using R. Page 496 Problem 5 Key Idea 8.8.1 gives the nth term of the Taylor series of common funcƟons. In Exercises 3 – 6, verify the formula given in the Key Idea by finding the first few terms of the Taylor series of the given funcƟon and ide...
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DATA 605 HW 14
Problem 1 Find the Taylor Series expansion of \(f(x)=\frac{1}{1-x}\) Solution 1 If \(f(x)=\frac{1}{1-x}\), then… \(f'(x)=(-1)(1-x)^{-2}(-1)=(-1)^2(1-x)^{-2}\\f''(x)=(-2)(-1)^2(1-x)^{-3}(-1)=(2)(-1)^4(1-x)^{-3}\\f'''(x)=(-3)(2)(-1)^4(1-x)^{-4}(-1)=(3)(2)(-1)^6(1-x)^{-4}\\f''''(x)=(-4)(3)(2)(-1)^6(1-x)^{-5}(-1)=(4)(3)(2)(-1)^8(1-x)^{-5}\) We can s...
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DATA 605 HW 13
Task 1: Use integration by substitution to solve the integral below. \(\int4e^{-7x}dx\) Solution 1: Let \(u=-7x\). Then \(du=-7dx\) Now, \(\int4e^{-7x}dx=4\int e^{-7x}dx=-\frac{4}{7}\int e^{-7x}(-7)dx=-\frac{4}{7}\int e^udu=-\frac{4}{7}e^u+C=-\frac{4}{7}e^{-7x}+C\) Final Answer: \(\int4e^{-7x}dx=-\frac{4}{7}e^{-7x}+C\) Task 2: Biologists are tre...
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DATA 605 Discussion 13
Page 360 Problem 13 Task: Find the total area enclosed by the functions \(f\) and \(g\). \(f(x)=2x^2+5x-3\), \(g(x)=x^2+4x-1\) Solution: First we need to know where the functions intersect: \(2x^2+5x-3=x^2+4x-1\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0\text{ OR } x-1=0\\x=-2\text{ OR } x=1\) So the area enclosed by the functions covers the range of \(x\) v...
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DATA 605 HW 12
Task 1: Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error, and p-values only. Discuss whether the assumptions of simple linear regression met. Solution 1: The scatter plot is shown below: who_data <- read.csv("https://raw.githubuser...
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DATA 605 Discussion 11
Task Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? Introduction I’m a Yankees fan, so it has been a hard few years. During the difficult summer of 2021, the manager of the Yankees (Aaron Boone) tried to explain the high number of double plays that the t...
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DATA 605 HW 11
Task: Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) Model Construction library(ggplot2) cars_data <- cars cars_model <- lm(dist ~ speed, data = cars_data) cars_mode...
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