I am currently completing my dissertation on the the impact of salary expenditure on club performance using a quantitative research design.
I have used a simple linear regression with my predictor variable as Salary to Revenue ratio and my dependent variable as Revenue. Is this allowed, or does it violate the assumption of independence because the variables inherently use the same measures, i.e. revenue, and therefore are effectively related?
Appreciate any help and advice.
Yes, it violates the assumption of independence. The results of the regression analysis may be incorrect.
You can conduct this experiment yourself: generate uncorrelated x and y, then y will not depend on x, but, obviously, y WILL depend on x/y.
Perhaps, you need to explore Revenue vs Salary dependency without using the ratio.
Basically, your model is y = x/y + other covariates. You can't have your dependent variable (revenue) both as dependent and independent variables.
Hello Sam,
Both Andrey and Guillaume are correct; you'll have a difficult time interpreting an unconfounded explanation of how your DV and the implicit IV of Salary relate.
Here's a challenge for you: Create two random variables, X and Y, each with 100 cases. Then compute a third variable, X / Y. Now regress Y on X / Y and see what you get (a negative relationship!). (See R code at bottom for demo of this trial.)
Good luck with your work.
# Demo of Y ~ X/Y
#
# number of cases to create
n = 100
#
# create X scores (from normal distribution)
x
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