How do you even practically use correlations for business decisions?

Question

My question is not about how correlations are calculated or what the correlation coefficient tells me, but what I can practically and realistically use it for?

If we take the classical case of real estate evaluation and I have data that I want to analyze and get information of. I have i.e. 20 features and the target variable, the real estate value. Now I check for some correlations and see some strong correlations ~1/-1 and little to no correlations ~0.

And now? What can I do with the information that some features have a linear relationship with my target variable?

Example: I get a correlation coefficient of 0.9 with my feature "population 500m radius" and "real estate value". Now I can't say that we should invest in real estate with a high population, because it could mean that for 50.000 more people in the 500m radius the real estate value increases linearly for 5\$ or 500.000$. So even though it has a strong linear relationship, practically I can't use the correlation coefficient for better decision making and need to run a regression anyway.

So, what does it help me with to calculate the correlations practically?

Answer 1

Be careful not to mistake the correlation coefficient with the correlation itself. I guess you refer to Pearson correlation coefficient, however there are many descriptive statistics trying to give some insight into the quantitative relationship between two (or more) variables.

As you correctly point out, Pearson correlation coefficient do not inform about the strength of the relationship. In most cases the best information you are informed about by correlation coefficient is the accuracy of the prediction we can get using this variable (however it is not always that simple). So if you had to pick only one variable to predict the price of the real estate, the one with highest Pearson correlation coefficient would not be a bad choice.

The only real and reasonable use of correlation coefficient I know is that some people like to check them in the preliminary data analysis. As they are familiar with this measure because it is probably the first thing they learned, then they have a feeling, that they are informed more about the data.

However, much more informative picture of correlation between two variables gives simple linear regression (with one variable). I always suggest running it instead of calculating the correlation coefficient. This is because the interpretation of R$^2$ in this regression is more natural than Pearsons correlation coefficient, and they have mathematical relationship of: $\sqrt{R^2} = corr(x,y)$. Then calculation one variable regression you have the same information and more.

Still, even after such an upgrade, Pearson correlation coefficient (or any measure of correlation between two variables) is a bad tool to make predictions or inferences. As in business the predictions are most popular, there are much better tools to predict any values (mostly machine learning strategies). Also, if you want to make inferences about causality between the variables, much more sophisticated tools of causal inference are needed.