Question 1. How do you plan to use correlation in your example of ethical studies?
Question 2. "Correlation analysis is a mathematical method that allows one to investigate the link, if any exists, between variables and the results, of research. "Key statement is "if any exists". We can show strong correlations and still there is NO relationship or link between the variables. This is called a spurious correlation and is very common in the real world. Yes, frequency analysis is a tool that can be used to help detect correlations though often running a multivariable correlation is also a quick method for scouting for correlations.
Does a low correlation value of say .4 indicate that there is not a correlation and so should be ignored ?
Question 3. Now what happens when we change the definition of 'best fit', then do the values of b0 and b1 change? Why change the definition of best fit?
Question 4. There are several ways common to measuring the volatility (degree of movement or spread) in a sample. Volatility is a common expression.
We are familiar with standard deviation and variance of a sample. However these are often NOT useful when comparing two different samples.
A measure often used when comparing the variation or variability or volatility of two samples is the COEFFICIENT OF VARIATION. The coefficient of variation is the ratio of the standard deviation to the mean of the sample.
Why is this more useful in indicating volatility than just the standard deviation?
Note: the coefficient of variation is often used in stock analysis for indicating volatility.