# ROC curve for outcome variable and individual variable [closed]

Suppose we have a binary outcome variable $y$ and we plot an ROC curve with a predictor variable $x$. What is the interpretation of this? An ROC curve plots the FPR (false positive rate) and TPR (true positive rate) across all thresholds. Here, we don't have any probabilities/thresholds.

## closed as unclear what you're asking by AdamO, kjetil b halvorsen, Michael Chernick, Peter Flom♦Oct 5 '17 at 10:50

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• The ROC is FPR/TPR. I don't understand the question. – AdamO Oct 4 '17 at 19:45

1. Sort your $X$ variable in ascending order
2. At each point $x_i \in X$ (or every $n$ points if the set is too big) calculate:
$b_i = (\#$ of $0$'s in $Y \, | \, X < x_i)/(\#$ of $0$'s in $Y) =$ propotion of negative observations when $X < x_i$ and all negative observations.
$g_i = (\#$ of $1$'s in $Y \, | \, X < x_i)/(\#$ of $1$'s in $Y) =$ propotion of positive observations when $X < x_i$ and all positive observations.
3. Plot each pair $(b_i, g_i)$ and you receive a curve similar to ROC.
Interpretation is quite analoguous to the ROC curve - area under the curve you just plotted will be a measure of discriminatory power of given variable. Line y = x will indicate that variable X won't be a good predictor. If the curve is convex, the variable is promising, you should check how it performs in a model.