# Correlation between quantitative and qualitative variables

I have a dataset composed by 5000 observations. Each observation contains the income per year of a person (from 50 to 50.000.000) and the fact of having a car (yes/no).

I would like to check if a correlation exists between these two features. Which test I should run?

$\log(\frac{\Pr(Car)}{1-\Pr(Car)})=\beta_0+\beta_1income$
One can then test whether or not $\beta_1=0$, which is a test of the hypothesis that income influences car ownership.
You can also use the Kendall Tau : $$\tau = \frac{c - d}{\binom{n}{2}}$$ where $c =$ number of concordant pairs and $d =$ number of discordant pairs. Under the null hypothesis (of independence), $\tau$ is approximately normally distributed. Further information here: http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient#Significance_tests