I can't imagine it would be a good idea to use the dividend yield of an index as a proxy for individual stock yields.
Looking at the Google Finance stock screener for NYSE-listed stocks, the bulk of the stocks are in a dividend range 0-9% and the distribution of yields is fairly flat.
Also, you don't know how the index's dividend yield is calculated exactly. I generally find that the people who construct indices are reluctant to divulge much information unless you are a paying customer. So, there is probably a timing difference between when a company declares or pays a dividend and when that new dividend is incorporated into the index.
Most importantly, however, stocks react to a change in the expectation of dividends not the current or trailing dividend.