Blog Archives

When Does the Kinetic Theory of Gases Fail? Examining its Postulates with Assistance from Simple Linear Regression in R

When Does the Kinetic Theory of Gases Fail?  Examining its Postulates with Assistance from Simple Linear Regression in R

Introduction The Ideal Gas Law, , is a very simple yet useful relationship that describes the behaviours of many gases pretty well in many situations.  It is “Ideal” because it makes some assumptions about gas particles that make the math and the physics easy to work with; in fact, the simplicity that arises from these

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Exploratory Data Analysis – Computing Descriptive Statistics in R for Data on Ozone Pollution in New York City

Exploratory Data Analysis – Computing Descriptive Statistics in R for Data on Ozone Pollution in New York City

Introduction This is the first of a series of posts on exploratory data analysis (EDA).  This post will calculate the common summary statistics of a univariate continuous data set – the data on ozone pollution in New York City that is part of the built-in “airquality” data set in R.  This is a particularly good data set

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How to Calculate a Partial Correlation Coefficient in R: An Example with Oxidizing Ammonia to Make Nitric Acid

How to Calculate a Partial Correlation Coefficient in R: An Example with Oxidizing Ammonia to Make Nitric Acid

Introduction Today, I will talk about the math behind calculating partial correlation and illustrate the computation in R with an example involving the oxidation of ammonia to make nitric acid using a built-in data set in R called stackloss.  In a separate post, I will also share an R function that I wrote to estimate partial correlation.

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Using the Golden Section Search Method to Minimize the Sum of Absolute Deviations

Using the Golden Section Search Method to Minimize the Sum of Absolute Deviations

Introduction Recently, I introduced the golden search method – a special way to save computation time by modifying the bisection method with the golden ratio, and I illustrated how to minimize a cusped function with this script.  I also wrote an R function to implement this method and an R script on how to apply this

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Scripts and Functions: Using R to Implement the Golden Section Search Method for Numerical Optimization

Scripts and Functions: Using R to Implement the Golden Section Search Method for Numerical Optimization

In an earlier post, I introduced the golden section search method – a modification of the bisection method for numerical optimization that saves computation time by using the golden ratio to set its test points.  This post contains the R function that implements this method, the R functions that contain the 3 functions that were

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The Golden Section Search Method: Modifying the Bisection Method with the Golden Ratio for Numerical Optimization

The Golden Section Search Method: Modifying the Bisection Method with the Golden Ratio for Numerical Optimization

Introduction The first algorithm that I learned for root-finding in my undergraduate numerical analysis class (MACM 316 at Simon Fraser University) was the bisection method.  It’s very intuitive and easy to implement in any programming language (I was using MATLAB at the time).  The bisection method can be easily adapted for optimizing 1-dimensional functions with

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Checking the Goodness of Fit of the Poisson Distribution in R for Alpha Decay by Americium-241

Checking the Goodness of Fit of the Poisson Distribution in R for Alpha Decay by Americium-241

Introduction Today, I will discuss the alpha decay of americium-241 and use R to model the number of emissions from a real data set with the Poisson distribution.  I was especially intrigued in learning about the use of Am-241 in smoke detectors, and I will elaborate on this clever application.  I will then use the Pearson chi-squared

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How do Dew and Fog Form? Nature at Work with Temperature, Vapour Pressure, and Partial Pressure

How do Dew and Fog Form?  Nature at Work with Temperature, Vapour Pressure, and Partial Pressure

In the early morning, especially here in Canada, I often see dew – water droplets formed by the condensation of water vapour on outside surfaces, like windows, car roofs, and leaves of trees.  I also sometimes see fog – water droplets or ice crystals that are suspended in air and often blocking visibility at great

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Checking for Normality with Quantile Ranges and the Standard Deviation

Checking for Normality with Quantile Ranges and the Standard Deviation

Introduction I was reading Michael Trosset’s “An Introduction to Statistical Inference and Its Applications with R”, and I learned a basic but interesting fact about the normal distribution’s interquartile range and standard deviation that I had not learned before.  This turns out to be a good way to check for normality in a data set.

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Estimating the Decay Rate and the Half-Life of DDT in Trout – Applying Simple Linear Regression with Logarithmic Transformation

Estimating the Decay Rate and the Half-Life of DDT in Trout – Applying Simple Linear Regression with Logarithmic Transformation

This blog post uses a function and a script written in R that were displayed in an earlier blog post. Introduction This is the second of a series of blog posts about simple linear regression; the first was written recently on some conceptual nuances and subtleties about this model.  In this blog post, I will use

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