If is the target variable and is the predictor variable, then this is a linear relationship between the target and the predictor.
However, let’s evaluate the natural logarithm of each side. If is the target variable and is the predictor variable, then it is clear that the above equation is not linear between and. It can be shown mathematically using differential equations that a chemical will decay exponentially if the following conditions are satisfied:ġ) There is no influx of the chemical into the system in question.Ģ) The rate of decay (or outflux) of the chemical is proportional to its amount in the system. This is especially common for radioactive decay. – is the concentration of the chemical at time – is the initial concentration of the chemical The exponential decay of a chemical’s concentration can be mathematically described as follows: The exponential decay of an environmental pollutant is an example of such a model that can be linearized for simple linear regression to be used. The relationship between the target (Y) and the predictor (x) may not be linear to begin with, and some transformation may be required to linearize the predictor-target relationship. 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.Īs I mentioned previously in my last blog post about some conceptual foundations of simple linear regression, the “linear” term in the name refers to the linearity between the target and the regression coefficients ( and ). 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. 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. This is especially worthwhile for a basic yet powerful tool like simple linear regression. 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.Ī 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. The data document the decay of dichlorodiphenyltrichloroethane (DDT) in trout in Lake Michigan I found it on in the book “ Elements of Environmental Chemistry” by Ronald A.
LOGARITHMIC REGRESSION EXCEL HOW TO
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.
LOGARITHMIC REGRESSION EXCEL SERIES
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. This blog post uses a function and a script written in R that were displayed in an earlier blog post.
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