Publications by Andrew Bowen
DATA 621: Blog 1
Power Transforms in R The R-function boxCox from the car package can be used to implement maximum likelihood transformations of data when modeling. This can be used to transform data to create a more linear relationship between predictor and dependent variables. We’ll use the built-in mtcars dataset. Let’s plot our horsepower variable against o...
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DATA605 Final Project - Probability & Stats
Problem 1 set.seed(1234) n <- 5 lambda <- 8 X <- rgamma(1:10000, shape=n, scale=1/lambda) Calculating our sum of exponential distributions: Y and Z: Y <- 0 for (i in 1:n){ Y <- Y + rexp(1:10000, rate=lambda) } Z <- rexp(1:10000, rate=lambda) Expected value and variance of our PDFs print(mean(X)) ## [1] 0.6228281 print(mean(Y)) ## [1] 0.6242317...
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DATA605: Final Project - Regression
Load our Datasets I uploaded the kaggle datasets to my GitHub, reading them here for reproducability. test_url <- "https://raw.githubusercontent.com/andrewbowen19/computationalMath605/main/data/test.csv" train_url <- "https://raw.githubusercontent.com/andrewbowen19/computationalMath605/main/data/train.csv" test <- read.csv(test_url) train <- read....
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DATA605: Problem Set 14
Question 1 Compute the taylor series (to order 4) of: \[\begin{aligned} f(x) = \frac{1}{1-x} \end{aligned}\] We can use the taylor function included in the calculus library within R for this. The above functon is valid everywhere except \(x=1\) f1 <- function(x){ 1 / (1 - x)} taylor(f1, var="x", order=4) ## $f ## [1] "(1) * 1 + (1.00000000000064...
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DATA605: Problem Set 13
Question 1 Let’s pick our substitution function \(u = -7x\), so \(\frac{\,du}{\,dx} = -7\), meaning \(\frac{\,du}{-7} = \,dx\). Plugging in we get \[\begin{aligned} \int 4e^{-7x}\,dx = 4\int e^{-7x} \,dx\newline = 4\int \frac{1}{-7}e^{u} \,du\newline = \frac{-4}{7}\int e^u \,du \newline ...
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DATA605: Univariate calculus
Exercise 4.2.15 - Related Rates A company that produces landscaping materials is dumping sand into a conical pile. The sand is being poured at a rate of \(5 ft^3/s\); the physical properties of the sand, in conjunction with gravity, ensure that the cone’s height is roughly \(2/3\) the length of the diameter of the circular base. How fast is the ...
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DATA605: Problem Set 12
Read-in our CSV data # TODO: replace local file path with GitHub URL df <- read.csv("~/CUNY/computationalMath605/data/real-world-data.csv") head(df) ## Country LifeExp InfantSurvival Under5Survival TBFree PropMD ## 1 Afghanistan 42 0.835 0.743 0.99769 0.000228841 ## 2 Albania 71 ...
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DATA605 Discussion Post Week 12
Multiple Regression We can use the Seatbelts dataset built into R. First, we can set it up as a dataframe in R # Load the dataset into a dataframe df <- as.data.frame(Seatbelts) We can use the law variable as our dichotomous value, as this takes a value of 0 or 1, depending on if the seatbelt law was in effect that month. We want to predict the val...
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DATA 605: Problem Set 11 - Regression
Load the Cars Dataset First, let’s load the built-in cars dataset to a native R dataframe df <- as.data.frame(cars) head(df) ## speed dist ## 1 4 2 ## 2 4 10 ## 3 7 4 ## 4 7 22 ## 5 8 16 ## 6 9 10 Model Creation We can use R’s built-in linear model (lm) to create model <- lm(cars$dist ~ cars$speed) sum...
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DATA605: Discussion Post Week 11
Dataset For this exercise, I chose the faithful dataset which is available as an R dataset First, let’s load the built-in cars dataset to a native R dataframe df <- as.data.frame(faithful) head(df) ## eruptions waiting ## 1 3.600 79 ## 2 1.800 54 ## 3 3.333 74 ## 4 2.283 62 ## 5 4.533 85 ## 6 2....
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