Quote from: OP
a is the independent variable, b is the dependent variableI know that this is normal terminology, but it implies a causal direction.
- If there is some variable in your experiment that you can easily control, and another variable that you can easily measure, then it is fair to say that "when I changed variable x, variable y changed in a (linear/parabolic/exponential) manner"
However, when it comes to complex things like the impact of obesity in a human population on heart attacks:
- There is no easy way to control obesity in a whole population
- There is no easy way to control heart attacks in a whole population
- There are many factors which can cause heart attacks (eg genetics, congenital problems, education on exercise, stress)
- There are many factors which can cause obesity (eg genetics, income, education on healthy diet, stress)
- So the easiest thing to do is to do some sort of scatterplot of obesity vs age of first heart attack
- Then do a regression line through it, to conclude that "with increased variable x, variable y changes in a (linear/parabolic/exponential) manner"
- You could hypothesize that obesity contributes to heart attacks (since the obesity was present before the first heart attack), but it's not guaranteed: Someone who has an underlying heart condition may be predisposed to a sedentary lifestyle, which may make them obese.
- You could make comments like "For patients with BMI > 30, a weight reduction of 1 kg is associated with a delay of z years in age of first heart attack."
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