# Guess Relationship/Association between two quantitatives variables

I have no idea about how to tackle a problem with 2 quantitative variable X and Y. How can i model $Y=f(X)$ ? What is $f$ if i just have a look of the data ? how can i even guess if such an $f$ exist ?

I feel like i have no key to determine a relationship and the kind of relationship between two variable... (and i don't find anything in Hasti Tibshirani 's book)

For example i try to manage a complete data project. One question asked is to "determine the dependance between two variable: "age" and "note" (grade)".

I have 2 quantitative variable so:

1. I first plot them (the colours distinguish the class variable: 0 and 1 but is not important here!) We can see that there isn't any linear correlation on the graph. Moreover i can't see any other kind of relationship (like log aor squared root, polynomial,...)

2. I didn't know what to do to "evaluate" the "dependance" between my two variable so i did a linear model and without any surprises the coefficient $R^2$ is really small wich indicate a really poor linear relationship.

I don't know what to do next ...

If you have any suggestions please share it.

Thanks

• Chapter 3. Linear Methods for Regression (The Elements of Statistical Learning) – AidanGawronski Apr 12 '18 at 16:14
• I am sorry but i have the book and can't find any suggestion in the chapter 3 about choosing $f$ ... – laurent pincemaille Apr 12 '18 at 17:35
• You don't choose the function, you fit the regression line, and the coefficients which minimize the sum of squared errors are the function. – AidanGawronski Apr 12 '18 at 18:00
• Yes i fear that i was not clear enough, my main concern is to determine a candidate for $f$, and i wanted to know if an automatic procedure could achieve it? – laurent pincemaille Apr 12 '18 at 18:39
• Imagine we have a big dataset (lots of variable) and we have to predict a quantitative variable Y. Hence we want to know wich independant variable Xi are relevant. If we have more than 2 independant variable we can' t make a graph and guess intuitively from the graph wich f could convey Y=f(X1,...,Xn) . – laurent pincemaille Apr 12 '18 at 19:12