Publications by Bryan Persaud
Data 605 HW 15
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: dataframe1 <- data.frame(X = c(5.6, 6.3, 7, 7.7, 8.4), Y = c(8.8, 12.4, 14.8, 18.2, 20.8)) model1 <- lm(Y ~ X, data = dataframe1) summary...
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Data 605 HW 14
This week, we’ll work out some Taylor Series expansions of popular functions. • f(x) = 1 / (1−x) • f(x) = e^x • f(x) = ln(1 + x) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assignment as a R-Markdown document. Solution: The Taylor Seri...
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Data 605 Discussion 14
Chapter 8 Section 8.8 Exercise 7 In Exercises 7 – 12, find a formula for the nth 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 paƩern. (The formulas for several of these are found in Key Idea 8.8.1; show work verifying these formula.) f(x) = cos x; c = π/2 Soluti...
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Data 605 HW 13
1 Use integration by substitution to solve the integral below. \(\int { 4{ e }^{ -7x }dx }\) Solution: Let u = -7x, then du = -7dx. In terms of dx, dx = \(-\frac { 1 }{ 7 } du\) Rewrite integral in terms of u. \(\int { 4{ e }^{ u }(-\frac { 1 }{ 7 }) du }\) Take out constants. \(-\frac { 4 }{ 7 }\int { { e }^{ u } du }\) Integrate. \(-\frac { 4 }...
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Data 605 Discussion 13
Chapter 7 Section 7.1 Exercise 13 In Exercises 13 – 20, find the total area enclosed by the functions f and g. \(f(x) = 2x^2 + 5x − 3, g(x) = x^2 + 4x − 1\) Solution: Let’s use R to create two function, f(x) and g(x). function_f <- function(x) { 2 * (x ^ 2) + 5 * x - 3 } function_g <- function(x) { (x ^ 2) + 4 * x - 1 } We ne...
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Data 605 HW 12
who <- read.csv("https://raw.githubusercontent.com/bpersaud104/Data605/master/who.csv") head(who) ## Country LifeExp InfantSurvival Under5Survival TBFree PropMD ## 1 Afghanistan 42 0.835 0.743 0.99769 0.000228841 ## 2 Albania 71 0.985 0.983 0.99974 0.00114312...
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Data 605 Discussion 12
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? I chose to again use the candy dataset fro...
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Data 605 HW 11
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.) Solution: Linear Model linear_model <- lm(dist ~ speed, data = cars) linear_model ## ## Call: ## lm(formula = dist ...
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Data 605 Discussion 11
Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? The data I chose to use is the candy dataset from fivethiryeight. https://github.com/fivethirtyeight/data/tree/master/candy-power-ranking candy <- read.csv("https://raw.githubusercontent.com/fivethirtyeight/d...
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Data 605 Discussion 10
Chapter 12 Section 12.1 Exercise 13 Using Stirling’s Formula, prove that \((\frac { 2n }{ n } )\sim \frac { { 2 }^{ { 2 }^{ n } } }{ \sqrt { \pi n } }.\) Solution: Stirling’s Formula is \(n!\sim \sqrt { 2\pi n } { (\frac { n }{ e } ) }^{ n }\) Taking the fornula twice would give us \(n!n!\sim 2\pi n{ (\frac { n }{ e } ) }^{ 2n }\) We can also...
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