Here is a historical chart of the 10 year bond yield

Yes, that's exactly the chart I referenced when I made the point that the S&P 500 still delivered a total return of 28% during a 3-year period (2004-2006) when interest rate levels were similar to today's 5% level.

If you had listened to a pessimist who wrote an academic paper on why you should avoid the market because interest rates had risen to 5%, you would have given up 28% of compounded gains, to the detriment of your retirement.

At first glance it would appear there is very little correlation between the rates and equity returns.

It's not just at first glance. You'll see it on the chart on your 2nd and 3rd glance as well.

Interest rates dropped significantly from 2000 - 2010 yet stock returns were pretty dismal.

Yep. This again shows the lack of a clear correlation between interest rates and market returns. There may be a vague correlation but it's not consistently actionable.

So keep dollar cost averaging into the market even during downturns like 2000-2010, thereby snapping up shares of quality companies at bargain prices. People who did this became 401K millionaires during the decade that followed, and there are tens of thousands of us. What we most certainly did not do is to listen to pessimists and their gloom and doom forecasts.