There is definitely a relationship between the price of bitcoin and altcoins. Altcoins drop as bitcoin moves harder. In fact, whether the bitcoin rises or falls, the first reaction of altcoins is falling. After Bitcoin is fixed and stays stable, altcoins start to increase.
I would better say, they were correlated for a very long time. Meanwhile, look at the cryptocurrencies market now. When Bitcoin is going up, most altcoins are sliding down. Some alts manage to jump very high from time to time. Nevertheless, they do not stay on the top for long.