Assume that you have datapoints $(x_i,y_i)$ that have an exponential relationship: $(x_i,\log(y_i))$ approximate a straight line. This means that the statistical variables $X$ and $\log(Y)$ are positively correlated. But what can you say about $X$ and $Y$ in this case?

# Solved – the correlation of two variables that have an exponential relationship

correlationregression

## Best Answer

I understand your question is asking around the relationship between $X$ and $Y$, which you have some understanding of already, but would like to explore the statistical basis of.

I don't know of a statistical process that will enable you to test this effectively. One problem is often in the assumptions about distribution of the variables. If $X$ and $Y$ are related by a exponential relationship, then even if the distribution of $log(Y)$ is normal, the distribution of $Y$ cannot be.

I think best is one of two directions (I would choose the former, personally)

Then once you have statistically proved the relationship, then you can extrapolate the statistical basis to the underlying data.