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

March 24, 2013 1 Comment

**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 simple linear regression to analyze a data set with a logarithmic transformation and discuss how to make inferences on the regression coefficients and the means of the target on the original scale. The data document the decay of dichlorodiphenyltrichloroethane (DDT) in trout in Lake Michigan; I found it on Page 49 in the book “*Elements of Environmental Chemistry*” by Ronald A. Hites. Future posts will also be written on the chemical aspects of this topic, including the environmental chemistry of DDT and exponential decay in chemistry and, in particular, radiochemistry.

Dichlorodiphenyltrichloroethane (DDT)

Source: Wikimedia Commons

A serious student of statistics or a statistician re-learning the fundamentals like myself should always try to understand the math and the statistics behind a software’s built-in function rather than treating it like a black box. This is especially worthwhile for a basic yet powerful tool like simple linear regression. Thus, instead of simply using the lm() function in R, I will reproduce the calculations done by lm() with my own function and script (posted earlier on my blog) to obtain inferential statistics on the regression coefficients. However, I will not write or explain the math behind the calculations; they are shown in my own function with very self-evident variable names, in case you are interested. The calculations are arguably the most straightforward aspects of linear regression, and you can easily find the derivations and formulas on the web, in introductory or applied statistics textbooks, and in regression textbooks.

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