The first ten pages of the total 490 in the book “Understanding Regression Analysis - a conditional distribution approach” will not blow your mind. However, reading things you already understand is always nice as it makes you feel smart.
The book lays down some terminology and spends (too) many words stating that what you observe through measurements is not an accurate representation of what is.
Example (taken from the book, but significantly shortened):
The circumference (Y) of a measured circle is Y = π*x^2. This model is only accurate or deterministic if the measured circle is mathematically perfect. Since this is never the case, the model is wrong, as the measured circle is naturally flawed, and the measurement system is uncertain.
Highlighted: “The data targets the process that produces the data.”
If you measure a diameter of a circle with a caliper, the data you produce targets the process of your measurement system (the caliper) rather than measurand.
In fewer words: Your data represents how accurately you measure rather than being an actual estimate of the measurand.
The book indicates that Y = f(x) must be corrected as it ignores any population Y or x might follow. The book uses instead Y | X = x ~ p(y|x), where p indicates the distribution of y and x. This is the general idea of the “conditional distribution approach.”
I am hyped to read more so stay tuned.
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