More specifically, how can one use Log to relate seemingly unrelated variables, or at least describe a linear relationship with them?
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A logarithmic function does not describe linear relationships, they describe a logarithmic relationship.
y=mx+b is a linear relationship between x and y
y= log (x) is a logarithmic relationship
Linear relationships are straight lines in a graph but a logarithmic function is a curve.
Have you an example of what you are asking about? There has to be some miscommunication.
https://data.library.virginia.edu/interpreting-log-transformations-in-a-linear-model/
“Another reason is to help meet the assumption of constant variance in the context of linear modeling ”
“..This further implies that our independent variable has a multiplicative relationship with our dependent variable instead of the usual additive relationship. Hence the need to express the effect of a one-unit change in x on y as a percent.
If we fit the correct model to the data, notice we do a pretty good job of recovering the true parameter values that we used to generate the data…”
**all snippets are from source linked**
I suppose the idea is that one person can describe dependent and independent relationships between state variables and using log as a way to satisfy the need for framing complex problems in an c =a+b (or variable 1 and 2 results in desired output based on direct relationships).
From another, non academic source.
“The original model is not linear in parameters, but a log transformation generates the desired linearity. (Recall that linearity in parameters is one of the OLS assumptions.)..”
*from* https://www.dummies.com/article/business-careers-money/business/economics/the-linear-log-model-in-econometrics-156470/
Maybe I misinterpreted this, but I was hoping that I could potentially use log to describe relationships between outliers in outliers in data points, or brain networks in this instance.
The model will be presumably obscured by noise, so with some fancy math techniques, I would hope to incorporate noise variables into the computations needed to understand the local dynamic model, or linearlize otherwise unstable or outlying values in any model I develop, or correlating these data points to a specific constraint that I may develop.
However, making the math make sense is easier said than done.
Whilst the brain model in question will incorporate a hierarchy of state variables, and the relationships are *usually* linear, noise will presumably obscure the data.
Not sure if I’m making sense or not, I’m a math novice.
But figured it’s worth a shot lol.
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